UNITED STATES of America, Plaintiff-Appellee, v. Donatos SARRAS, Defendant-Appellant, 571 F.3d 1111

HULL, Circuit Judge: Defendant-Appellant Donatos Sarras appeals his convictions and sentences for persuading his minor step-daughter to engage in sexually explicit conduct for the purpose of producing photos of such conduct and for knowingly possessing child pornography. After review and oral argument, we affirm. I. BACKGROUND In 2000, the minor victim (“E.M.”) was seven years old, and defendant Sarras married her mother. In October 2005, Sarras and E.M.’s mother divorced, but they did not tell E.M. about the divorce until July 2006.

Sarras did not move out of the family residence (the “Wheatfield residence”) until August 2006. After moving out, Sarras kept a bedroom for E.M. in his new home (the “Tweed residence”). E.M. stayed overnight with Sarras at the Tweed residence three times a week during the fall of 2006, which is when the sexual conduct occurred. Sarras was charged with knowingly persuading E.M. to engage in sexually explicit conduct on October 16,17, and 23, 2006, in violation of 18 U.S.C. § 2251(a), (e) (Counts I, II, and III), and knowingly possessing child pornography on May 7, 2007, in violation of 18 U.S.C. § 2252A(a)(5)(

B) and (b)(2) (Count IV). The first trial resulted in a hung jury. Sarras was convicted on all counts in the second trial. We detail the procedural history and evidence from the second trial. A. Officer Ortiz’s Recorded Interview On May 7, 2007, E.M., then fourteen years old, reported to the Seminole County, Florida, Sheriffs Office that, when she was thirteen years old, Sarras had engaged in sexual intercourse with her and had taken pictures. On May 7, Dana Ortiz, an investigator with the office’s Division of Crimes against Children, conducted a sworn, recorded interview of E.M.

E.M. told Ortiz that Sarras was her stepfather and she stayed with him at the Tweed residence several nights a week. According to E.M., around October or November 2006, Sarras began having sexual intercourse and oral sex with E.M. during her visits to his Tweed residence unless she “made up an excuse” to avoid it. Sarras had sexual intercourse with E.M. more than ten times, performed oral sex on her about three times, and had her perform oral sex on him more than ten times.

E.M. was unsure of the dates of these sexual encounters and could not say for sure whether they were before or after Thanksgiving or Christmas. E.M. told Officer Ortiz that, on one occasion, Sarras took “a lot” of pictures while she was naked and while she was performing sexual acts on and with him. Sarras used a digital camera that he kept at his Tweed residence. Asked if Sarras had shown her pictures of other girls, E.M. said he had not. Sarras tried to show E.M. the pictures he took of her, but she did not want to look at them and refused.

E.M. said that Sarras’s laptop computer was always on the coffee table in front of the television. E.M. believed that Sarras had downloaded the pictures to his laptop because “he said that he wanted to store them so he could ... look at them sometimes.” Under the supervision of Officer Ortiz, E.M. telephoned Sarras. During the recorded call, Sarras repeatedly denied any involvement in the alleged offenses and asked if E.M. needed help. Sarras told E.M. that he was going to call her mother immediately about the call. Sarras attempted to call several times, but, at Ortiz’s direction, E.M.’s mother did not answer.

Within minutes of the call, Sarras deleted 41 sexual images of E.M. on his laptop, uninstalled his access to LimeWire, and deleted adult pornographic images downloaded earlier that day through Lime-Wire. B. Search of Sarras’s Home Immediately after the Sarras call, Officer Ortiz prepared an affidavit for a warrant to search Sarras’s home. Ortiz’s affidavit said the victim reported that: (1) her stepfather, Sarras, sexually battered her at his residence from October 2006 through January 2007;

(2) Sarras had sexual intercourse with her more than ten times, licked her breast approximately two times, performed oral sex on her approximately three times, and received oral sex from her over ten times; and

(3) Sarras took numerous pictures of their sexual activities with a digital camera that he kept in his home. The affidavit listed types of erotic depictions that computer forensic examiners should look for in the seized media and identified computers and other devices capable of storing such depictions digitally.

Finding that Ortiz’s affidavit established probable cause, a state circuit judge issued a warrant authorizing the officers (1) to search Sarras’s residence “for computer or digital data, programs, applications, files, electronic communications, or other digitally stored date [sic], dynamic data such as processes, open files, services, data in memory, data in an encrypted or decrypted state ... in the form of graphics files ... or other visual depiction or other physical eomputer/digital data of [a] child of less than eighteen (18) years of age” engaging in sexual acts and (2) to image forensieally “[t]he data storage devices” onsite or at the Sheriffs Office computer forensic lab depending on any technical limitations encountered at the described location.

At Sarras’s Tweed residence, officers seized a laptop computer from the coffee table, a Sony Cybershot digital camera, and other computer equipment. A search of the camera’s memory stick revealed 41 images of E.M. engaged in sexually explicit conduct. A search of the laptop computer revealed the same 41 images (“the laptop photos”). A computer forensics examiner determined that (1) all of the pictures were taken with a Sony Cybershot digital camera, (2) 15 photos were taken on October 16, 2006, (3) 10 were taken on October 17, 2006, and (4) 16 were taken on October 23-24, 2006.

Of the 41 laptop photos, 27 capture E.M. alone, posing nude, and 14 showed E.M. engaging in sex acts with an adult male. These 14 images appear to have been taken by the adult male in the images because they do not show his face and show only the top side of his erect penis. The 14 images show the man and E.M. engaged in oral and vaginal intercourse. Most of these 14 pictures appear to have been taken during intercourse and thus display only a part of the shaft of the erect penis.

Of the 14 photos showing the penis, 1 was taken on October 16, 2006, in Sarras’s bedroom at the Tweed residence, 5 were taken on October 17, 2006, in E.M.’s mother’s bedroom at the Wheatfield residence, and 8 were taken on October 23-24, 2006, in Sarras’s bedroom at the Tweed residence. The 27 photos showing E.M. alone, posing nude, also were spread over the 3 days. C. Sarras’s Motion to Suppress Sarras moved to suppress the evidence seized from his Tweed residence, alleging that

(1) Ortiz’s affidavit contained deliberate and material falsehoods and omissions and (2) a Franks hearing was required. The magistrate judge’s report recommended denial of Sarras’s suppression motion.

The magistrate judge found “no basis to conclude that Investigator Ortiz acted intentionally or with reckless disregard in omitting material facts from the affidavit.” Rather, the magistrate judge determined that “the claimed omissions are selective characterizations of what the child said, most of which are immaterial to the probable cause determination in any event.” The magistrate judge concluded that “[tjhere is no indication how these statements, even if true, vitiate the allegations in the Affidavit or the crux of the case: the child’s testimony that her stepfather had sex with her and took photographs of her, on a digital camera which he kept at his house.” The district court denied Sarras’s suppression motion and request for a Franks hearing.

The district court found that “there existed a fair probability that evidence of the crimes charged would be found in the Defendant’s residence” and, as to the search affidavit, “[t]he level of detail the Defendant demands is legally unsupportable.” The district court agreed with the magistrate judge’s finding that there was no basis to conclude that Officer Ortiz acted intentionally or with reckless disregard in omitting material facts from her affidavit and that there was no indication of how the statements Sarras contends were omitted, even if true, “vitiate the allegations in the Affidavit or the crux of the case.” D.

Defense and Government Photos At trial, Sarras argued that he was not the man in the laptop photos because he has a mole on his penis, and no mole is visible in the laptop photos. However, the government contended that no mole is visible in the laptop photos because they show only the top of the penis and that Sarras’s mole is actually near the bottom of his penis. At trial, it was undisputed that Sarras has a mole on his penis, but the mole’s location was vigorously disputed. We thus review the photos of Sarras’s penis introduced at the second trial.

Defense counsel had pictures of Sarras’s penis taken to permit the jury to visually compare Sarras’s penis and the penis depicted in the laptop photos. The court designated Thomas Hemphill of the Medical Examiner’s Office as the photographer, and the government’s case agent attended. Hemphill photographed Sarras’s genitalia, both flaccid and with an erection (“the defense photos”). As Sarras “prepared” himself for the erection pictures, all others present — Sarras’s counsel, the marshals, and the FBI case agent — turned their backs. When they turned around, Sarras had his hands near his erect penis.

Sarras kept his hands there while Hemphill stood on a chair and took overhead pictures of Sarras’s penis. A mole on the top of Sarras’s erect penis is visible in the defense photos. Before the second trial, the government took another set of photos of Sarras’s penis, but this time with a doctor holding it. Specifically, the government moved to take more pictures of Sarras’s penis alleging (1) the defense photos were not taken from the same angle as the laptop photos but were taken over Sarras’s right shoulder and

(2) Sarras had strategically manipulated his penis in the defense photos so that his mole would be visible from that viewpoint. The government proposed that Dr. David Jablonski, a board-certified urologist, be present for another set of photos. The district court granted the government’s motion. At the second photo shoot, Sarras stood while Dr. Jablonski held Sarras’s flaccid penis between his thumb and forefinger to ensure that the penis was completely straight. Dr.

Jablonski continued to hold Sarras’s flaccid penis while an unidentified photographer took photos from the top and from the side (“the government photos”). The government photos taken from overhead do not show a mole on the top of Sarras’s penis. In the pictures taken from the side, the mole appears to be at the 8 o’clock position, near the bottom of the penis rather than on or near the top. Before the second trial, Sarras moved in limine to exclude Dr. Jablonski’s testimony or, in the alternative, for a Daubert hearing. Although Dr.

Jablonski stated that he placed Sarras’s penis in a neutral position for photographing, Sarras claimed that Dr. Jablonski (1) actually “turned the skin of the Defendant’s penis in order to manipulate the position of the ‘mole’ and veins” and (2) there was “no indication that the testimony of Dr. Jablonski would comply with Daubert.” Prior to jury selection in the second trial, the district court orally denied Sarras’s motion. The court stated that “Dr. Jablonski’s credentials are sufficient for him to testify to what he intends to testify to.

So I don’t need a Daubert hearing.” The government explained that it intended to introduce its photos on rebuttal only if Sarras introduced the defense photos. E. Sarras’s Expert Dr. Ferdon Another trial issue involved the testimony of Sarras’s retained expert, Dr. Edward J. Ferdon. Dr. Ferdon specialized in erectile dysfunction and premature ejaculation. Dr. Ferdon examined Sarras in both the flaccid and erect states. The examination took about 15 to 20 minutes. His 2007 report offered these opinions:

(1) Sarras’ erect penis has “a several millimeter mole on the proximal right shaft dorsolaterally at approximately the 2:00 o’clock position” when looking from Sarras’s perspective out from Sarras’s body; (2) “[tjhis mole is not seen on the penis in any of the [laptop] photographs”; (3) “the position and lengths of the visible dorsal vein and other superficial veins on the shaft of Mr. Sarras’s [erect] penis are different from those of the penis in the [laptop] photographs”; and (4) “[a]ll of these facts lead me to conclude that Mr.

Sarras’s penis is not seen in the [laptop] photographs.” The government moved to exclude Dr. Ferdon’s testimony on numerous substantive grounds discussed later. Before the first trial, the district court granted the government’s motion. The district court found that: (1) jurors were equally capable of making a visual comparison between the penises in the defense and laptop photos; (2) “this is not a subject necessitating expertise; no specialized knowledge is required here”; (3) “[t]he doctor’s observations are simply a visual comparison between the characteristics of the penises”;

(4) Dr. Ferdon’s testimony “concerns a matter within the understanding of the average layperson”; (5) “[t]he same visual comparison can be made just as easily by a non-expert, including the jurors themselves (from photographs)”;

(6) Sarras “fails to establish the reliability of Dr. Ferdon’s [vein] methodology,” “[i]n fact, the Defendant does not address the [methodology-reliability] issue,” and thus Dr. Ferdon’s proposed testimony fails to meet the Daubert standard; and (7) even if it met the Daubert standard, the testimony would be unduly prejudicial because of its potential to mislead the jury. Despite its ruling on the motion, the district court in the second trial ultimately admitted considerable testimony by Dr. Ferdon.

It still precluded him from giving an identification opinion that, based on his visual comparison of the veins in the erect penises in the defense and laptop photos, Sarras was not the person in the laptop photos. The district court relied on its earlier Daubert and other rulings as to Dr. Ferdon to support that decision. F. Government’s Evidence at Second Trial We now turn to the evidence in the second trial. The government’s first witness was E.M., who testified that Sarras married her mother in 2000, when E.M. was seven years old. Sarras was like a father to E.M.

After Sarras and E.M.’s mother stopped living together in August 2006, he continued to see E.M. During the fall of 2006, Sarras kept a bedroom for E.M. in his Tweed residence, where E.M. stayed overnight three times a week. At some point, Sarras began talking with E.M. about sex. Later, Sarras lifted up her shirt and licked her left nipple before tucking her into bed.

Eventually, Sarras began having sex with E.M. every time she stayed at his Tweed residence unless E.M. “made up an excuse that [she] was sick or [she] had a headache.” At least once, Sarras had sex with E.M. after school in her mother’s bedroom at the Wheatfield residence while E.M.’s mother was at work. E.M. testified that Sarras threatened to take away her home and kill her, her mom, or her dog if she told anyone that Sarras forced her to have sex with him. E.M. eventually confided in a friend. When her friend’s father found out in May 2007, E.M. told her mother and then the police.

E.M. also explained that in October or November 2006, Sarras used a Sony Cybershot camera to take pictures of E.M. performing sex acts on him. E.M. identified the Sony Cybershot camera seized from Sarras’s Tweed residence as the camera Sarras used to take the laptop photos (exhibits 1-41). E.M. identified where each of the 41 laptop photos was taken based on the furniture in the pictures. Exhibits 1-15 were taken in Sarras’s bedroom at his Tweed residence. Exhibits 16-25 were taken at E.M.’s mother’s bedroom at his Wheatfield residence. Exhibits 26-41 were taken in Sarras’s bedroom at his Tweed residence.

Fourteen of the 41 exhibits depict an adult male, whose penis is shown but whose face is not, engaged in sex acts with E.M. E.M. identified the male in these 14 pictures as Sarras. E.M. appears nude and alone in the other 27 pictures. E.M. testified that, in exhibits 26-41, she had a red ribbon around her wrist. Her middle school gave students the ribbon to wear during “Drug Free Week.” E.M. testified that the ribbon was given out in October or November 2006. The school passed the ribbons out on Monday and asked the students to wear them all week if they intended to stay drug free.

On cross-examination, Sarras’s counsel highlighted the inconsistencies between

(1) E.M.’s testimony on direct and (2) her testimony in the first trial and her interview with Officer Ortiz. E.M. previously could remember Sarras taking photos on only one occasion and could not remember exactly when that was. E.M. did not tell Officer Ortiz that a Sony Cybershot camera was used. E.M. did not remember any distinguishing marks or moles in Sarras’s genital area and told Officer Ortiz that Sarras did not have any such marks. E.M. created her own MySpace page and used Sarras’s Sony Cybershot camera to take pictures for it.

Sarras taught her how to use a computer and what the various parts of a computer were. E.M. took a “beginning web design” class at school. E.M. knew that Sarras had a new girlfriend and was getting ready to leave Florida. E.M. knew the security code to Sarras’s Tweed residence. E.M. was unhappy that he blocked MTV at his home. On redirect examination, E.M. testified that she was “scared” during her sexual encounters with Sarras and had “blocked some of it out.” E.M. stated that it had been the most traumatic thing that had ever happened to her.

Based on this testimony, Sarras’s counsel argued that he should be permitted to ask E.M. about her post-abuse sexual relationship with her boyfriend.

The district court denied Sarras’s request, stating, “[Federal Rule of Evidence 412] is pretty clear that this kind of evidence does not come in, whether or not — that’s the whole point of it is the victims can be traumatized whether or not they’ve had other sexual relationships.” The government also called Officer Ortiz, who was with the Seminole County Sheriffs Office since 1999, is part of the Crimes against Children Unit, and investigates cases involving sex crimes against children, child abductions, and child abuse. Ortiz testified only that she monitored and recorded the phone call E.M. placed to Sarras.

The recording was played for the jury without objection. On cross-examination, Sarras’s counsel asked Officer Ortiz about the information she included in and excluded from her search warrant affidavit. On redirect, Ortiz testified that, based on her training and experience as a sex-crimes investigator, it is not unusual for a thirteen-year-old child to forget the exact dates and times of her abuse.

On re-cross, Officer Ortiz admitted that, based on her “training and experience as a sexual crime and child abuse investigator,” it is very common in cases involving child pornography to find other photos of child pornography. She acknowledged that investigators found no other pornographic photos in Sarras’s home or on his computers. The government next called Officer Erik Zabik, a forensic investigator for the Seminole County Sheriffs Office. Zabik examined (1) the memory stick and camera card from the Sony Cybershot and

(2) Sarras’s laptop computer. Zabik found the 41 laptop photos on its hard drive in an encrypted, “hidden” folder that was deleted at 3:59 p.m. on May 7, 2007. This was ten minutes after the 3:32 p.m.-3:49 p.m. controlled phone call between E.M. and Sarras. Officer Zabik testified that, at various points throughout the day, Windows “automatically ... takes a snapshot of the Windows registry and other files” so that a user can restore his computer to a certain date and time in the event of a crash. These “restore points” are automatically saved in “restore point folders” on the computer.

Zabik explained that, starting at 4:12 p.m. on May 7, 2007, all of the approximately 80 restore point folders on Sarras’s laptop, containing restore points going back several months, were manually deleted. Officer Zabik testified that “neither remote assistance [n]or remote desktop had been accessed [on Sarras’s laptop] in quite sometime [sic]” and that the “exchangeable image file data” embedded into the graphic files containing the images of E.M. established that all of the pictures were taken with the same make and model Sony Cybershot camera that was seized from Sarras’s home.

By using software that analyzes the picture files and determines the exact time they were taken, Officer Zabik was able to determine exactly when the laptops photos were taken. The images of E.M. in exhibits 1-15 (in Sarras’s bedroom at his Tweed residence) were taken on October 16, 2006, between 10:31 p.m. and 11:52 p.m. The images in exhibits 16-25 (in E.M.’s mother’s bedroom at the Wheatfield residence) were taken on October 17, 2006, between 5:48 p.m. and 6:53 p.m. The images in exhibits 26-41 (in Sarras’s bedroom at his Tweed residence) were taken on October 23-24, 2006, between 11:47 p.m. and 12:18 a.m.

Officer Zabik also detailed the use of Sarras’s laptop computer throughout May 7, 2007, the day of the controlled call from 3:32 p.m.-3:49 p.m. According to Zabik, the forensic examination showed that between 1:15 p.m.-2:45 p.m. Sarras’s laptop began downloading adult pornography through LimeWire. The laptop also accessed an online management course and Greek sports websites throughout most of May 7. At 3:21 p.m., the laptop was used to access Sarras’s email account. At 3:51 p.m., two minutes after the controlled phone call, Sarras’s laptop was used to access LimeWire. LimeWire was uninstalled at 3:55 p.m.

At 3:58 p.m., Sarras’s laptop was used to access the “hidden” folder containing the laptop photos. The folder was deleted at 3:59 p.m. Between 4:12 and 4:15 p.m., the adult pornography downloaded earlier in the day and the computer’s restore points were deleted. On cross-examination, Officer Zabik testified that the date and time applet on Sarras’s laptop (that Zabik used to construct his May 7 chronology) was accessed on May 6, 2007, at 3:59 p.m. He could not say if the computer’s date and time were altered on May 6.

Zabik admitted that someone could access the program and change the date and time to whatever the person wanted, thus causing a false date and time to be placed on a file. There was no way to tell if the dates were changed in this case. Officer Zabik admitted that, out of approximately 115,000 files and folders on Sarras’s laptop, and millions of files on Sarras’s other computers, the folder containing the laptop photos was the only encrypted folder and the only child pornography that Zabik found.

The laptop photos did not appear on the laptop until April 19, 2007, and Zabik did not know where they had been stored before that date. Zabik did not find that. Sarras had conducted any internet searches for child pornography. This was Zabik’s only child pornography case that did not involve more than one set of images or more than one child. Officer Zabik also testified that Sarras’s laptop operated on a wireless network, and he agreed that someone could access a computer that is on a wireless system and had an open port.

Zabik admitted that (1) he never tested E.M.’s computer, (2) he did not determine if there was an interconnection between E.M.’s computer and Sarras’s laptop, and (3) anyone could turn on Sarras’s computer because it was not password protected. Zabik also found pictures on the seized computer media that showed that E.M. was in possession of a Sony Cybershot camera “prior to the time frame of the charged images.” Finally, Zabik testified that, if someone wanted to make the laptop photos unrecoverable, even from the police forensic software, the person could have done that. G.

Sarras’s Evidence at Second Trial Sarras testified in his defense. At the time of the second trial, Sarras was 35 years old. He was born and raised in Greece. He was trained in electrical engineering and computer science and had worked in the computer industry since the early 1990s. He built between 140-200 computers, including the ones seized in this case. In 2004, Sarras started his own company, which grossed $1.8 million in 2005. Sarras met E.M.’s mother in late 1999, and they married in August 2000. Sarras’s defense was that he was set up and the images of E.M. were planted on his laptop.

According to Sarras, marital problems began in late 2003, when he noticed $10,000 missing from his bank account. In August 2004, he bought the Wheatfield residence and began building his Tweed residence. The couple divorced in October 2005 but did not tell E.M. about the divorce until July 2006. Sarras continued to live with E.M.’s mother at his Wheatfield residence until August 2006, when he finished construction on his Tweed residence. Sarras continued to pay the mortgage and bills on his Wheatfield residence until November 2006.

In December 2006, Sarras told E.M.’s mother about his new girlfriend, and in April 2007, he told her that he had decided to move to Massachusetts. Sarras and E.M.’s mother had financial dealings and even a joint bank account well into 2007. Sarras paid off the mortgage on the Wheatfield residence in January 2007. On January 31, he transferred the deed to the Wheatfield residence to E.M.’s mother for a $120,000 check, which covered about half of the home’s equity. The bank refused to cash the check, saying E.M.’s mother did not have enough money in her individual account.

Sarras later admitted that E.M.’s mother did take out a mortgage and deposit $123,470 into their joint bank account even though she also kept her own account. Sarras admitted that he still had a joint account with E.M.’s mother on May 7, 2007, but testified that on May 7, 2007, he learned that $70,000 was missing from that joint account. Sarras later denied talking E.M.’s mother into forgoing an attorney for their divorce in exchange for $70,000. Both E.M. and her mother had keys to Sarras’s Tweed residence.

Sarras acknowledged that E.M. visited his Tweed residence at least once a week from September 15 to November 15, 2006. E.M. liked to stay at Sarras’s Tweed residence on Fridays because it was very near one of her favorite places to spend time with friends. Sarras taught E.M. how to use computers, which she “was fascinated with.” An open port allowed the exchange of files between Sarras’s Tweed and Wheatfield residences. E.M. and her mother primarily used the Sony Cybershot camera. Sarras said he was not interested in taking photos.

At some point, Sarras blocked MTV on his main television and imposed dating rules on E.M. As a result, E.M. stopped coming over to Sarras’s Tweed residence. His relationship with E.M. was “effectively terminated” by mid-November 2006. Sarras denied having any physical relationship with E.M. and taking the laptop photos. He did not know they were on his laptop computer and did not delete them or the restore points feature. Sarras testified that his penis is not circumcised, he has a mole on the top side of his penis, and the laptop photos show no mole on the top of the penis.

Sarras testified that his mole would have appeared in the laptop photos if in fact the photos were of his penis. On cross-examination, Sarras admitted that, on May 7, 2007, he logged into the online management course described by Officer Zabik and was at his home when he received the controlled phone call from E.M. Sarras acknowledged that the government moved to have a second set of photos taken with Dr. Jablonski present. Sarras denied that he opposed the second photos because they would show that his mole is on the side of his penis and not on the top.

When presented with the government’s photos (exhibits 77-79), Sarras admitted that his mole did not appear in exhibit 77, the overhead photo showing the top of his penis. He acknowledged that in the side-view picture (exhibit 79), the mole appeared to be on the side of his penis. On redirect, Sarras testified that he objected when Dr. Jablonski twisted his penis before the government photos were taken. Sarras’s counsel then called Hemphill, who took the defense photos. Hemphill stated that the men in the room turned their backs so that Sarras could “prepar[e] himself’ for the photos.

After Sarras achieved an erection and arranged himself, the men turned around and Hemphill stepped on a chair and photographed Sarras’s penis from over Sarras’s shoulder. Sarras also called Donald Rehman, Sr., a former law enforcement officer and owner of Rehman Technology Services, Inc., which offers computer forensics services. Rehman examined the media seized from Sarras’s home, including the mirror image of the laptop’s hard drive and the Sony Cybershot. Rehman found no sign of the laptop photos on the camera’s memory card.

He believed that the laptop photos first appeared on the laptop on April 19, 2007, and were last accessed on April 30, 2007. Rehman found that LimeWire was installed on February 19, 2007, reinstalled on May 7, 2007, at 4:57 p.m., and then uninstalled later on May 7, 2007, at an undeterminable time. Rehman testified that it was possible to change a computer’s date to some time in the past, put items on that computer, change the date to tomorrow, delete the files, and change the computer back to today’s date.

Rehman stated that the date applet on the laptop was accessed at 3:59 p.m. on May 6, 2007, and the date changed to May 7, 2007, to make it appear that the images had been deleted on May 7. Rehman found no other pornography on Sarras’s laptop and no evidence that Sarras had searched the internet for child pornography. Sarras also called Dr. Ferdon. The court allowed Dr. Ferdon to testify about the features of Sarras’s penis and the photos in evidence. Although he had not formally studied urology, Dr. Ferdon had examined between 15,000 and 16,000 male genitalia over the six years before Sarras’s second trial. Dr.

Ferdon examined Sarras’s penis in both the erect and non-erect states. Dr. Ferdon explained that “dorsal” means the top of the penis and “lateral” means the side. Dr. Ferdon stated that Sarras’s mole “is in the dorsolateral, meaning towards the top, towards the side but in — between the direct side and the actual top.” In terms of a clock, with the top of the penis being 12 o’clock and the bottom 6 o’clock, Dr. Ferdon described the location of the mole from 2 viewpoints. The mole was at 10 o’clock when standing directly in front of and looking back at Sarras’s penis.

The mole was at 2 o’clock when looking from Sarras’s perspective out from Sarras’s body. Dr. Ferdon examined the defense photos of Sarras’s penis, in which the mole is visible in the overhead pictures, and said that the penis appeared to be in the “neutral position,” not rotated. Dr. Ferdon also testified that Sarras’s penis was uncircumcised. Dr. Ferdon studied the 14 laptop photos showing the penis and testified that, in his medical opinion, 2 of the 14 photos showed a penis that is “clearly completely circumcised.” As to whether the penis in the other 12 laptop photos was circumcised, Dr.

Ferdon testified that: (1) as to 7 photos, he “[could] not tell” or was “uncertain”; (2) as to 1 photo, he “would say circumcised”; (3) as to 3 photos, it “appeared] to be” or “apparently” was circumcised; and (4) as to 1 photo, he “th[ought]” uncircumcised. Dr. Ferdon also examined the government photos and testified that the urologist (Dr. Jablonski) “appears to be pulling the skin of the base of [Sarras’s] penis and in the groin area towards the right,” which would have pulled the mole to the bottom of the penis so that it would not be visible from overhead. Sarras’s counsel also questioned Dr.

Ferdon about penis veins. Dr. Ferdon explained that the dorsal vein is “the prominent vein seen subcutaneously just beneath the skin on the top portion of the penis.” He also testified that there are other veins in the penis, but the dorsal vein is the most prominent. Dr. Ferdon explained that, when he examined Sarras’s erect penis, its veins were in the same position as the veins shown in the defense photos. H. Government’s Rebuttal Evidence In rebuttal, the government called Dr. Jablonski, who also examined Sarras’s penis. According to Dr.

Jablonski, if the viewer is facing Sarras’s penis and the top of the penis is 12 o’clock and the bottom is 6 o’clock, Sarras’s mole is at the 8 o’clock position. When Sarras’s penis is in the neutral position, his mole would not be visible when looking from overhead. Dr. Jablonksi stated that the penis in the laptop photos was in the neutral position. Dr.

Jablonski testified that (1) for the government’s photos, he personally held Sarras’s penis in the straight, neutral position, (2) the mole was not visible in the government photos, (3) the vertical position of Sarras’s urethra in the government photos confirmed his penis was in the neutral position, (4) based on the position of the dorsal vein and the location of Sarras’s mole at 10 o’clock in the defense photos, the penis had to have been rotated in the defense photos, and (5) an uncircumcised penis can appear to be circumcised when fully erect because the skin stretches as the penis elongates. Dr.

Jablonski also explained that the frenulum “is a concentration of tissue which is always present right at the 6:00 o’clock position, where the two halves of the head of the penis, the glans[,] have come together and fused around the urethra.” He pointed to the position of the urethra in one of the government photos and explained that it confirmed that Sarras’s penis was in the neutral position in that photo. The jury convicted Sarras on all counts. I.

Sentencing The Presentence Investigation Report (“PSI”) calculated Sarras’s base offense level under the Sentencing Guidelines as (1) level 32 for each of Counts I, II, and III and (2) level 18 for Count IV. See U.S.S.G. §§ 2G2.1(a), 2G2.2(a)(l). The PSI did not group the offenses together because the different counts did not involve “substantially the same harm”; instead, the criminal acts against E.M. on different occasions involved multiple, separate instances of fear and risk of harm. See U.S.S.G. § 3D1.2.

As to each of Counts I — III, the PSI recommended increasing Sarras’s total offense level from 32 to 40 based on: (1) a two-level increase pursuant to § 2G2.1(b)(l)(

B) because the offenses involved a minor between the ages of 12 and 16; (2) a two-level increase pursuant to § 2G2.1(b)(2)(

A) because the offenses involved the commission of a sex act or sexual contact; (3) a two-level increase pursuant to § 2G2.1(b)(5) because the minor was in Sarras’s custody, care, or supervisory control; and (4) a two-level increase pursuant to § 3C1.1 because Sarras “knowingly altered evidence presented at trial” by rotating his penis in the defense photos to make it appear that his mole is on the top side of his penis.

As to Count IV, the PSI recommended increasing Sarras’s total offense level from 18 to 29 based on: (1) a five-level increase pursuant to § 2G2.2(b)(5) because Sarras engaged in a pattern of activity involving sexual abuse or exploitation of a minor; (2) a two-level increase pursuant to § 2G2.2(b)(6) because the offense involved the use of a computer; (3) a two-level increase pursuant to § 2G2.2(b)(7)(

A) because the offense involved at least 10 images, but fewer than 150 images; and (4) a two-level increase pursuant to § 3C1.1 for obstruction of justice by knowingly introducing altered evidence. Because each of the four counts was individually considered and not grouped together, the PSI applied the unit calculation in § 3D1.4 to determine Sarras’s combined offense level. The PSI calculated 1 unit for Count I because it had “the highest offense level” and 1 unit each for Counts II and III because they had an “equally serious” offense level. U.S.S.G. § 3D1.4(a).

Based on these 3 units for Counts I — III, the PSI added 3 levels to Sarras’s highest offense level of 40. See U.S.S.G. § 3D1.4. Sarras had a combined adjusted offense level of 43. Based on Sarras’s total offense level of 43 and his criminal history category of I, Sarras’s advisory guidelines range was life imprisonment. However, the statutory maximum imprisonment is 30 years for each of Counts I, II, and III, 18 U.S.C. § 2251(e), and 10 years for Count IV, 18 U.S.C. § 2252(b)(2).

Because the statutory maximum on each count was less than the advisory guidelines range of life imprisonment, the statutory maximum on each Count became the advisory guidelines range for each count, i.e. 30 years on each of Counts I — III and 10 years on Count IV. See U.S.S.G. § 5Gl.l(a) (“Where the statutorily authorized maximum sentence is less than the minimum of the applicable guideline range, the statutorily authorized maximum sentence shall be the guideline sentence.”). In the particular circumstances of this case, § 5G1.2(

d) in turn provided that the statutory maximum sentences shall run consecutively. See U.S.S.G. § 5G1.2(d).

Section 5G1.2, entitled “Sentencing on Multiple Counts of Conviction,” provides that “[i]f the sentence imposed on the count carrying the highest statutory maximum is less than the total punishment, then the sentence imposed on one or more of the other counts shall run consecutively, but only to the extent necessary to produce a combined sentence equal to the total punishment.” Id. Here the “total punishment” under the sentencing guidelines called for life imprisonment. See U.S.S.G. § 5G1.2 cmt. n. I. Yet, the statutory maximum for the count with the highest maximum (Counts I — III) was 30 years.

Because the statutory maximum was less than the total guidelines punishment of life imprisonment, § 5G1.2(

d) of the guidelines called for the sentences for multiple counts to run consecutively as the advisory guidelines sentence. See id.-, United States v. Davis, 329 F.3d 1250, 1253-54 (11th Cir.2003) (interpreting § 5G1.2(

d) to call for consecutive sentences as the guidelines sentence) Accordingly, the PSI stated that Sarras’s advisory guidelines range became 1,200 months (i.e., 30 + 30 + 30 + 10 = 100 years). Sarras filed numerous written objections to the PSI’s calculations, including the two-level enhancement for obstruction of justice. Sarras also argued that the 18 U.S.C. § 3553(

a) factors required the least severe sentence possible. Sarras renewed his objections at sentencing. At sentencing, the district court adopted the PSI’s factual statements and guidelines calculations and determined that Sarras’s advisory guidelines sentence was 1,200 months. The court rejected Sarras’s claim that Counts I, II, and III should be grouped under § 3D1.2 and overruled Sarras’s objections to the PSI’s calculations. The court found that the government proved obstruction of justice and the PSI properly applied the two-level obstruction-of-justice enhancement.

The court sentenced Sarras to “360 months on each of counts one, two, and three; and [a] term of 120 months on count four. All such terms to run consecutive.” The court explained that it had “imposed the selected sentence after considering the advisory sentencing guidelines, the minimum mandatory sentence required by statute, and all the factors identified in Title 18 United States Code Sections 3553(a) 1 through 7.” The court found that the guidelines sentence of 1,200 months was sufficient but not greater than necessary to fulfill the purposes of sentencing.

The court further stated: Among the factors that [this] Court has considered are the despicable offense that [Sarras] committed, and the fact that the victim will probably, even with counseling, never fully recover from this. [Sarras’s] lack of remorse is also a basis for the Court imposing a guideline sentence in this case. I see no reason to depart below the guideline in any event. Sarras objected to the sentences on several grounds, including “on procedural grounds as well as a violation of Booker. ” II. DISCUSSION On appeal, Sarras challenges seven evidentiary rulings and raises several sentencing claims.

We review each in turn. A. Dr. Ferdon Sarras contends that the district court improperly limited Dr. Ferdon’s testimony. Sarras argues that Dr. Ferdon would have testified that

(1) Sarras’s erect “penis has a several millimeter mole on the proximal right shaft dorso-laterally at approximately the 2:00 [position],” (2) “[t]his mole is not seen on the penis in any of the [laptop] photographs,” (3) “[t]his mole would most certainly have been visible in the [laptop] photographs,” (4) “the position and lengths of the visible dorsal vein and other superficial veins on the shaft of Mr. Sarras’ penis are different from those of the penis in the [laptop] photographs,” and (5) the penis in the laptop photos was not Sarras’s penis.

Sarras’s arguments fail because the trial transcripts reveal that Dr. Ferdon effectively testified to the substance of these matters at trial. As to the mole, it was undisputed that the laptop photos show no mole on the top of the penis and that Sarras has a mole on his penis. As to the location of Sarras’s mole, Dr.

Ferdon testified that he examined Sarras’s erect penis and the mole “is in the dorsolateral, meaning towards the top, towards the side but in — between the direct side and the actual top.” He essentially testified that, in terms of a clock, Sarras’s mole was visible at 10 o’clock when standing directly in front of and looking back at Sarras’s penis and at 2 o’clock when looking from Sarras’s perspective out from Sarras’s body. Dr.

Ferdon further testified that he examined the defense photos (which showed the mole on the top of Sarras’s erect penis) and determined that the penis appeared to be in the neutral position and not rotated by Sarras. By contrast, Dr. Ferdon testified that, in the government photos, Dr. Jablonski appeared to be pulling Sarras’s penis down and to the right, which would have pulled the mole to the bottom of the penis. Dr. Ferdon also testified about the dorsal vein and that, when he examined Sarras, the veins in Sarras’s penis were in the same positions as the veins in the defense photos.

Thus, the jury heard from Dr. Ferdon that the defense photos (that showed the mole) were accurate but that Dr. Jablonski manipulated the government photos (that did not show the mole). Dr. Ferdon further testified that he examined Sarras’s penis, that it was uncircumcised, and that he examined the laptop photos. In his medical opinion, two of the laptop photos showed a penis that, unlike Sarras’s, was “clearly completely circumcised.” Three of the laptop photos showed a penis that “appearfed] to be” or “apparently” was circumcised.

One of the laptop photos showed a penis he “would say [was] circumcised.” The clear import of Dr. Ferdon’s testimony was that he had examined Sarras’s erect penis and Sarras, having an uncircumcised penis with a mole at the 2 o’clock position in the accurate defense photos, could not have been the male in the laptop photos, where the penis is circumcised and no mole is visible. Given the nature and extent of Dr. Fer-don’s admitted testimony, Sarras’s real complaint on appeal is that Dr.

Ferdon was not allowed to issue an identification opinion concluding that, based on a comparison of the veins in the laptop and defense photos, Sarras is not the person in the laptop photos. What happened in the district court materially informs this issue. In the district court, the government’s motion in limine argued that Ferdon’s vein comparison as an identification methodology was unreliable under Daubert.

The government’s motion stated that “[t]here is no peer reviewed literature, text book, medical science or other scientific body of data on which the opinion is based, and there is no indication that ‘vein-mapping’ as a means of identification is generally accepted in the medical or scientific community, has been tested, or has been subjected to peer review or publication.” The government claimed that Dr.

Ferdon’s vein-comparison methodology was unreliable because, inter alia, “the degree to which the veins in a male’s genitalia are enlarged and visible depends on blood flow and degree of arousal, among other things.” Sarras’s response in the district court addressed neither argument. Rather, Sarras responded that Dr. Ferdon had examined 15,000 penises, specialized in erectile dysfunction, and was qualified to give an opinion that it was not Sarras in the laptop photos. The district court then concluded that Sarras had not shown that Dr.

Fer-don’s vein-comparison methodology was a reliable identification technique under Daubert. On appeal, Sarras contends that (1) the jury was not equally capable of visually comparing the veins in the photos of Sarras’s penis to those in the penis in the laptop photos and

(2) Dr. Ferdon had specialized knowledge warranting his giving an identification opinion about whether Sarras was the person in the laptop photos. See Fed.R.Evid. 702 (stating that the trial court may permit expert testimony when “scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue”). In other words, the issue is whether the jury was equally capable of comparing the penises in the photos, or whether expert testimony was permissible to identify the person in the laptop photos. That is a close issue.

But we need not decide it because, in any event, the district court did not abuse its discretion in its Daubert ruling that Sarras had not established that Dr. Ferdon’s methodology — comparing veins in erect penises— was a reliable identification methodology. See United States v.

Frazier, 387 F.3d 1244, 1260 (en banc) (11th Cir.2004) (“The proponent of expert testimony always bears the burden to show that his expert is qualified to testify competently regarding the matters he intended] to address; [] the methodology by which the expert reach[ed] his conclusions is sufficiently reliable; and [] the testimony assists the trier of fact.” (alterations in original) (quotation marks omitted)). Notably, Sarras fails to distinguish between the doctor’s qualifications to testify about penises and the method by which the doctor reaches his conclusion. The district court did not rule Dr.

Ferdon was unqualified to testify about penises. Rather, the court ruled that Sarras had not shown that the doctor’s methodology— comparing veins in erect penises — was a sufficiently reliable identification technique for Dr. Ferdon to opine that Sarras was not the person in the laptop photos. In fact, no record evidence explains the so-called methodology of comparing veins in erect penises as an identification technique. Perhaps blood flow or degree of arousal has no visual effect on the veins in penises. Who knows? The record is silent.

Sarras thus has not shown error, much less reversible error, in the district court’s Daubert ruling as to Dr. Ferdon’s methodology. See United States v. Brown, 415 F.3d 1257, 1264-66 (11th Cir.2005) (explaining the limited nature of appellate review of Daubert issues, “why it is difficult to persuade a court of appeals to reverse a district court’s judgment on Daubert grounds,” and that “[w]hat is true about the review of evidentiary issues in general applies with equal or even greater force to Daubert issues in particular, an area where the abuse of discretion standard thrives”). B.

Rehman Sarras next argues, given that only pictures of E.M. were found on Sarras’s computer, the district court erred by not allowing Rehman to give an expert opinion that child pornography cases generally involve multiple images of multiple children. The jury heard several times, and indeed it was undisputed, that no other child pornography was found on any of Sarras’s computers. The parties first disagree as to whether Rehman was qualified as an expert in this regard. We need not decide that thorny question either because Rehman’s testimony would have been cumulative.

Perhaps the district court said it best when it told Sarras, “Everything you have said to me you can argue ... based on the evidence that’s already there.” Two government witnesses — Officers Ortiz and Zabik- — already had covered these same points. Specifically, Officer Ortiz testified that, based on her “training and experience as a sexual crime and child abuse investigator,” it is very common in cases involving child pornography to find other photos of child pornography. Officer Ortiz also stated that investigators found no other pornographic photos in Sarras’s home or on his computer.

Additionally, Officer Zabik testified that, out of the millions of files on Sarras’s computers, the folder containing the images of E.M. was the only child pornography that he found. Importantly, Officer Zabik added that this was his only child pornography case that did not involve more than one set of images or more than one child. Officer Zabik further explained that he did not find that Sarras conducted any internet searches for child pornography. If anything, this evidence had more impact coming from the government’s witnesses.

And, in closing, Sarras argued that child pornography eases usually involve multiple images of multiple children and he had no such images. The exclusion of Rehman’s testimony did not eliminate, or materially impinge upon, Sarras’s ability to argue that he did not fit the profile of the average offender. Rehman’s testimony was cumulative, and Sarras has not demonstrated prejudice or reversible error. See Frazier, 387 F.3d at 1266 n. 20 (explaining that evidentiary ruling can be reversible error only if it prejudices substantial rights). C. Limitation on Cross of E.M.

Notwithstanding the federal rape-shield law, Sarras contends that the district court erred in refusing to permit Sarras to ask E.M. questions about a post-abuse sexual relationship with her boyfriend. Federal Rule of Evidence 412 provides that, subject to narrow exceptions, “[ejvidence offered to prove that any alleged victim engaged in other sexual behavior” or “to prove any alleged victim’s sexual predisposition” is not admissible in any criminal proceeding involving alleged sexual misconduct.

Rule 412(b)(1) allows such evidence to be admitted when its “exclusion ... would violate the constitutional rights of the defendant.” At trial, Sarras contended that E.M.’s testimony that she was traumatized by the sexual abuse opened the door to questions about her sexual history. Sarras claims broadly that the district court’s limitation “left the jury with the false impression that E.M. was traumatized by the sexual activity and had not been photographed nude, although E.M. admitted to police that she engaged in explicit sexual activities with her boyfriend.” Again, we conclude the district court did not err.

First, as the district court aptly recognized, victims of sexual abuse can be traumatized whether or not they have had other sexual relations. Second, we reject Sarras’s argument that E.M.’s sexual relationship with her boyfriend shows that Sarras did not abuse her. The laptop photos show sexual abuse of E.M. The only issue is the identity of the male in the photos. That E.M. had a sexual relationship with her boyfriend is irrelevant to the identity of the adult male in these photos. It is equally irrelevant to whether Sarras knowingly possessed the materials found on his laptop computer.

Third, the district court afforded Sarras a constitutionally adequate opportunity to attempt to impeach E.M. Sarras questioned E.M. about her possible motives for framing him; her access to the camera; his house and computers; her knowledge of computers; her anger over Sarras’s restrictions against her dating and watching MTV; and the inconsistencies between her interview with Officer Ortiz and the facts developed at both trials. Simply put, Sarras has not met his burden of demonstrating that the district court’s application of Rule 412 violated a constitutional guarantee.

See Frazier, 387 F.3d at 1271 (“While the Constitution unquestionably provides a defendant with the right to be heard, this right is not unbounded. Thus, ‘[t]he accused does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence.’ ” (alteration in original) (quoting Taylor v. Illinois, 484 U.S. 400, 410, 108 S.Ct. 646, 653, 98 L.Ed.2d 798 (1988))). D.

Police Officers Sarras claims the district court abused its discretion by refusing to allow him to cross-examine law enforcement officers about the Sheriff Office’s financial interest in the forfeiture of Sarras’s house. Sarras argues that “the jury should have been allowed to learn that the Seminole County Sheriffs office — the agency these witnesses worked for — stood to gain a significant amount of money should Mr.

Sarras be convicted and the forfeiture be successful.” “The extent to which a witness may be cross-examined for the purposes of showing bias rests on the sounds discretion of the trial judge.” Howell v. Am. Live Stock Ins. Co., 483 F.2d 1354, 1357 (5th Cir.1973). “The task of the trial judge is to balance the probative value of the evidence sought to be introduced against the risks its admission may entail.” Id. (explaining that “[t]he potential risks may include ... the possibility of misleading or confusing the jury”); see United States v.

Novaton, 271 F.3d 968, 1006 (11th Cir.2001) (stating that “a defendant is only entitled to cross-examine a witness if ‘the information sought to be elicited [is] relevant’ ” (alteration in original) (citations and quotations marks omitted)).

In Howell, we concluded that the trial court properly limited the impeachment of a witness because of “[t]he possibility that the trial would become involved in a lengthy wrangle over a side issue.” 483 F.2d at 1358. “[Wjhile we [were] not prepared to say that we [found] the proferred evidence wholly irrelevant, ... we [were] unable to say that the district judge roamed beyond the bounds of his discretion in ruling as he did.” Id. In this case, the district court likewise did not abuse its discretion.

First, Sarras proffered no evidence showing any officer-witness had a direct or personal financial interest in the case. In fact, the officers’ alleged interest in the case is best described as just the opposite: indirect, impersonal, and tenuous. This case is about child pornography — not forfeiture. To suggest that the officers were biased because the Sheriffs Office that employed them may have benefitted from a forfeiture is rank speculation. Such testimony had little, if any, probative value as to bias.

Rather, such testimony had the potential to confuse the jury and distract it from the central issues, warranting the district court’s exclusion. Sarras’s reliance on United States v. Williams, 954 F.2d 668, 672 (11th Cir.1992), is misplaced. That case involved a witness with a direct, personal, and substantial financial interest in the case. In Williams, the district court allowed the government informant to testify about how long he was a paid informant, the percentage (25%) he received of the seized assets, and the amount of money he was paid in that case. Id. at 671.

However, the district court excluded testimony detailing the total amount of money the informant had received for his work as an informant because the sum was “outrageous” and therefore prejudicial. Id. at 671, 672 n. 3. That evidence included the fact that the informant had received $450,000 in reward money, including 25% of a $1,258,000 seizure (i.e.$314,500). We reversed, stating that the district court erred in excluding this evidence because “[t]he jury has the right to know what may be motivating a witness, especially a government paid, regularly employed, informant-witness.” Id. at 672.

We noted that “large and outrageous payments may be just the kind that are of the most help to the jury in arriving at the truth.” Id. In reversing, this Court also emphasized that “at trial, the informant testified that he did not expect to receive twenty-five percent of the possible $7.2 million involved in the transaction, which somewhat misled the jury in calculating his compensation.” Id. Here, the law enforcement officers did not have a direct or personal financial interest in this case.

If anything, Williams shows that the district court did not abuse its discretion by refusing to allow defense cross-examination of the officers as to the forfeiture. E. Production of Computers, Camera, and Medical Records Sarras next argues that the district court erred by denying his motion to require the government to produce E.M.’s and her mother’s computers and camera and certain medical records of tests performed on E.M. in May 2007. We disagree. None of these items was in the government’s possession or control.

It is well-settled that the government must permit a defendant to inspect tangible items within its “possession, custody, or control” if they are material to the defense, the government intends to use them in its case-in-chief, or they were obtained from the defendant. Fed.R.Crim.P. 16(a)(1)(E). But the government does not have a duty to disclose items it does not possess. See, e.g., United States v. Cannington, 729 F.2d 702, 711-12 (11th Cir.1984). Nor does it have a duty to obtain evidence it does not possess. See, e.g., United States v. Luis-Gonzalez, 719 F. 2d 1539, 1548 (11th Cir.1983).

None of these items was in the government’s possession, custody, or control. E.M.’s and her mother’s computers and camera were in the possession and control of E.M. and her mother, and the medical records were in the possession and control of the Kid’s House of Seminole County. Sarras could have followed the subpoena duces tecum procedures, pursuant to Fed.R.Crim.P. 17(c), for obtaining evidence from third parties, but he did not. It was not the government’s responsibility to track down third-party evidence for Sarras. This claim fails. F. Dr.

Jablonski Sarras also asserts that the district court erred in allowing Dr. Jablonksi to speculate that Sarras manipulated his penis in the defense photos and in permitting him to testify as to the location of the mole on Sarras’s penis. Sarras argues that Dr. Jablonski’s opinion lacked foundation and “was drawn from thin air.” This claim lacks merit too. First, Dr. Jablonski is an expert in urology and based his opinion on his personal examination and firsthand knowledge of what Sarras’s penis actually looked like. Indeed, Sarras’s criticism applies with equal force to the testimony of his own witness.

That is, Sarras conveniently ignores the fact that before Dr. Jablonski testified, Sarras’s expert, Dr. Ferdon, testified that Sarras’s penis had not been rotated in the defense photos. Although Sarras emphasizes that Dr. Jablonski was not present when the defense photos were taken, Dr. Ferdon also was not present. Moreover, Dr. Ferdon testified that Dr. Jablonski had rotated Sarras’s penis down and to the right in the government photos even though Dr. Ferdon was not present when the government photos were taken.

In short, both doctors based their respective opinions about manipulation and rotation on their personal observations of Sarras’s penis and the assumption that the defense and government photos were of Sarras’s penis. The district court did not abuse its discretion in permitting the government to call its own expert (Dr. Jablonksi) to rebut Sarras’s expert (Dr. Fer-don). G. Officer Ortiz Sarras claims two errors occurred as to Officer Ortiz’s testimony. Sarras’s first claim is that the district court erred in permitting Ortiz to testify that she believed E.M. when she initially reported the abuse.

However, it was Sarras who asked Ortiz the question in this regard. Sarras asked, “You assumed that what she said was true, and you had it made up in your mind when you went to his home---Correct?” Ortiz responded, “What — I believed my victim when she told me what happened to her.” Sarras concedes that he did not object to Ortiz’s response. Normally, we would review such a claim for plain error. But because Sarras’s claimed error is “invited error,” it is thus unreviewable. Sarras elicited Ortiz’s testimony that she believed E.M.

He wanted the jury to believe that Ortiz conducted an inadequate investigation based on her flawed belief that E.M. was telling the truth and Sarras was guilty. Because Sarras’s question elicited the very testimony about which he now complains, he is entitled to no relief. See United States v.

Baker, 432 F.3d 1189, 1215-16 (11th Cir.2005) (“[A] defendant can ‘invite’ non-responsive testimony when he insists on pursuing a line of questioning after it becomes apparent that further cross-examination will elicit potentially damaging testimony, and fails to object to the non-responsive answer when it is given.”); United States v. Silvestri, 409 F.3d 1311, 1327-28 (11th Cir.2005) (“Where invited error exists, it precludes a court from invoking the plain error rule and reversing.”); United States v.

Jemigan, 341 F.3d 1273, 1289-90 (11th Cir.2003) (where injection of allegedly inadmissible evidence is attributable to defense, defendant may not claim on appeal that its introduction constitutes reversible error); United States v. Parikh, 858 F.2d 688, 695 (11th Cir.1988) (holding that admission of improper testimony “when [government witness was] responding to an inquiry by defense counsel, creates ‘invited error’ ”).

Sarras’s second claim about Ortiz is that the district court erred in permitting her to testify, over Sarras’s objection, that it is not unusual for a thirteen-year-old child to fail to remember the exact times and dates of the abuse. The government concedes that Officer Ortiz was not qualified as an expert but argues that her testimony about children’s memories was lay, not expert, testimony.

Rule 701 permits a lay witness to provide opinion testimony if the opinion (1) is “rationally based on the perception of the witness,” (2) “helpful to a clear understanding of the witness’ testimony or the determination of a fact in issue,” and (3) “not based on scientific, technical, or other specialized knowledge within the scope of Rule 702.” Fed.R.Evid. 701; compare Fed.R.Evid. 702 (reserving for expert witnesses testimony based on “scientific, technical, or other specialized knowledge”).

The government argues that Officer Ortiz’s testimony is lay opinion because it is not based on scientific or specialized knowledge within the realm of an expert but rather on “particular knowledge gained by virtue of her position and repeated exposure to victims of sexual abuse.” See United States v. LeCroy, 441 F.3d 914, 927 (11th Cir.2006) (concluding that a police officer’s testimony that “a blood stain on the back of [the victim’s] shirt appeared to have been made by someone wiping a bloody knife off on the shirt” was a layperson observation that was admissible under Rule 701); United States v.

Tinoco, 304 F.3d 1088, 1119 (11th Cir.2002) (stating that an agent’s characterization of defendant’s boat as “go-fast” boat was proper lay opinion testimony because it was based on personal observation as well as past experience). In response, Sarras argues this type of memory evidence is usually provided by a mental health professional and is precisely the “specialized knowledge” contemplated by Rule 702. See Frazier, 387 F.3d at 1260-61 (“[Experience in a field may offer another path to expert status.”).

Sarras also points out that Officer Ortiz gave her victim-memory opinion without any evidence of how long she had been a sex crimes investigator, how many cases she had handled, how many involved minors, or what training she had as to sex crime victims. See id. at 1261 (“[I]f the witness is relying solely or primarily on experience, then the witness must explain how that experience leads to the conclusion reached, why that experience is a sufficient basis for the opinion, and how that experience is reliably applied to the facts.” (quotation marks and brackets omitted)).

We agree with Sarras that the government did not seek to qualify Officer Ortiz as an expert but offered her opinion testimony on this issue as a lay witness. And her opinion testimony does seem more like that of an expert with specialized knowledge. Nonetheless, we conclude that any potential error in admitting Officer Ortiz’s brief testimony about victims’ forgetfulness was harmless error. See United States v.

Henderson, 409 F.3d 1293, 1300 (11th Cir.2005) (when judge erroneously admits evidence in criminal prosecution, question is whether error had substantial influence on outcome of case or left grave doubt as to whether it affected outcome of case). In this case, the key issue involved identifying the abuser, not pinpointing precisely when the abuse occurred. Moreover, the forensic expert testified about the October dates on the camera. The red wristband E.M. wore in some pictures was consistent with those October dates.

We recognize that Sarras contends that E.M.’s inability to remember the exact dates of the abuse is evidence that she fabricated the story as part of her mother’s grand scheme to frame him. However, Sarras had ample opportunity to develop this theme at trial. Although the photos were deleted from his computer immediately after the recorded call, Sarras called an expert to testify that the date applet on his laptop had been accessed on May 6, within twenty-four hours of E.M. reporting the abuse to the police on May 7.

He repeatedly questioned witnesses about the interconnectivity between his and E.M.’s and her mother’s computers, his parental restrictions on E.M., and his financial dealings with E.M.’s mother. And the laptop photos showed the location of the abuse by depicting the furniture in them. Sarras developed his “I’ve been framed” theme extensively in both his opening and closing statements. We have no doubt that this isolated statement by Officer Ortiz — about a victim’s memory of dates and times— had no impact on the outcome of the trial. H.

Denial of a Franks Hearing Sarras contends that the district court abused its discretion by denying his motion to suppress evidence without first conducting a Franks hearing. Sarras argues that Officer Ortiz made material omissions and falsehoods in her search warrant affidavit and that this entitled him to a Franks hearing. “Affidavits supporting arrest warrants are presumptively valid.” See United States v. Kapordelis, No. 07-14499, 2009 WL 1508342, at *19-20, 569 F.3d 1291, 1318-19 (11th Cir. June 1, 2009) (citing Franks, 438 U.S. at 171, 98 S.Ct. 2674).

To be entitled to a Franks hearing, a defendant must make a “substantial preliminary showing that a false statement knowingly and intentionally, or with reckless disregard for the truth, was included by the affiant in the warrant affidavit, and if the allegedly false statement is necessary to a finding of probable cause.” 438 U.S. at 155-56, 98 S.Ct. at 2676. “When assessing whether the alleged false statements and omissions were material, the trial court is to disregard those portions of the affidavit which the defendant has shown are arguably false and misleading.” Kapordelis, 2009 WL 1508342, at *10, at 1309 (citing Franks, 438 U.S. at 171-72, 98 S.Ct. 2674). “[E]ven intentional or reckless omissions will invalidate a warrant only if inclusion of the omitted facts would have prevented a finding of probable cause.” Id. (quoting Madiwale v.

Savaiko, 117 F.3d 1321, 1327 (11th Cir.1997) (alteration in original)). “The defendant bears the burden of showing that, ‘absent those misrepresentations or omissions, probable cause would have been lacking.’ ” Id. (quoting Novaton, 271 F.3d at 987). For several reasons, we conclude that Sarras did not make the requisite “substantial preliminary showing” to warrant a Franks hearing. First, we agree with the magistrate judge and the district court that Sarras’s “omissions” are selective characterizations and exaggerations of what E.M. said that did nothing to strike at the core of the probable cause finding.

Rather, the relevant statements by E.M. were that Sarras had sex with her and took pictures of her. Sarras complains that the affidavit did not state that, according to the victim, Sarras took pictures on only one occasion. Whether it was one time or ten times, such conduct is criminal. And the omission of the fact that E.M. could only estimate the dates on which the abuse occurred also does not affect the finding of probable cause.

Second, we recognize that Ortiz’s affidavit did not specify that E.M. and her mother had used the camera before, that E.M. did not know where in thé house the camera was, and that E.M. was unsure but only thought the camera was in Sarras’s house. Nonetheless, the affidavit accurately represented E.M.’s statement that Sarras took the pornographic pictures while in his house. It is Sarras’s possession of the photos, not the camera, that constitutes a crime under Florida statute § 827.071(5) (making it a felony to unlawfully possess material known to include sexual conduct by a child).

Third, although Officer Ortiz’s affidavit did not mention that E.M. had not seen the pictures of herself or of any other girls, the affidavit demonstrated that Sarras had taken the photos. Whether E.M. had seen them is irrelevant. Plus, E.M. claimed that Sarras offered to show her the photos. Fourth, Sarras’s denial during the controlled phone call does not change the finding of probable cause. A self-serving denial, on its own, does not defeat probable cause.

Because Sarras failed to make a “substantial preliminary showing” that Officer Ortiz made intentional or reckless misstatements or omissions, the district court did not abuse its discretion in denying his request for a Franks hearing. I. Sentencing The final issue is Sarras’s sentence of 1,200-months’ imprisonment. A defendant challenging his sentence bears the burden of establishing that it is unreasonable. United States v. Talley, 431 F.3d 784, 788 (11th Cir.2005). We review the reasonableness of a sentence through a two-step process using a deferential abuse-of-discretion standard. United States v.

Pugh, 515 F.3d 1179, 1189-90 (11th Cir.2008) (relying upon Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 597 (2007)). First, we look at whether the district court committed any significant procedural error, such as miscalculating the advisory guidelines range, treating the guidelines range as mandatory, or failing to consider the 18 U.S.C. § 3553(

a) factors. Id. at 1190. In considering the § 3553(

a) factors, the district court need not discuss each of them individually. Rather, “an acknowledgment by the district court that it has considered the defendant’s arguments and the factors in

section 3553(

a) is sufficient under Booker.” Talley, 431 F.3d at 786. Second, we examine whether the sentence is substantively reasonable. Pugh, 515 F.3d at 1190. We consider the totality of the circumstances and evaluate whether the sentence achieves the sentencing purposes stated in § 3553(a). Id. at 1191; Talley, 431 F.3d at 788. A sentence may be substantively unreasonable if a district court unjustifiably relied on any one § 3553(

a) factor, failed to consider pertinent § 3553(

a) factors, selected the sentence arbitrarily, or based the sentence on impermissible factors. Pugh, 515 F.3d at 1191-92. Although now advisory, the guidelines are one of the § 3553(

a) factors to be considered by the sentencing judge, see 18 U.S.C. § 3553(a)(4), and thus play a role in our evaluation of whether a sentence is substantively reasonable. After Booker, this Court declined to adopt a presumption that a sentence within the guidelines range is per se reasonable. See Talley, 431 F.3d at 786-88. At the time, we did so because we believed Booker precluded our applying such a presumption. Id.

We said the presumption “does not comport with the Booker decision” because “[t]o say that a sentence within the Guidelines range is ‘by itself reasonable is to ignore the requirement that the district court, when determining a sentence, take into account the other factors listed in

section 3553(a).” Id. at 786. That statement indicates the type of presumption we thought would be inconsistent with Booker is a conclusive presumption, because only if it were conclusive would the presumption rule out consideration of the § 3553(

a) factors. Nevertheless, we recognized that “the use of the Guidelines remains central to the sentencing process” and stated that “ordinarily we would expect a sentence within the Guidelines range to be reasonable.” Id. at 787-88 (emphasis added). Our expectation about the ordinary case could be rebutted by circumstances in a specific case indicating that a sentence within the guidelines range is not reasonable in that case. In light of that, our expectation is tantamount to a rebuttable presumption. Subsequently, the U.S.

Supreme Court concluded that it is permissible for an appellate court to presume that a sentence within the guidelines is reasonable, so long as that presumption is rebuttable. Rita v. United States, 551 U.S. 338, 127 S.Ct. 2456, 2462-68, 168 L.Ed.2d 203 (2007). In Rita, the Supreme Court specifically rejected the argument that such a presumption conflicted with a sentencing judge’s mandate to consider the § 3553(

a) factors. See Rita, 127 S.Ct. at 2467-68 (“[Wjhere judge and [the Sentencing] Commission both determine that the Guidelines sentenee[ ] is an appropriate sentence for the case at hand, that sentence likely reflects the § 3553(

a) factors (including its ‘not greater than necessary’ requirement). This circumstance alleviates any serious general conflict between § 3553(

a) and the Guidelines, for the purposes of appellate review.” (citation omitted)). Subsequently, in Gall, the Supreme Court reiterated that “[i]f the sentence is within the Guidelines range, the appellate court may, but is not required to, apply a presumption of reasonableness.” Gall, 128 S.Ct. at 597. The Supreme Court’s decisions in Rita and Gall confirm the correctness of the expectation we announced in Talley, although they use presumption language to articulate the permissible scope of the expectation or presumption.

To avoid any confusion we will also use that language, as we did in our recent decision in United States v. Willis, 560 F.3d 1246, 1251 (11th Cir.2009) (concluding that because the defendant’s sentence was within the “properly calculated guideline range,” it was “presumptively reasonable”). In this Circuit, this Court presumes that a sentence within the guidelines range is reasonable, but the presumption may be rebutted by the circumstances of a particular case viewed in light of the § 3553(

a) factors. With this background, we turn to Sarras’s challenges to the reasonableness of his sentence. As to procedural error, Sarras argues that the district court erred in calculating the applicable guidelines when it imposed a two-level enhancement to his offense level based on the court’s finding that Sarras obstructed the administration of justice. The district court found that, despite the burden of proof being a preponderance of the evidence, the government had established, beyond a reasonable doubt, that Sarras had manipulated his penis in the defense photos.

The evidence at trial recounted above adequately supports that finding. Thus, the district court did not err in applying this two-level enhancement. Sarras next argues that his ultimate sentence is substantively unreasonable because the district court was governed solely by the Guidelines, without giving due consideration to other § 3553(

a) factors. The record belies this claim. After calculating the advisory guidelines range, the district court expressly stated that it had reviewed the PSI and the parties’ submissions and had considered the advisory guidelines, the minimum mandatory sentence required by statute, and the § 3553(

a) factors. Further, the court expounded on several of the § 3553(

a) factors. Specifically, the court considered “the despicable offense that [Sarras] committed,” “the fact that the victim will probably, even with counseling, never fully recover from this,” and “[Sarras’s] lack of remorse.” The court ultimately stated that it found no reason to depart or vary from the advisory guidelines sentence. As noted above, we presume that sentences within the advisory guidelines range are reasonable. That presumption has not been rebutted here.

Child sex crimes are among the most egregious and despicable of societal and criminal offenses, and courts have upheld lengthy sentences in these cases as substantively reasonable. See United States v. Johnson, 451 F.3d 1239, 1244 (11th Cir.2006) (upholding as reasonable a 140-year sentence for abusing and photographing three boys between the ages of 8 and 16 based on consecutive statutory máximums under 18 U.S.C. § 2251(

e) and § 2252A(b)(l)); United States v. Kapordelis, 2009 WL 1508342, at *19-20 (upholding as reasonable a 420-month sentence, which represented an upward variance from the 262-327-month advisory guidelines range and included 240-month sentences on counts charging production of child pornography under § 2251(

a) and 180-month consecutive sentences on counts charging receipt of child pornography under § 2252(A)(a)(2)(A)); United States v. Huffstatler, 561 F.3d 694, 698 (7th Cir. 2009) (upholding as reasonable an above-guidelines, 450-month sentence for producing pornographic pictures of a 14-year-old boy); United States v. Raplinger, 555 F.3d 687, 695 (8th Cir.2009) (upholding as reasonable a 457-month sentence for photographing and having sexual intercourse with a 15-year-old girl), petition for cert. filed, (U.S. May 12, 2009) (No. 08-10385); United States v.

Betcher, 534 F.3d 820, 827-28 (8th Cir.2008) (upholding as reasonable a 750-year sentence for a first-time offender who had taken pornographic pictures of five 8- to 11-year-old girls, including two of his granddaughters), cert. denied, — U.S. -, 129 S.Ct. 962, 173 L.Ed.2d 153 (2009); United States v. Vowell, 516 F.3d 503, 511-13 (6th Cir.2008) (upholding as reasonable a 780-month sentence for a 40-year-old man who had sexual intercourse with his girlfriend’s 8-year-old daughter while being videotaped by his girlfriend); see also United States v.

Paton, 535 F.3d 829, 837-38 (8th Cir.2008) (concluding that life sentence for five counts of production of child pornography was not cruel and unusual punishment in violation of the Eighth Amendment); Pugh, 515 F.3d at 1202 (“[W]e have typically treated child sex offenses as serious crimes, upholding severe sentences in these cases.”). Here, the district court imposed a sentence that reflects the nature and circumstances of the offense and the other considerations stated in § 3553(a).

Thus, the district court committed no sentencing error in choosing to impose an advisory guidelines sentence of 1,200 months’ imprisonment in this case. III. CONCLUSION For the foregoing reasons, we affirm Sarras’s convictions and sentences. AFFIRMED. . E.M. and her mother previously had used the camera to take pictures at Sea World or the Kennedy Space Center. . The LimeWire program is a peer-to-peer file sharing program which allows outsiders to access files on any computer also programmed with LimeWire. . Ortiz’s affidavit referenced Fla.

Stat. § 827.071(5), making it a crime for "any person to knowingly possess a photograph, motion picture, exhibition, show, representation, or other presentation which ... he ... knows to i

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