UNITED STATES, Appellee, v. Miguel RODRIGUEZ, a/k/a Negrito, Defendant, Appellant; UNITED STATES, Appellee, v. John ROSARIO, Defendant, Appellant; UNITED STATES, Appellee, v. Hector FAMANIA, a/k/a Dilenge, a/k/a Talinge, Defendant, Appellant. Appeals from the United States District Court for the District of Massachusetts [Hon. Richard G. Stearns, U.S. District Judge], 162 F.3d 135

TORRUELLA, Chief Judge. Following a jury trial, appellants Miguel Rodríguez, John Rosario, and Héctor Fama-nia were convicted of conspiracy to distribute cocaine base, in violation of 21 U.S.C. § 846. Rodriguez was additionally convicted on three counts of possession with intent to distribute cocaine base, in violation of 21 U.S.C. § 841(a)(1), and of engaging in a continuing criminal enterprise, in violation of 21 U.S.C. § 848. On appeal, the defendants raise numerous issues among which are the lack of sufficient evidence to convict and abuse of prosecutorial discretion.

For the following reasons, we affirm the convictions and sentences. BACKGROUND We review the facts of a criminal case on appeal from a conviction in the light most favorable to the verdict. See United States v. Gonzalez-Maldonado, 115 F.3d 9, 12 (1st Cir.1997). We sketch the facts presented at trial, providing further details as they become relevant to the discussion. This case concerns a crack cocaine distribution ring in Framingham, Massachusetts.

Through a joint investigation conducted by the Drug Enforcement Administration (“DEA”) and the Framingham police during 1994 and 1995, a drug-trafficking operation in the Framingham community known as “Beaver Park” came to light. At the helm of the operation was Miguel Rodriguez. Among his lieutenants were John Rosario and Héctor Famania. The operation worked in the following manner. An individual known as “Johnny” would cook powder cocaine into crack. Rosario and Famania would then cut, measure, and package the drugs at Rodriguez’s direction.

Typically, a prospective drug purchaser would contact Rodriguez to place an order. When the customer came to obtain her drugs, Rodriguez would direct her to one of his distributors' — Famania, Rosario, José Villafañe, Pedro De Jesús, Luis Torres, and others. Famania and Rosario acted as Rodriguez’s lieutenants. In addition to cutting and packaging the crack for distribution, they served as liaisons between Rodríguez and would-be distributors. Both regularly sold crack in Beaver Park. Famania sold Rodriguez-supplied crack out of his apartment.

One customer, Juan Car-vajal, visited Famania’s apartment on numerous occasions throughout 1995. Carvajal witnessed Famania sell $20 bags of crack daily to various customers, and twice saw Rodriguez give Famania an ounce of crack for distribution. On two occasions, Famania supplied Carvajal with an ounce of crack. Rosario also sold Rodriguez-supplied crack. Upon collecting payment from a prospective buyer, Rosario would spit a plastic bag containing the crack onto the ground, where it would be retrieved by the purchaser.

In January 1995, Rodriguez subordinate Pedro De Jesús made a crack sale to Angela Aurelio — who, unbeknownst to him, was an undercover police officer. The ounce of crack was supplied by Rodríguez and delivered by De Jesús to the officer in her vehicle. She paid $950 for the ounce of crack. A couple of weeks later, Officer Aurelio made another undercover buy from De Jesús. This time, Aurelio paid De Jesús $1000 for an ounce. Investigators also employed Alicia Eller-bee, one of Rodriguez’s regular customers, to make controlled buys.

On July 10, 1995, Ellerbee met Rodriguez at Beaver Park and placed an order for an ounce of crack. Later that day, at a pre-arranged place, Rodriguez drove up to Ellerbee. Upon giving him $900, Ellerbee was directed to the passenger seat of Rodriguez’s car, where a baggie covered by a piece of paper had been placed. Eller-bee took the baggie and paper, which she subsequently handed over to the authorities. Inside the paper, a Boston Globe subscription card carrying the name and address of Famania, was a baggie of crack. On July 27, 1995, Ellerbee again made a crack purchase from Rodriguez at the DEA’s direction.

After she ordered the crack from Rodriguez in the park, Rodriguez walked over to José Villafañe. Villafañe left, and Ellerbee gave Rodriguez $900. Villafañe then returned and dropped a package of crack into Ellerbee’s lap. On September 13, 1995, the grand jury indicted Rodríguez, De Jesús, and Villafañe, charging all the defendants with conspiracy to distribute cocaine and violations of substantive drug offenses. On December 22, 1995, the grand jury returned a seven count superseding indictment. Count I charged Rodríguez, De Jesús, Villafañe, Rosario, Fa-mania, Carvajal with conspiracy to distribute cocaine base.

Count II charged Rodriguez and De Jesús with possession of cocaine base with intent to distribute on January 26, 1995 and aiding and abetting. Count III charged De Jesús with possession of cocaine base with intent to distribute on February 10, 1995. Count IV charged Rodriguez with possession of cocaine base with intent to distribute on July 10, 1995. Count V charged Rodriguez and Villafañe with intent to distribute on July 27, 1995 and aiding and abetting. Count VI charged Rodriguez with engaging in a continuing criminal enterprise.

Count VII sought the criminal forfeiture of Rodriguez’s Suzuki Samurai and Nissan Maxima. Carvajal, De Jesús, and Villafañe pled guilty and were sentenced to terms ranging from time served to sixty months. Rodriguez, Famania, and Rosario proceeded to trial, and were convicted on all counts. Rodriguez was sentenced to life imprisonment, Rosario to 262 months imprisonment, and Famania to 235 months imprisonment. DISCUSSION I.

Continuing Criminal Enterprise Conviction A conviction under 21 U.S.C. § 848 for engaging in a continuing criminal enterprise (“CCE”) requires proof beyond a reasonable doubt that the defendant: (1) committed a felony drug offense; (2) as part of a continuing series of such violations; (3) in concert with five or more persons in relation to whom he acted as a supervisor, organizer, or manager; and (4) from which multiple operations he realized substantial income or other resources. United States v. Hahn, 17 F.3d 502, 506 (1st Cir.1994).

In challenging his conviction, Rodriguez attacks the sufficiency of the evidence on the latter two elements. Neither contention has merit. One who challenges the sufficiency of the evidence bears a heavy burden: he must show that no rational jury could have found him guilty beyond a reasonable doubt. See United States v. Fulmer, 108 F.3d 1486, 1492 (1st Cir.1997). We review the sufficiency of the evidence as a whole, in a light most favorable to the verdict, taking into consideration all reasonable inferences. See United States v. Scantleberry-Frank, 158 F.3d 612, 616 (1st Cir.1998).

We resolve all credibility issues in favor of the verdict. See id. The evidence may be entirely circumstantial, and need not exclude every hypothesis of innocence; that is, the factfinder may decide among reasonable

interpretations of the evidence. See id. at 616 (citation omitted). A. Organizer, Supervisor or Manager under CCE To be an organizer, supervisor or manager within the meaning of the CCE, the defendant “need not be the dominant organizer or manager of the enterprise; he need only occupy some managerial position with respect to five or more persons.” United States v. Hahn, 17 F.3d 502, 506 n. 4 (1st Cir.1994). Further, the jurors are not required to agree on the particular identities of the subordinates, but must only agree that there were at least five doing his bidding. See United States v.

David, 940 F.2d 722, 731 (1st Cir.1991). Rodriguez concedes that he organized, supervised or managed four individuals: Rosario, Famania, Villafañe, and De Jesús. See Def. Br. at 31. Contrary to his claim, the government has presented sufficient evidence as to a fifth individual. De Jesús, testified that, like him, “Peto” also worked for Rodriguez. See Tr. 10/17 at 11-12. The relevant testimony is as follows: Q: Did you ever see Miguel Rodriguez give drugs to Peto? A: (Through the Interpreter) Yes. Q: Where did you see those transactions take place? A: (Through the Interpreter) At the house, Peto’s.

Q: Did you see what Peto did with the money he made from the drugs? A: (Through the Interpreter) He would also give it to Miguel. Tr. 10/17 at 12-13. The jury was entitled to find that “Peto” was within Rodriguez’s sphere of influence and subject to his supervision in the course of his drug trafficking activities. B.

Substantial Income from the Enterprise The “substantial income” requirement may be met either by direct evidence of the revenues realized and resources accumulated by the defendant, or by such circumstantial evidence as the defendant’s position in the criminal organization, and the volume of drugs handled by the organization. See Hahn, 17 F.3d at 507. The substantial income test establishes no fixed minimum, but is intended to exclude trivial amounts derived from occasional drug sales. See id. (citation omitted).

There is overwhelming evidence that Rodriguez derived substantial income from the management of his drug activities. The government need only prove revenue, not profit. See id. Rodriguez himself spends over three single-spaced pages of his brief cataloging trial testimony concerning his drug-trafficking activity during the indictment period, see Def. Br. at 23-26, and admits that testimony indicates that he sold or oversaw the sale of approximately $70,000 worth of drugs during the period of the conspiracy. See id. at 23.

To argue that his activities constitute trivial amounts derived from occasional drug sales is disingenuous. The substantial income element of the CCE was established beyond a reasonable doubt. II. Evidentiary Rulings Rosario argues that the district court erred in making evidentiary rulings regarding: (1) testimony about his involvement in beating a suspected informant; and (2) an eye-witness account of one of his drug transactions. Famania challenges the admission of a Boston Globe subscription card bearing his name and address that was wrapped around a package of crack sold by Rodriguez to informant Ellerbee.

We review the district’s court determination to admit evidence for abuse of discretion. See United States v. Houlihan, 92 F.3d 1271, 1297 (1st Cir.1996), cert. denied, - U.S. -, 117 S.Ct. 963, 136 L.Ed.2d 849 (1997). Only in a rare, extraordinary, and compelling instance will we, “from the vista of a cold appellate record, reverse a district court’s on-the-spot judgment concerning the relative weighing of probative value and unfair effect.” David, 940 F.2d at 737 (internal quotations and citations omitted). None of the defendants’ claims approaches such a circumstance. A.

Evidence of Rosario’s Violent Acts In the summer of 1995, an unidentified man approached Rodriguez, Rosario, and “Joe” at Beaver Park and asked for drugs. Rodriguez, suspicious that the man was an informant, told him to get “out of my face because you’re going to get your butt kicked.” Tr. 10/16 at 29. When the man insisted on purchasing drugs, Rosario reiterated the threat. When the man failed to leave, Rosario “just whacked him,” id., according to an eye witness. Rodríguez and Joe escalated the brawl, and all three punched, kicked, and yelled at the man.

After the man left the scene, Rosario and Rodriguez concluded that the man was “one of those rats ... one of those guys that work for the cops, ... giv[ing] [drugs] to the cops so we get busted for it.” Id. at 30. Rosario argues that the fight had “no connection” to the crack distribution conspiracy, and that a “[r]efusal to sell drugs to one with whom one fights” frustrated, rather than furthered, the objectives of the conspiracy. See Def. Br. at 32-33. This is an artful, but incorrect

interpretation of the evidence. This was not an attempt by Rodríguez and Rosario to prevent a drug transaction. Rather, the evidence shows an attempt to set a tone for their drug-trafficking operation: that suspected informants would be dealt with harshly. As the district court found: [The beating] was part of a campaign of intimidation, to further the interest of the conspiracy in maintaining discipline in its ranks, by treating anyone suspected of being an informant with hostility. Tr. 10/16 at 134.

Rosario’s violence against a suspected informant is relevant to prove his membership in the conspiracy and his acceptance of its objectives. See David, 940 F.2d at 737 (evidence of threats and violent acts in aftermath of cocaine theft is admissible to prove defendant’s role in a drug-trafficking conspiracy). Contrary to Rosario’s claim, the evidence of the beating does not stand alone as proof of his membership in the conspiracy. This is not a case of guilt by association.

In addition to his discussion with Rodriguez about how to deal with suspected informants, four witnesses testified that they either saw Rosario selling drugs and/or purchased drugs directly from him. One witness testified that Rosario delivered an “eight ball” of crack to him on consignment, explaining the terms of repayment to Rodriguez. Another witness testified that she saw Rosario cut and package large amounts of crack along with Fama-nia. Consequently, Rosario’s participation in the conspiracy was established beyond a reasonable doubt. B.

Testimony Regarding Rosario’s Drug Dealing Alicia Ellerbee testified that she saw Rosario give a customer drugs — by spitting a baggie holding crack onto the ground — in exchange for money. Rosario’s primary challenge to this evidence is that Ellerbee failed to provide a temporal proximity as to when these events occurred, and thus the testimony should have been excluded under Fed.R.Evid. 404(b). See Def. Br. at 36. A close reading of the record reveals no such defect. The witness dated the event between the summer of 1994 and September 1995, see Tr. 10/10 at 88-89, and, more specifically, at around May of 1995.

See id. at 89. The drug transaction fell squarely within the time frame of the charged conspiracy. Further, Rosario argues that “[s]ince the direct evidence against the Defendant is of such a tenuous nature, any fact directly linking the Defendant to the sale of crack would be extremely prejudicial.” Def. Br. at 37. Aside from the obvious, that “[b]y design, all evidence is meant to be prejudicial,” United States v. Rodriguez-Estrada, 877 F.2d 153, 155 (1st Cir.1989), there is more than sufficient evidence establishing that Rosario was a distributor and member of the Rodriguez drug-trafficking organization.

Rosario’s argument here is part and parcel of his guilt by association theory: that he was not a co-conspirator, but a friend of Rodriguez’s with the misfortune of continually being in the wrong place at the wrong time when drugs were present. This argument was presented to the jurors, and rejected by them. There is no reason to quarrel with their verdict. Finally, Rosario claims that the court “exacerbated [the] prejudice,” Def. Br. at 38, of Ellerbee’s testimony by foreclosing cross-examination into her attempted suicide and an incident in which she supposedly tried to burn her hair.

The district court properly found that the evidence was not relevant either to her ability to tell the truth or to her partiality. C. Famania and the Boston Globe Subscription Card Alicia Ellerbee made a controlled purchase of crack from Rodriguez on July 10, 1995. After negotiating the terms in Beaver Park, Ellerbee and undercover DEA Agent Russell met Rodriguez near his home. From the driver’s side of his blue Honda, Rodriguez directed Ellerbee to the passenger seat, from where she retrieved a package wrapped in paper.

Ellerbee testified that she gave the package directly to Agent Russell, and that the two then rendezvoused with DEA Agent Farley, who took the package from Russell. Farley testified that he received the package — a baggie of crack wrapped in a Boston Globe subscription card bearing Fa-mania’s name and address — within five minutes of the transaction between Ellerbee and Rodríguez. The subscription card was admitted into evidence through Agent Farley, who testified that it was in the same condition as it was when he received it from Agent Russell.

Famania argues that the card and Farley’s testimony were admitted in violation of Fed. R.Evid. 602, which requires that a witness have personal knowledge about the matter to which he testifies. Evidence is- inadmissible under Rule 602 “only if in the proper exercise of the trial court’s discretion it finds that the witness could not have actually perceived or observed that which he testified to.” United States v. Neal, 36 F.3d 1190, 1206 (1st Cir. 1994), cert. denied, — U.S. -, 117 S.Ct. 519, 136 L.Ed.2d 407 (1996) (citation omitted).

Personal knowledge can include “inferences and opinions, so long as they are grounded in personal observations and experience.” Id. (citation omitted). Here, Agent Farley testified that he personally received the drugs, wrapped in the subscription card, from Agent Russell five minutes after the transaction between Eller-bee and Rodriguez.

Indeed, on cross-examination, Farley acknowledged that he did not personally view the transaction between El-lerbee and Rodríguez, and that he did not see the card when Ellerbee picked it up, or know the precise configuration of the card at the time of the transaction with Rodriguez. As a result, Farley’s testimony was based on his personal knowledge, and is therefore admissible under Fed.R.Evid. 602. Famania’s argument with respect to the subscription card is essentially a complaint about the chain of custody.

He contends that “[t]here was no evidence that Agent Farley or Agent Russell signed the card at the time of the transaction or otherwise secured it as evidence.” Def. Br. at 9. His concern is that there was no evidence as to what Agent Russell did with the card in the five minutes that transpired before he met with Agent Farley. A possible defect in the chain of custody for a certain piece of evidence factors into the weight given to the evidence rather than its admissibility. See United States v. Abreu, 952 F.2d 1458, 1467 (1st Cir.1992). A defendant can attempt to cast doubt on an exhibit’s authenticity.

Such an issue, however, is to be resolved by the jury, and not the judge. Thus, the subscription card was properly admitted into evidence. III. Jury Instruction Rodriguez contends that the district court’s jury instructions understated the government’s constitutional burden of proving his guilt beyond a reasonable doubt. After a close reading of the instructions, we find no such error. Our review of the instructions is de novo. Gilday v. Callahan, 59 F.3d 257, 260 (1st Cir.1995), cert. denied, 516 U.S. 1175, 116 S.Ct. 1269, 134 L.Ed.2d 216 (1996).

The constitutional inquiry is whether “there is a reasonable likelihood that the jury understood the instruction to allow conviction based on proof insufficient to meet the [reasonable doubt] standard.” Victor v. Nebraska, 511 U.S. 1, 6, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994). The challenged remark must be examined along with the rest of the charge to see, if taken as a whole, the instructions correctly convey the concept of reasonable doubt to the jury. See id. A.

The “Real Possibility” Instruction One of the cornerstones of the criminal trial is that the government must prove beyond a reasonable doubt every element of the offense. See In re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). The term “beyond a reasonable doubt” is one of the most bandied, but perhaps least precisely defined phrases in criminal law.

Here, the trial judge used a modified version of the Federal Judicial Center form book instruction for “beyond a reasonable doubt.” Below is the instruction as given, underlined to show the part we discuss: In a criminal case the burden of proving guilt is on the government. It has that burden throughout the entire trial. A defendant never has to prove his innocence. The right of a defendant to put the government to its proof is one of the most fundamental guarantees of our Constitution. It means that the defendant has no obligation to produce any evidence or to testify.

Thus, you may not draw an inference of guilt from the fact that a defendant did not testify. You may not even discuss that fact in your deliberations. Again, the burden rests solely upon the government to prove a defendant guilty beyond a reasonable doubt. Now, what is proof beyond a reasonable doubt? The term is often used, and probably pretty well understood intuitively, although it is not easily defined. Proof beyond a reasonable doubt does not mean proof beyond all possible doubt or proof to a mathematical certainty. Everything in our common experience is open to some possible or imaginary doubt.

It does, however, mean that the evidence must exclude any reasonable doubt as to a defendant’s guilt. A reasonable doubt may arise not only from the evidence produced but also from the lack of such evidence. A reasonable doubt exists when, after weighing and considering all the evidence in the case, using your reason and common sense, you cannot say that you have a firm and settled conviction that the charge is true. It is not enough for the government to establish a probability, even a strong probability, that a defendant is more likely guilty than not. That is not enough.

Proof beyond a reasonable doubt must be proof of such a convincing character that you can, consistent with your oath as jurors, conscientiously base your verdict upon it. If you so find as to a defendant, you will return a verdict of guilty. On the other hand, if you think there is a real possibility that the defendant is not guilty of the charges, you must give the defendant the benefit of that doubt and find him not guilty. Tr. 10/21 at 108-09. The challenged sentence in this instruction is substantially copied from the Federal Judicial Center form book.

See Federal Judicial Center, Pattern Criminal Jury Instructions 28 (1988) (Instruction 21).

Rodriguez’s argument is directed at the phrase “real possibility” in the sentence, “On the other hand, if you think there is a real possibility that the defendant is not guilty, you must give him the benefit of the doubt and find him not guilty.” He argues that the trial judge equated reasonable doubt with “real possibility.” Rodriguez contends that the district court exacerbated an already bad situation when it further explained that the jury could draw inferences using “reason and logic” and “in light of reason and common sense.” He claims that worse still, the district court then failed to give an instruction stating that the standard for drawing an inference is not the same as the standard for finding guilt, thus creating a reasonable likelihood that the jury would apply an imper-missibly low standard of proof to the government’s case against the defendants.

The Supreme Court has held that a reasonable doubt is, at a minimum, one based on reason, so “[a] fanciful doubt is not a reasonable doubt.” Victor, 511 U.S. at 17, 114 S.Ct. 1239. Victor makes that distinction in the context of approving the phrase “not a mere possible doubt.” Id. “[T]he Constitution does not require that any particular form of words be used in advising the jury of the government’s burden of proof.” Id. at 5, 114 S.Ct. 1239. The challenged passage from the Federal Judicial Center -form book instruction is recommended by Justice Ginsburg in her concurrence in Victor.

See id. at 26-27, 114 S.Ct. 1239 (Ginsburg, J., concurring). The trial judge may require a “real possibility” of doubt because “[a] fanciful doubt is not a reasonable doubt.” Id. at 17, 114 S.Ct. 1239. The phrase “real doubt” does not suffer the infirmity of requiring the jury to have “grave uncertainty,” “substantial doubt,” and a “real tangible substantial basis” for doubt, before they can acquit, as the unconstitutional instruction did in Cage v. Louisiana, 498 U.S. 39, 40, 111 S.Ct. 328, 112 L.Ed.2d 339 (1990), overruled on other grounds by Estelle v.

McGuire, 502 U.S. 62, 72 n. 4, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). Here, the likelihood of juror confusion or mistake is extremely remote. We conclude that the instructions overall left the jury with an accurate impression of the presumption of innocence and of the substantial burden faced by the prosecution in establishing the defendant’s guilt beyond a reasonable doubt. There was nothing improper with either the challenged sentence or the instructions as a whole. IV.

Brady Claims Based on their post-trial discovery of additional impeachment evidence concerning two of the government’s witnesses, appellants moved for a new trial. The district court denied the motions, which Famania claims was an abuse of discretion. We disagree. The denial of a motion for a new trial is reviewed only for manifest abuse of discretion. United States v. Henry, 136 F.3d 12, 22 (1st Cir.1998). A. Nancy Muñiz At trial, one of the government’s witnesses, Nancy Muñiz, claimed that she was employed as a financial consultant at Merrill Lynch.

After trial, this testimony was discovered to be false; Muñiz was in fact making her living as a prostitute. The district court found that “[t]here is no suggestion that the government was aware of Ms. Muñiz’s perjury.” July 22, 1997, Mem. and Order at 3. Subsequent to the trial, and allegedly unbeknownst to the prosecution, appellant ascertained that the Framingham police had charged Muñiz with operating a motor vehicle without a license, a charge which was pending at the time of her testimony. See id. at 1. We begin by noting the relevant legal standards.

A Brady error occurs when the prosecution suppresses “material” evidence that is favorable to the accused. See Kyles v. Whitley, 514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). In most circumstances, exculpatory evidence is material only if there is a “ ‘reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.’ ” Id. at 435, 115 S.Ct. 1555 (quoting United States v. Bagley, 473 U.S. 667, 682, 685, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)). We refer to this as the Bagley standard.

A standard of materiality more favorable to the defendant applies, however, when previously undisclosed evidence reveals that the prosecutor knowingly used perjured testimony or, equivalently, knowingly failed to disclose that testimony used to convict the defendant was false. See Bagley, 473 U.S. at 678-80, 105 S.Ct. 3375. In such situations, “ ‘a conviction ... is fundamentally unfair, and must be set aside if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury.’” Kyles, 514 U.S. at 433 n. 7, 115 S.Ct. 1555 (quoting United States v.

Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976)). We refer to this as the Agurs standard. Here, the district court assumed that the government “should have known” about Muñiz’s perjury, and applied the Agurs standard of materiality. See July 22, 1997 Mem. and Order at 3. Applying this standard, it found that “there is no reasonable possibility that one more piece of impeaching evidence tarnishing an already blemished witness by degree rather than kind, could have affected the jury’s judgment.” Id. at 4. With regard to the traffic citation, the district court found that it was not Brady material.

See id. at 5. Applying the Kyles /Bagley materiality test, the court found that had the jury been made aware of the infraction, “there is no reasonable possibility, much less a probability,” id., that it would have influenced the verdict. The district court’s rulings were not an abuse of discretion.

Muñiz admitted to the jurors that she had supported a thirteen-year addiction to heroin by working as a prostitute, that she had frequently used other illegal drugs, that she had offered herself to the government as an informant because she needed the money, and most importantly, that she had lied to the grand jury about having been a prostitute in the past. The jury was already on notice about her tendency to commit perjury.

In addition, the thrust of her testimony, that defendants Rodriguez, Rosario and Fa-mania were in the business of distributing crack cocaine, was corroborated by the testimony of five other cooperating witnesses, and by police surveillance and physical evidence. Even examining her perjury under the Agurs standard, there is little chance that her false testimony affected the verdict. Similarly, the district court’s ruling with respect to the traffic citation does not constitute an abuse of discretion.

Assuming ar-guendo, but with little basis in the record, that the prosecutors or their agents knew or should have known of the information in question, we agree with the district court that there is no reasonable possibility that their lack of awareness of a traffic citation would have influenced their verdict. See United States v. Sepulveda, 15 F.3d 1216, 1220 n. 5 (1st Cir.1993)(“[0]ur decisions ... have [not] been sympathetic to new trial claims based solely on the discovery of additional information useful for impeaching a government witness.”). B.

Pedro De Jesús Defendants argue that they were not told about the government’s notice to De Jesús under 21 U.S.C. § 851, which exposed De Jesús to harsh recidivist penalties, enhancing his “motivation to tell the government what it wanted to hear.” Def. Br. at 26. The government’s nondisclosure of its § 851 filing does not entitle the defendants to a new trial.

Defendants knew full well that De Jesús had a long criminal history, see Tr. 10/17 at 21-23 (Rodriguez’s cross-examination detailing De Jesús’ prior convictions), and that a § 5K1.1 motion would trump any mandatory sentence that De Je-sús would otherwise receive. As a result, there is no Brady violation. See United States v. Hicks, 848 F.2d 1, 4 (1st Cir.1988). The government has no Brady burden when the necessary facts for impeachment are readily available to a diligent defender, as they were here. See Lugo v. Munoz, 682 F.2d 7, 9-10 (1st Cir.1982).

Further, the government’s failure to disclose its promise to apprise state law enforcement authorities about De Jesús’ cooperation does not entitle the defendants to a new trial. At trial, there was confusion about the status of De Jesús’ state drug charges. The court initially told the jury that state court records indicated that De Jesús had already pled guilty and been sentenced to probation on drug-trafficking charges. After further investigation, it was discovered that the charges were still pending.

As a result, the court corrected the factual inaccuracy and specifically instructed the jury that you may consider whether any expectancy of leniency on this pending [state] charge might have had an influence on what he said when [De Jesús] testified before you. Tr. 10/21 at 117. This charge, along with the extensive cross-examination conducted by the defendants concerning De Jesús’ alliance with the government and his motivation for a reduced sentence, rendered the government’s failure to disclose its aid to De Jesús insignificant. V.

Request for an Evidentiary Hearing Appellants argue that the district court erred in refusing their request for an evidentiary hearing to determine whether Mufiiz perjured herself on matters other than her occupation, and to discover whether the government had disclosed all of its pretrial promises and inducements to Carvajal and De Jesús. We are not persuaded. The substantive test to be applied when a criminal defendant seeks an evidentiary hearing is whether the movant has made an adequate threshold showing that the material facts are in genuine doubt or dispute. See United States v.

Lilly, 983 F.2d 300, 311 (1st Cir.1992). If the district court declines to hold an evidentiary hearing, we will disturb its decision only for an abuse of discretion. See id. Appellants argue that Mufiiz’s “he about her employment was not likely her only lie about herself.” Def. Br. at 38. They speculate that her prostitution “clearly suggested that she was hardly a recovered heroin addict.” Id. However, they offered no evidence to support their theories, and the district court rejected their request for an evidentia-ry hearing.

With regard to the issue of the government’s pre-trial promises and inducements, the district court ordered the government to file a declaration stating that it had disclosed all inducements given to cooperating witnesses. In response, the government represented that all pre-trial promises, rewards, and inducements had been disclosed. In its final order denying an evidentiary hearing, the court stated: [I]n the absence of any evidence to the contrary, I accept the government’s representation ... that it has disclosed all such inducements. June 5,1998 Order at 1.

As this Court has stated in the past, “[a] criminal defendant has no constitutional right to conduct a fishing expedition.” Lilly, 983 F.2d at 311. Appellants have made no showing, in this Court or below, that material facts were in doubt or dispute. Conclusory allegations and pure speculation, without more, do not merit an evidentiary hearing. Accordingly, the district court acted well within its discretion when it denied the appellants’ request. VI.

Challenge to the Composition and Voir Dire Examination of the Jury Rosario contends: (1) that the district court wrongly rejected his challenge to the grand and petit jury venires on the ground of systematic exclusion of Hispanics; and (2) that the court violated his due process and fair trial rights by denying his motion to directly question the venire. Neither claim is compelling. A. Systematic Exclusion Claim At base, Rosario’s argument is that the dissent in United States v.

Pion, 25 F.3d 18 (1st Cir.1994)(rejecting an attack on the composition of juries in the district court of Massachusetts based on under-representation of the Hispanic population), was correct. He offers nothing new in the way of statistics or legal authority to buttress his claim. Nor does he provide any reason why we should reconsider our recent reaffirmation of Pion in United States v. Lopez, 147 F.3d 1 (1st Cir.1998). Consequently, there is no need to go any further. B. Voir Dire Claim Fed.R.Crim.P. 24(

a) provides that the trial court may decide to conduct the voir dire itself or may allow the parties to conduct it. See Rosales-Lopez v. United States, 451 U.S. 182, 101 S.Ct. 1629, 68 L.Ed.2d 22 (1981); Fed.R.Crim.P. 24(a). Rosario argues, contrary to the language of Rule 24(a), that due process requires that he should have been allowed to question the venire. There is simply no authority, as Rosario himself admits, for the proposition that defense counsel must be allowed — as a matter of right — to question the venire.

Rather, the law states that the trial court has the option of allowing counsel to conduct voir dire or conducting the examination itself. If the court chooses the latter option, as it did in this case, it must permit counsel to “supplement the examination by such further inquiry as it deems proper or shall itself submit to the prospective jurors such additional questions by the parties or their attorneys as it deems proper.” Fed.R.Crim.P. 24(a). The trial court complied with the requirements of Rule 24(

a) by asking the venire, at defense counsel’s request, about their possible prejudices against Hispanics. See Tr. 10/7 at 18. After noting that the law enforcement officials would all be Caucasians, the district court additionally asked whether any juror would be inclined to take the word of a white police officer over a Hispanic defendant, or otherwise give “some edge” to the officer’s testimony. See id. at 19. Accordingly, the court’s conduct of voir dire was entirely proper. VII. Sentencing Issues Famania and Rosario challenge their sentences on numerous grounds. None is convincing and all are thus rejected.

A. The Sentences A narcotics conspirator is responsible not only for drugs he actually handled or saw but also for the full quantity of drugs that he reasonably could have foreseen to be embraced by the conspiracy he joined. See United States v. De La Cruz, 996 F.2d 1307, 1314 (1st Cir.1993); U.S.S.G. §§ 2D1.4, 2D1.1, 1B1.3 & comment n. 1. The district court’s findings as to the quantity embraced by the conspiracy and reasonably foreseen by the defendant is a factual one and will not be disturbed unless clearly erroneous. See De La Cruz, 996 F.2d at 1314.

Where no drugs have been seized, the guidelines instruct the district court to approximate the amounts involved, see U.S.S.G. § 2D1.1 comment, (note 12), and we uphold such an approximation as long as it represents a reasoned estimate of the quantity. See United States v. Webster, 54 F.3d 1, 5 (1st Cir.1995). First, the district court found that Rodriguez, Rosario, and Famania had joined the conspiracy by December 1994, and that the conspiracy continued until Rodriguez’s arrest in September 1995. See Tr. 7/11/97 at 7.

Second, it found that “a fair and conservative figure would attribute the distribution of five ounces of crack cocaine to the conspiracy on a weekly basis.” Id. at 9. Over a 36-week period, that would involve the distribution of approximately 5,000 grams of crack cocaine. The district court based its approximation on the following factors: (1) the ability of the conspirators to produce crack cocaine on short notice in amounts ranging from 13 grams to an ounce; (2) the four undercover purchases;

(3) Carvajal’s testimony that he and Rodriguez agreed to the purchase of an ounce of crack weekly on consignment; (4) numerous eyewitness accounts and surveillance of the come-and-go traffic at Famania’s apartment and at Beaver Park; and (5) accounts of the conspiracy’s customers. See id. at 9-10. All three defendants were assigned a Base Offense Level (“BOL”) of 38. See id. at 10. With no adjustments to the BOL and based on a Category II criminal history, the district court sentenced Rosario to 262 months, the lowest end of the applicable 262-327 months range. See id. at 11.

It sentenced Famania to 235 months imprisonment, the minimum of the 235-293 month range, again with no adjustments to the BOL and based on a Category I criminal history. See id. at 12. The district court’s approximation was a reasoned, if not conservative, estimate of the drug quantity involved. Consequently, the sentences imposed were proper and without error. B. Denial of an Evidentiary Hearing Contrary to Famania’s claim, the district court did not err in making its drug quantity calculations without first holding an evidentiary hearing.

Under the federal sentencing guidelines, “when any factor important to the sentencing determination is reasonably in dispute, the parties shall be given an adequate opportunity to present information to the court regarding that factor.” U.S.S.G. § 6A1.3. This provision does not mean that every factual dispute pertinent to the imposition of sentence demands a full evidentiary hearing. See United States v. Robles-Torres, 109 F.3d 83, 85 (1st Cir.1997). Evidentiary hearings at sentencing are, and should remain, the exception rather than the rule. See id.

In the final analysis, the decision to hold or eschew an evidentiary hearing lies within the sound discretion of the sentencing court. See id. In his request for an evidentiary hearing, Famania proposed to take the stand and refute various pieces of trial testimony, and also to cross-examine Carvajal. In denying the request, the district court noted: (1) that Carvajal was vigorously cross-examined at trial; (2) that the court had an opportunity to assess Carvajal’s credibility; and (3) that the defendants had offered nothing of substance to impugn the specifics of Carvajal’s account.

The district court indicated that it would consider any relevant affidavits or statements submitted by appellants for sentencing purposes. Taking his cue from the district court, Famania submitted an affidavit disputing the trial testimony of Carvajal, De Jesús, and Muñiz, as well as the grand jury testimony of another witness describing Famania as a drug distributor. He also presented an affidavit from one of his sisters-in-law, who attested that Famania’s large family had free access to his apartment, and that they did not witness any drug activity.

Not satisfied with the above, Famania now attacks his sentence on the basis that the defendants were entitled to an evidentiary hearing: (1) to further the fact-finding process; and (2) to combat the government’s proffer and the court’s reliance on the grand jury testimony of a witness who corroborated trial testimony as to the nature of the conspiracy. Famania’s arguments are not well founded. Under U.S.S.G. § 6A1.3, he was given his proverbial day in court when the district court invited the submission of affidavits and statements by the defendants for sentencing purposes.

Given that opportunity to present information to the court, the district court’s decision not to hold an evidentiary hearing was not in error. Moreover, a “sentencing judge is vested with wide discretion to determine the information on which sentencing guideline decisions will be based, and may consider reliable hearsay evidence.” United States v. Montoya, 967 F.2d 1, 3 (1st Cir.1992) (citation omitted).

Evidence with “sufficient in-dicia of reliability to support its probable accuracy” may be considered at sentencing “without regard to its admissibility under the rules of evidence applicable at trial.” U.S.S.G. § 6A1.3. Mindful of these tenets, the district court’s consideration of grand jury testimony to corroborate the general nature of the conspiracy was entirely proper. C.

Disparate Sentencing/Prosecutorial Discretion Claim Defendants Rosario and Famania argue that they should be resentenced because their sentences were significantly higher than those of their co-conspirators who pled guilty rather than choosing to go to trial. They claim that the disparity in sentencing constituted an impermissible burden on their Sixth Amendment right to a jury trial and violated the Due Process and Equal Protection Clauses of the Constitution. The government indicted six defendants, charging all of them with engaging in the same conspiracy to distribute crack cocaine.

The district court found this conspiracy accountable for the distribution of approximately 5,000 grams of crack cocaine over a 36-week period. At sentencing, the court held Rosario and Famania accountable for all 5,000 grams of the crack cocaine. In contrast, the district court accepted the agreement of the three defendants who had pled guilty — Carvajal, De Jesús, and Villafañe— which was based on responsibility only for the amount of drugs which each had personally handled. Carvajal, for example, was held accountable for 5 to 20 grams of crack cocaine.

This disparity in the drug-quantity attribution led to an even more striking disparity in sentencing, which is the subject of the defendants’ complaint. Carvajal was sentenced to the time he had already served, De Jesús to 17 months of imprisonment, and Villafañe to 60 months of imprisonment. Fa-mania was sentenced to 235 months of imprisonment, and Rosario to 262 months of imprisonment. Rodriguez, who was also charged with engaging in a continuing criminal enterprise, was sentenced to life imprisonment.

The thrust of the defendants’ complaint is that this vast disparity in sentencing — a difference of more than 21 years between Car-vajal and Rosario, for example — is an inevitable consequence of the application of a different drug-quantity attribution algorithm for those defendants who plead guilty as opposed to those who did not. They identify the plea-bargaining practice of the Office of the United States Attorney as the source of this disparity. The defendants claim that the U.S.

Attorney fashioned plea agreements with the “pleading defendants” which attributed to them an amount of drugs no greater than the amount for which the pleading defendants were personally responsible, or had personally handled. Those who did not plead guilty but exercised their right to go to trial, by contrast, had attributed to them all of the drugs that could be accounted to the entire conspiracy. Those who chose to go to trial, therefore, were necessarily sentenced on the basis of a far greater amount of drugs than those who pled guilty.

According to the defendants, this practice discriminates against those who exercise their right to a jury trial. The government, which characterizes the defendants’ argument as an improper motion for a downward departure from the applicable sentencing range, argues that we have no jurisdiction to consider the defendants’ complaint because the disparate sentences of co-conSpirators do not provide a basis for resen-tencing.

The government further asserts that even if this court did have jurisdiction, it should find no constitutional violation because the sentences of the pleading defendants were properly based on their plea agreements and allowed by U.S.S.G. § lB1.8(a). We begin, as we must, with the government’s jurisdictional objection. It is settled that “we have no appellate jurisdiction to review a sentence within the applicable sentencing guidelines range if that range was correctly determined.” United States v. Panet-Collazo, 960 F.2d 256, 261 (1st Cir. 1992).

The defendants’ argument is focused on the argued unconstitutional effects of the practices that led to the imposition of such disparate sentences. They do not say that their sentences were improperly calculated. Instead, they claim that the pleabargaining practice of the U.S. Attorney’s Office puts undue pressure on defendants, such as Rosario and Famania, to waive their right to a trial and violates Due Process and Equal Protection principles. Because there is no jurisdictional barrier to such an argument, we evaluate the defendants’ argument.

The defendants’ challenge to the plea-bargaining practice of the U.S. Attorney here finds little support in the law. We begin by noting that “prosecutorial charging, plea, and motion practices are ... a wellspring of sentencing disparity.... In the federal system, prosecutors have always enjoyed great discretion in deciding what eases to pursue and what charges to bring.” Kate Stith & José A. Cabranes, Fear of Judging: Sentencing Guidelines in the Federal Courts 140-41 (1998).

As Professor Stith and Judge Cabranes state: The major reason that such broad [pros-ecutorial] discretion has been accorded to prosecutors is the large number and complexity of factors that prosecutors must (legitimately) take into account in making charging and other decisions.

These include many considerations that the Sentencing Guidelines, or any other sentencing authority, would recognize as relevant also to sentencing — including the nature and seriousness of the offense, the deterrent effect of prosecution, the defendant’s culpability in the offense, the defendant’s criminal history and a wide range of other personal circumstances, the charges against accomplices in the crime, and the defendant’s willingness to cooperate in the prosecution of others.

In addition, prosecutors must pay attention to a variety of considerations that sentencing authorities ordinarily do not take into account after the defendant has been convicted — the strength or paucity of the admissible evidence, the priority accorded by the federal government as well as by the local community to prosecution of the particular offense, the capability and availability of prosecutorial resources and adjunct investigatory resources, the alternatives to prosecution, and the likelihood of prosecution in another jurisdiction. Id. at 141.

The government, it appears, negotiated plea bargains with some of the defendants and promised, according to U.S.S.G. § lB1.8(a), not to use any of the information provided by cooperating defendants against them. The government then charged each of them only with the amount of drugs they had personally handled, rather than the entire amount distributed by the conspiracy. This practice led to the enormous sentencing disparity for the defendants who chose to put the government to its burden in proving its case.

Nevertheless, the law allows the government to do this, even if it results in sentences of such disparity as would strike many as unfair. The fact that those who plead generally receive more lenient treatment, or at least a government recommendation of more lenient treatment than co-defendants who go to trial, does not in and of itself constitute an unconstitutional burden on one’s right to go to trial and prove its case. See Corbitt v.

New Jersey, 439 U.S. 212, 219, 99 S.Ct. 492, 58 L.Ed.2d 466 (1978) (noting that every burden on the exercise of a constitutional right is not invalid and that there is no per se rule against encouraging guilty pleas, even where those pleas promise the certainty of a lesser penalty). To be sure, the differential which resulted here exacts a high price from those who exercise their constitutional right to trial, but the price is not high enough to constitute a constitutional violation. Corbitt provides guidance on this issue.

In Corbitt, the Court addressed a claim under the New Jersey homicide statutes, which mandated life imprisonment for a jury conviction of first-degree murder and a maximum term of 30 years’ imprisonment for a jury conviction of second-degree murder. Although guilty pleas were not permitted in murder cases, a plea of non vult (or nolo contendere) was allowed.

If such a plea was accepted, the judge would not need to decide whether the murder was first or second-degree, but could sentence the defendant to either life imprisonment or to the same sentence that would be imposed for second-degree murder (i.e., a maximum of 30 years’ imprisonment). See id. at 214-15, 99 S.Ct. 492. The Court rejected the claim that because a plea of non vult might produce a lesser sentence than going to trial, the statutes imposed an unconstitutional burden on the defendant’s right to a jury trial and violated his right to equal protection under the laws. See id. at 218, 99 S.Ct. 492.

The Court, quoting its earlier decision in Bordenkircher v. Hayes, 434 U.S. 357, 98 S.Ct. 663, 54 L.Ed.2d 604 (1978), explained that: While confronting a defendant with the risk of more severe punishment clearly may have a discouraging effect on the defendant’s assertion of his trial rights, the imposition of these difficult choices [is] an inevitable — and permissible — attribute of any legitimate system which tolerates and encourages the negotiation of pleas.

It follows that, by tolerating and encouraging the negotiation of pleas, this Court has necessarily accepted as constitutionally legitimate the simple reality that the prosecutor’s interest at the bargaining table is to persuade the defendant to forgo his right to plead not guilty. Corbitt, 439 U.S. at 220-21, 99 S.Ct. 492 (quoting Bordenkircher, 434 U.S. at 364, 98 S.Ct. 663) (internal quotation marks and citation omitted). The Court also indicated that the defendant’s reliance on United States v. Jackson, 390 U.S. 570, 88 S.Ct. 1209, 20 L.Ed.2d 138 (1968), was inapposite.

See Corbitt, 439 U.S. at 216-17, 99 S.Ct. 492. In Jackson, the Court found that one portion of the Federal Kidnapping Act, 18 U.S.C. § 1201(a), needlessly chilled the exercise of one’s right to a jury trial. See Jackson, 390 U.S. at 582, 88 S.Ct. 1209. Corbitt distinguished Jackson, and thus its rule, on several grounds. Jackson involved the death penalty, “which is unique in its severity and irrevocability.” Corbitt, 439 U.S. at 217, 99 S.Ct. 492 (quoting Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976)).

The pressures in Corbitt, which compared to those stemming from the practice alleged here, were substantial, but they did not rise to the level of those in Jackson. See id. at 217, 99 S.Ct. 492 (declining to hold “that the Jackson rationale is limited to those cases where the plea avoids any possibility of the death penalty’s being imposed,” but noting that “it is a material fact that under the New Jersey law the maximum penalty for murder is life imprisonment, not death”). Further, in Jackson, all risk of receiving the death penalty could be avoided by pleading guilty.

In Corbitt, although the punishment for a jury conviction of first-degree murder was life imprisonment, the risk of receiving the same punishment was not completely avoided by pleading non wit, as the judge accepting the plea still maintained the power to impose a life term. See Corbitt, 439 U.S. at 217, 99 S.Ct. 492. The defendants here, of course, cannot avoid the imposition of a significantly greater sentence without pleading guilty, but that fact alone cannot help these defendants to avoid Corbitt and bring their case within the ambit of Jackson.

The defendants do not dispute that a conspirator may be held responsible for the reasonably foreseeable amount of drugs embraced by the jointly undertaken activity. See De La Cruz, 996 F.2d at 1314. It is, however, within the government’s discretion to charge similarly situated defendants differently. Only when a prosecutor discriminates against defendants based on impermissible criteria such as race or religion is a prosecutor’s discretion subject to review and rebuke.

See Bordenkircher, 434 U.S. at 364, 98 S.Ct. 663 (noting that “the conscious exercise of some selectivity in enforcement is not in itself a federal constitutional violation so long as the selection was [not] deliberately based upon an unjustifiable standard such as race, religion, or other arbitrary classification”) (internal quotation marks omitted); cf.

Corbitt, 439 U.S. at 225-26, 99 S.Ct. 492 (holding that there was no Equal Protection violation where those who pled guilty could potentially serve the same sentence as those who chose to contest their guilt, and asserting that to “fit the problem ... into an equal protection framework is a task too Proeruste-an to be rationally accomplished”) (citation omitted).

To the extent that the defendants’ argument can be characterized as seeking to equalize their sentences with those of their co-defendants, their argument, “without more, will not permit a departure from a properly calculated guideline sentencing range.” United States v. Wogan, 938 F.2d 1446 (1st Cir.1991); see United States v. Pierro, 32 F.3d 611, 622 (1st Cir.1994)(same); United States v. Figueroa, 976 F.2d 1446, 1460 (1st Cir.1992); United States v. Butt, 955 F.2d 77, 90 (1st Cir.1992); see also United States v.

Jackson, 950 F.2d 633, 637-38 (10th Cir.1991) (“Because Jackson’s claim is based solely on the lesser sentence imposed on his codefendant and because his sentence falls within the range established by the Sentencing Guidelines, we must reject this claim.... ”); United States v. Carpenter, 914 F.2d 1131, 1136 (9th Cir.1990) (holding that a defendant cannot base a challenge to his sentence solely on the lesser sentence given by the district court to his codefendant); United States v.

Guerrero, 894 F.2d 261, 267 (7th Cir.1990) (stating that there is nothing “in the legislative history suggesting that the sentences within the Guidelines should be reviewed because of a claim that a particular sentence is draconian or too lenient”); United States v. Sanchez Solis, 882 F.2d 693, 699 (2d Cir.1989) (rejecting defendant’s claim that a disparity in sentences violates the Sentencing Reform Act and rejecting his suggestion that he was penalized for exercising his right to a trial). CONCLUSION For the reasons stated in this opinion, we affirm. .

Spitting drugs on the ground was Rosario's odd practice of dispensing drugs to customers, and thus, an identifying modus operandi. . Some modicum of judicial power to alleviate unfairness lies in the ability of judges, under Fed.R.Crim.P. 11(e)(1)(B), to reject sentencing recommendations made by the parties when a guilty plea is tendered. . It appears that the pleading defendants were minor participants compared with the defendants who went to trial. But the Guidelines account for such difference in roles in U.S.S.G. § 3B1.2 (

a) and (b), and not by attributing a smaller amount of drugs to co-conspirators who play a more minor role.