BARBER et al. v. THOMAS, WARDEN, 560 U.S. 474

Justice Breyer delivered the opinion of the Court. Federal sentencing law permits federal prison authorities to award prisoners credit against prison time as a reward for good behavior. 18 U. S. C. § 3624(b). Petitioners, two federal prisoners, challenge the method that the Federal Bureau of Prisons uses for calculating this “good time credit.” We conclude that the Bureau’s method reflects the most natural reading of the statute, and we reject petitioners’ legal challenge.

I A A federal sentencing statute provides: “[A] prisoner who is serving a term of imprisonment of more than 1 year . . . may receive credit toward the service of the prisoner’s sentence, beyond the time served, of up to 54 days at the end of each year of the prisoner’s term of imprisonment, beginning at the end of the first year of the term .... [Cjredit for the last year or portion of a year of the term of imprisonment shall be prorated and credited within the last six weeks of the sentence.” § 3624(b)(1).

The Bureau of Prisons (BOP) applies this statute using a methodology that petitioners in this case challenge as unlawful. In order to explain the BOP method, we shall use a simplified example that captures its essential elements. The unsimplified calculations described by the BOP in its policy statement, see App. 96-100, will reach approximately the same results as, and are essentially the mathematical equivalent of, the simplified system we describe (there may be other ways to describe the calculation as well).

To the extent that there are any differences between the methodology employed by the BOP and that reflected in our example, they are of no consequence to the resolution of petitioners’ challenge and are therefore not before us. Similarly, although petitioners committed their crimes before the current version of §3624 was enacted and are therefore subject to a previous version that differed slightly in certain details, see 18 U. S. C. § 3624 (1988 ed.), the differences between the two versions are immaterial to the questions presented by this case.

The parties refer to the current version as the relevant provision of law, see Brief for Petitioners 2-3; Brief for Respondent 8, n. 2, and we shall do the same. In our example we shall imagine a prisoner who has received a sentence of 10 years’ imprisonment. We shall assume that his behavior throughout his confinement is exemplary and that prison authorities will consequently consider him to merit the maximum good time credit that the statute will allow. And we shall ignore leap years. Thus, at the end of the first year (Year 1) that prisoner would earn the statute’s maximum credit of 54 days.

The relevant official (whom we shall call the “good time calculator”) would note that fact and, in effect, preliminarily put the 54 days to the side. At the end of Year 2 the prisoner would earn an additional 54 days of good time credit. The good time calculator would add this 54 days to the first 54 days, note the provisional total of 108 days, and again put the 108 days’ credit to the side. By the end of Year 8, the prisoner would have earned a total of 432 days of good time credit (8 years times 54 days).

At that time, the good time calculator would note that the difference between the time remaining in the sentence (2 years, or 730 days) and the amount of accumulated good time credit (432 days) is less than 1 year (730 minus 432 equals 298 days, which is less than 365). The 432 days of good time credit that the prisoner has earned by the end of Year 8 are sufficient to wipe out all of the last year of the 10-year prison term and to shorten the prisoner’s 9th year of imprisonment by 67 days. Year 9 of the sentence will consequently become the prisoner’s last year of imprisonment.

Further, because the prisoner has already earned 67 days of credit against that year (432 days already earned minus 365 days applied to Year 10 leaves 67 days to apply to Year 9), the prisoner will have no more than 298 days left to serve in Year 9. Now the good time calculator will have to work out just how much good time the prisoner can earn, and credit against, these remaining 298 days.

As we said, the statute provides that “good time” for this “last year or portion” thereof shall be “prorated.” Thus, the good time calculator must divide the 298 days into two parts: (1) days that the prisoner will have to serve in prison, and (2) credit for good behavior the prisoner will earn during the days served in Year 9. In other words, the number of days to be served in Year 9 plus the number of good time credit days earned will be equal to the number of days left in the sentence, namely, 298.

And to keep the award of credit in the last year proportional to awards in other years, the ratio of these two parts of Year 9 (i. e., the number of good time days divided by the number of days served) must be 54 divided by 365, the same ratio that the BOP applies to full years served. We can use some elementary algebra, described in the Appendix, infra, to work out the rest. The result is that if the prisoner serves 260 days, he can earn an additional 38 days of credit for good behavior.

That is to say, of the 298 days remaining in his sentence, the prisoner will have to serve 260 days in confinement, after which point, his sentence will be fully accounted for (given the additional 38 days’ credit earned), and he will be released. In sum, a prisoner subject to a 10-year (3,650-day) sentence who earns the maximum number of days the statute permits will serve 3,180 days in confinement and receive 470 days of “good time” credit, about 15% of the prison time actually served. B In this case petitioners claim that the BOP’s calculation method is unlawful.

They say that § 3624(b)(1) (2006 ed.) requires a straightforward calculation based upon the length of the term of imprisonment that the sentencing judge imposes, not the length of time that the prisoner actually serves. Thus, if a sentencing judge imposes a prison term of 10 years (as in our example), then, in petitioners’ view, the statute permits a maximum good time award of 540 days (10 years times 54 days), not the 470 days that the method described above would allow.

And if the judge imposes a prison term of 10 years and 6 months, then the statute permits 567 days (540 days for the 10 years plus 27 days for the extra 6 months), not the 494 days that the method above would allow. According to petitioners, the BOP’s method causes model prisoners to lose seven days of good time credit per year of imprisonment, and because their sentences are fairly long (one, Michael Barber, was sentenced to 26 years and 8 months; the other, Tahir Jihad-Black, was sentenced to 21 years and 10 months), the difference in their cases amounts to several months of additional prison time.

The District Court in each of these cases rejected the prisoner’s challenge. Civ. No. 08-226 MO (D Ore., Oct. 27,2008), App. 13; Jihad-Black v. Thomas, Civ. No. 08-227 MO (D Ore., Oct. 27, 2008), App. 25. And in each instance the Court of Appeals affirmed the District Court. Tablada v. Thomas, No. 07-35538 (CA9, Apr. 10, 2009), App. 11; see also Tab-lada v. Thomas, 533 F. 3d 800 (CA9 2008). Because the BOP’s administration of good time credits affects the interests of a large number of federal prisoners, we granted the consolidated petition for certiorari to consider petitioners’ challenge.

II Having now considered petitioners’ arguments, we conclude that that we must reject their legal challenge. The statute’s language and its purpose, taken together, convince us that the BOP’s calculation method is lawful. For one thing, that method tracks the language of § 3624(b). That provision says that a prisoner (serving a sentence of imprisonment of more than a year and less than life) “may receive credit... of up to 54 days at the end of each year” subject to the “determination by the Bureau of Prisons that, during that year, the prisoner” has behaved in an exemplary fashion. § 3624(b)(1) (emphasis added).

And it says that credit for the “last year or portion of a year . . . shall be prorated and credited within the last six weeks of the sentence.” Ibid. As the example in

Part I makes clear, the BOP’s

interpretation provides a prisoner entitled to a maximum annual credit with 54 days of good time credit for each full year of imprisonment that he serves and a proportionally adjusted amount of credit for any additional time served that is less than a full year. And, as § 3624(

b) directs, the BOP awards the credit at the end of each year of imprisonment (except, of course, for Year 9, which is subject to the statute’s special instruction requiring proration and crediting during the last six weeks of the sentence). We are unable similarly to reconcile petitioners’ approach with the statute. Their system awards credit for the sentence imposed, regardless of how much time is actually served. Thus, a prisoner under petitioners’ system could receive 54 days of credit for Year 10 despite the fact that he would be released after less than, 8V2 years in prison.

The good time calculation for Year 10 would not be made “at the end of” Year 10 (nor within the last six weeks of a sentence ending during that year). Neither could the BOP determine whether the prisoner had behaved in exemplary fashion “during that year.” 18 U. S. C. § 3624(b)(1) (emphasis added); see also White v. Scibana, 390 F. 3d 997, 1001 (CA7 2004) (“The Bureau cannot evaluate a prisoner’s behavior and award credit for good conduct if the prisoner is not still in prison”); cf. McGinnis v. Royster, 410 U.

S. 263, 273 (1973) (“Where there is no evaluation by state officials and little or no rehabilitative participation for anyone to evaluate, there is a rational justification for declining to give good-time credit”). We cannot say that this language (“at the end of,” “during that year”) found its way into the statute by accident. Under the previous good time provision, a prisoner was “entitled to a deduction from the term of his sentence beginning with the day on which the sentence commences to run.” 18 U. S. C. §4161 (1982 ed.) (repealed 1984).

This deduction, granted at the outset of a prisoner’s sentence, was then made subject to forfeiture if the prisoner “committed] any offense or violatefd] the rules of the institution.” §4165 (repealed 1984).

The present statute, §3624 (2006 ed.), in contrast, creates a system under which “credit” is “earned” “at the end of” the year based on an evaluation of behavior “during that year.” We agree with the Government that “[t]he textual differences between the two statutes reveal a purpose to move from a system of prospective entitlement to a system of retrospective award.” Brief for Respondent 33; see also White, supra, at 1002, n. 3. For another thing, the BOP’s method better furthers the statute’s basic purpose. The “good time” provision in § 3624 is part of the Sentencing Reform Act of 1984, 98 Stat. 1987, 18 U. S.

C. §3551 et seq., 28 U. S. C. §§991-998, a comprehensive law that reformed federal sentencing practice and directed the newly created United States Sentencing Commission “to devise guidelines to be used for sentencing” in district courts, Mistretta v. United States, 488 U. S. 361, 367 (1989). Under the previous regime, the United States Parole Commission, “as a general rule, [could] conditionally release a prisoner any time after he serve[d] one-third of the judicially fixed term.” United States v. Grayson, 438 U. S. 41, 47 (1978).

If, for example, a judge imposed a prison term of 15 years, the Parole Commission might have released the prisoner after only 5 years. And it routinely did so. See United States Sentencing Commission, Guidelines Manual §1A3, p. s., p. 1.2 (Oct. 1987) (USSG) (“[Defendants often servfed] only about one-third of the sentence handed down by the court”). The result was “confusion and implicit deception.” Ibid. With the Sentencing Reform Act, Congress sought to achieve both increased sentencing uniformity and greater honesty by “mak[ing] all sentences basically determinate,” Mistretta, supra, at 367.

See USSG § 1A3, p. s., at 1.2 (statutory objectives included “honesty in sentencing,” “uniformity,” and “proportionality” (emphasis deleted)). Thereafter, the sentence the judge imposed would be the sentence the offender actually served, with a sole statutory exception for good time credits. Mistretta, supra, at 367 (a “prisoner is to be released at the completion of his sentence reduced only by any credit earned by good behavior while in custody” (citing § 3624(b))).

The reason for this exception is provided in § 3624(b)(1) itself: to provide an incentive for prisoners to “compl[y] with institutional disciplinary regulations.” The good time exception is limited (to 54 days per year) and tailored to its purpose — credit is earned at the end of the year after compliance with institutional rules is demonstrated and thereby rewards and reinforces a readily identifiable period of good behavior. ' The BOP’s approach furthers the objective of §3624. It ties the award of good time credits directly to good behavior during the preceding year of imprisonment.

By contrast, petitioners’ approach, insofar as it would award up to 54 days per year of time sentenced as opposed to time served, allows a prisoner to earn credit for both the portion of his sentence that he serves and the portion of his sentence that he offsets with earned good time credit. In other words, petitioners argue that the BOP should award good time credit not only for the days a prisoner spends in prison and behaves appropriately, but also for days that he will not spend in prison at all, such as Year 10 in our example.

By doing so, it loosens the statute’s connection between good behavior and the award of good time and transforms the nature of the exception to the basic sentence-imposed-is-sentence-served rule. And to that extent, it is inconsistent with the statute’s basic purpose. Ill A We are not convinced by petitioners’ several arguments against the BOP’s methodology.

First, petitioners point to the statement in § 3624(b)(1) that a prisoner “may receive credit ... at the end of each year of the prisoner’s term of imprisonment.” (Emphasis added.) The words “term of imprisonment,” they say, must refer to the years of the term that the sentencing judge imposed (10 years in our example), not the (less-than-10) years of the term that the prisoner actually served once good time credits were taken into account.

After all, the very first phrase of that provision makes eligible for good time credits “a prisoner who is serving a term of imprisonment of more than 1 year other than a term of imprisonment for the duration of the prisoner’s life.” Ibid, (emphasis added; footnote omitted). The words “term of imprisonment” in this phrase almost certainly refer to the sentence imposed, not to the time actually served (otherwise prisoners sentenced to a year and a day would become ineligible for credit as soon as they earned it).

And, as petitioners emphasize, we have recognized a “presumption that a given term is used to mean the same thing throughout a statute,” Brown v. Gardner, 513 U. S. 115, 118 (1994). The problem for petitioners, however, is that this presumption is not absolute. It yields readily to indications that the same phrase used in different parts of the same statute means different things, particularly where the phrase is one that speakers can easily use in different ways without risk of confusion. Atlantic Cleaners & Dyers, Inc. v. United States, 286 U. S. 427, 433 (1932); General Dynamics Land Systems, Inc. v.

Cline, 540 U. S. 581, 595-596 (2004). See, e. g., id., at 596-597 (“age” has different meanings in the Age Discrimination in Employment Act of 1967); United States v. Cleveland Indians Baseball Co., 532 U. S. 200, 213 (2001) (same for “‘wages paid’” in the Internal Revenue Code); Robinson v. Shell Oil Co., 519 U. S. 337, 343-344 (1997) (same for “employee” in Title VII of the Civil Rights Act of 1964). The phrase “term of imprisonment” is just such a phrase.

It can refer to the sentence that the judge imposes, see, e. g., § 3624(a) (“A prisoner shall be released” at the end of “the prisoner’s term of imprisonment, less any time credited” for good behavior), but it also can refer to the time that the prisoner actually serves. Thus, § 3624(

d) of the statute before us requires the BOP to “furnish [a] prisoner with . . . suitable clothing[,] . . . money, . . . and . . . transportation” “[u]pon the release of [the] prisoner on the expiration of the prisoner’s term of imprisonment.” (Emphasis added.) The statute here means to ensure that the prisoner is provided with these necessities at the time of his actual release from prison (sometime during Year 9 in our example), not at the end of the term that the judge imposed (which would be over a year later). Since the statute uses the same phrase “term of imprisonment” in two different ways, the presumption cannot help petitioners here. And, for the reasons we have given, see

Part II, supra, context here indicates that the particular instance of the phrase “term of imprisonment” at issue refers to prison time actually served rather than the sentence imposed by the judge. Second, petitioners seek to draw support from the statute’s legislative history. But those who consider legislative history significant cannot find that history helpful to petitioners here.

Petitioners point, for example, to a statement in the Senate Report accompanying the Sentencing Reform Act, which says that the “method of calculation” of good time “will be considerably less complicated than under current law in many respects,” and that “credit toward early release is earned at a steady and easily determined rate that will have an obvious impact on the prisoner’s release date.” S. Rep. No. 98-225, pp. 146-147 (1983); see Brief for Petitioners 31-32. But these statements are consistent with the BOP’s

interpretation of the statute. Its method, as we understand it, is not particularly difficult to apply and it is certainly less complex than prior law, which provided for the accumulation of two different kinds of good time credit (general and industrial), calculated in different manners (prospectively and retrospectively), and awarded at different rates, depending on the length of sentence imposed on the prisoner (5 to 10 days per month for general) or the year of employment (3 or 5 days per month for industrial). See 18 U. S. C. §§4161, 4162 (1982 ed.).

Petitioners also point to various statements contained in the Act’s Conference Report and made by individual legislators that describe good time credit as providing sentence reductions of 15%. See Brief for Petitioners 34-36 (citing, e. g., H. R. Conf. Rep. No. 98-1159, p. 415 (1984); 131 Cong. Rec. 488 (1985) (remarks of Rep. Hamilton)). But there is nothing in the context of these statements to suggest that they amounted to anything other than rough approximations or that they were made with the present controversy in mind. See, e. g., H. R. Conf. Rep.

No. 98-1159, at 415 (noting simply that an increase in the amount of maximum annual credit from 36 days to 54 days “increases ‘good time’ that accrues from 10 percent to 15 percent”); 131 Cong. Rec. 488 (statement of Rep. Hamilton) (“Under [pre-Senteneing Reform Act] law, about 80% of all criminals are paroled after serving one third of their time. Now sentences will be reduced only 15% for good behavior”).

And whatever interpretive force one attaches to legislative history, the Court normally gives little weight to statements, such as those of the individual legislators, made after the bill in question has become law. See, e. g., Heintz v. Jenkins, 514 U. S. 291, 298 (1995). Third, petitioners rely on a statement in the United States Sentencing Commission’s Supplementary Report on the Initial Sentencing Guidelines and Policy Statements issued in 1987 (hereinafter Supplementary Report).

In that Report, the Commission summarized its analysis of recent pre-Guidelines sentencing practice, which it had used to help draft the Guidelines. The results of the analysis were presented in a table that permits comparison of the likely prison-time consequences of the new Guidelines with prison time actually served under pre-Guidelines practice (specifically, by identifying the Guidelines “offense level that is closest to the average time . . . served by first-time offenders” convicted of a particular crime, Supplementary Report 23).

Because the Guidelines “refer to sentences prior to the awarding of good time” (i. e., because a Guidelines sentence of, say, 30 months’ imprisonment does not necessarily mean that the offender will serve the entire 30 months in prison), the Commission adjusted the average time served “by dividing by 0.85 good time when the term exceeded 12 months.” Ibid. This adjustment, the Commission explained, “made sentences in the [t]able comparable with those in the guidelines.” Ibid.

Pointing to this adjustment and a reference in later editions of the Guidelines to a potential credit of “approximately fifteen percent for good behavior,” see, e.g., USSG §1A3, p. s., at 3 (Nov. 2009), petitioners maintain that the Commission .set its Guidelines ranges, with the expectation that well-behaved prisoners would receive good time credit of up to 15% of the sentence imposed, not 15% of the time actually served. They add that, in setting the Guidelines ranges in this way, the Commission exercised congressionally delegated power to interpret the Sentencing Reform Act, see Mistretta, 488 U.

S., at 371-379 (approving Congress’ delegation of the power to promulgate sentencing guidelines), and that as long as that

interpretation is reasonable, courts must defer to it, see Chevron U. S. A. Inc. v. Natural Resources Defense Council, Inc., 467 U. S. 837, 843-844 (1984). Again, however, we can find no indication that the Commission, in writing its Supplementary Report or in the Guidelines themselves, considered or referred to the particular question here before us, that is, whether good time credit is to be based on time served or the sentence imposed. The Guidelines Manual itself, a more authoritative account of the Commission’s interpretive views than the Supplementary Report, says nothing directly on that subject.

Moreover, with respect to comparisons between Guidelines sentences and pre-Guidelines practice, the original 1987 Manual cautioned that the Guidelines did not “simply cop[y] estimates of existing practice as revealed by the data,” but rather “departed from the data at different points for various important reasons.” USSG § 1A3, p. s., at 1.4; see also id., §lA4(g), p. s., at 1.11 (while “Guideline sentences in many instances will approximate existing [i. e., pre-Guidelines] practice,” the Commission did “not conside[r] itself bound by existing sentencing practice” (emphasis added)).

Because the Commission has expressed no view on the question before us, we need not decide whether it would be entitled to deference had it done so. If it turns out that the calculation of good time credit based on prison time served rather than the sentence imposed produces results that are more severe than the Commission finds appropriate, the Commission remains free to adjust sentencing levels accordingly.

See id., §1A2, at 1.2 (acknowledging that “the guideline-writing process [is] evolutionary” and that the Commission functions “as a permanent agency to monitor sentencing practices in the federal courts throughout the nation”). Fourth, petitioners ask us to invoke the rule of lenity and construe § 3624 (2006 ed.) in their favor, that is, in a way that will maximize the amount of available good time credit. We may assume for present purposes that § 3624(

b) can be construed as imposing a criminal penalty. See Bifulco v. United States, 447 U. S. 381, 387 (1980) (rule of lenity applies to “interpretations of... the penalties” imposed by “criminal prohibitions”); but see Sash v. Zenk, 428 F. 3d 132, 134 (CA2 2005) (Sotomayor, J.) (holding that § 3624(

b) is not a criminal statute for the purposes of the rule of lenity). Even so, the rule of lenity only applies if, after considering text, structure, history, and purpose, there remains a “grievous ambiguity or uncertainty in the statute,” Muscarello v. United States, 524 U. S. 125, 139 (1998) (internal quotation marks omitted), such that the Court must simply “ ‘guess as to what Congress intended,” Bifulco, supra, at 387 (quoting Ladner v. United States, 358 U. S. 169, 178 (1958)). See United States v. Hayes, 555 U. S. 415, 429 (2009); United States v. R. L. C., 503 U. S. 291, 305-306 (1992) (plurality opinion).

Having so considered the statute, we do not believe that there remains a “grievous ambiguity or uncertainty” in the statutory provision before us. Nor need we now simply “guess” what the statute means. Finally, we note that petitioners urge us not to defer to the BOP’s implementation of § 3624(b). In our view, the BOP’s calculation system applies that statute as its language is most naturally read, and in accordance with what that language makes clear is its basic purpose.

No one doubts that the BOP has the legal power to implement the statute in accordance with its language and purposes; hence we need not determine the extent to which Congress has granted the BOP authority to interpret the statute more broadly, or differently than it has done here. Cf. Chevron, supra, at 844-845. B Acknowledging that petitioners’ arguments cannot carry the day, the dissent has proposed a “third possibility,” post, at 495 (opinion of Kennedy, J.), not raised by either party nor, to our knowledge, used elsewhere in the Criminal Code.

The dissent reads the statutory phrase “term of imprisonment” to refer to “the administrative period along which progress toward eventual freedom is marked.” Ibid. It derives from this reading the following method of calculation as applied to our 10-year example. First, “[t]he sentence is divided into ten 365-day segments.” Ibid. At the end of the first segment, a prisoner may receive up to 54 days of credit for good behavior.

These credits immediately “go toward completion of the next year” so that the prisoner need only serve “another 311 days behind bars before the second year of his term of imprisonment is at an end.” Post, at 496. This process repeats itself until the “10th segment,” in which a prisoner receives an unspecified “credit in a prorated amount.” Ibid. In the end, the prisoner will have served 10 “administrative segments,” ibid., collectively comprising 3,117 days in prison and 533 days of credit. The dissent claims “[r]eading ‘term of imprisonment’ this way is consistent with all parts of the statute.” Ibid.

We see at least four problems. First, the opening sentence of § 3624(

a) instructs that “[a] prisoner shall be released” upon “the expiration of the prisoner’s term of imprisonment, less any time credited” for good behavior. But if a prisoner’s “term of imprisonment” is the “period that a prisoner must complete in order to earn his freedom,” post, at 497, and it is “accounted for through a combination of prison time and credits,” post, at 495, then a prisoner should be released exactly at the end of his term of imprisonment (without any further adjustment).

Because the dissent’s approach would require us to read words out of the statute, or give prisoners double credit, its definition cannot be used here. Second, § 3624(b)(1) tells us that a prisoner receives credit “at the end of each year” based on behavior “during that year.” Under the dissent’s approach, however, a prisoner may receive credit at the end of each “administrative segment]” presumably based on his behavior during that segment. And because an “administrative segmen[t]” is made up of some “combination of service and credits,” post, at 496, each one lasts less than a calendar year.

We do not see how a system in which “a prisoner may complete a particular year of his term in less than 365 calendar days,” ibid., and receive full good time credit for doing so, can possibly represent the most natural reading of this statutory language.

Nor do we know, because the BOP has not had an opportunity to tell us, whether a system in which a “year” lasts anywhere from 311 to 365 calendar days (and in which the “years” of a single prisoner’s sentence may all be of different lengths) is easily administrable. (We doubt that this system will be more comprehensible to prisoners than one, like the BOP’s, that provides credit for actual years.) Third, under the dissent’s approach, credit is earned at different rates during a single sentence.

For the first “administrative segmen[t]” in its 10-year example, the prisoner serves 365 days and earns 54 days of credit. The ratio of credit earned to days served is 0.148. For the second “administrative segmen[t],” the prisoner serves 311 days and earns 54 days of credit. This time, the ratio of credit earned to days served is 0.174. (For the last “administrative segment],” the dissent tells us the prisoner will receive “credit in a prorated amount,” but it does not tell us which ratio should be used for the proration. Post, at 496.) The use of different rates finds no support in the statute.

The dissent objects that the statute “prescribes no particular rate,” post, at 499, but in fact it does — 54 days of credit per year of good behavior — and it further requires that credit for the last year be “prorated” using the same proportion. Moreover, the dissent’s application of different rates leads to odd results. For example, a model prisoner sentenced on two separate 5-year terms (with a break in between) will serve a different number of days from one sentenced to a single 10-year term. How can this be if both prisoners are earning 54 days of credit for each of their 10 years in prison?

Fourth, § 3624(b)(2) provides that good time credit “shall vest on the date the prisoner is released from custody.” (This provision does not apply to prisoners, like petitioners, who committed their offenses before it was amended in 1996, but the dissent plainly intends for its approach to apply more broadly. See post, at 501 (noting the effect on “almost 200,000 federal prisoners”).) Yet under the dissent’s approach, credit appears to vest immediately.

See post, at 496 (Days of credit for the first year “go toward completion of the next year” so that the prisoner “would need another 311 days behind bars before the second year of his term of imprisonment is at an end”). And if it does not, then the situation quickly becomes complicated. What happens if, say, on the last day of the 10th “administrative segmen[t]” (somewhere in the 8th calendar year), a prisoner badly misbehaves and prison officials punish him by taking away all of his previously earned credit? Cf. 28 CFR § 541.13 (2009) (prescribing sanctions for prohibited acts).

Does the BOP retroactively adjust the duration of all of his administrative segments to 365 days so that the prisoner now finds himself in the middle of the 8th “administrative segmen[t]”? (Again we do not know if the BOP would find such a system administrable, and we doubt that this system would be more comprehensible to a prisoner.) If so, does the prisoner have a second opportunity to earn credit for good behavior for the 9th “administrative segmen[t]” that he had previously completed but now must account for again? Cf. § 3624(b)(1) (“Credit that has not been earned may not later be granted”).

Or, having previously awarded (and taken away) credit for that segment, are prison authorities left without any incentive to offer for good behavior? Finally, the dissent, like petitioners, invokes the rule of lenity to support its

interpretation. But, the best efforts of the dissent notwithstanding, we still see no “grievous ambiguity or uncertainty” that would trigger the rule’s application. We remain convinced that the BOP’s approach reflects the most natural reading of the statutory language and the most consistent with its purpose. Whatever the merits of the dissent’s policy arguments, the statute does not require the BOP to accept them. For all of these reasons, we conclude that the BOP’s methodology is lawful. The Ninth Circuit’s judgment is Affirmed.

APPENDIX A fuller example of the BOP’s method for calculating “credit for the last year or portion of a year of the term of imprisonment” The defendant is sentenced to 10 years’ imprisonment. As a prisoner he exhibits exemplary behavior and is awarded the maximum credit of 54 days at the end of each year served in prison. At the end of Year 8, the prisoner has 2 years remaining in his sentence and has accumulated 432 days of good time credit.

Because the difference between the time remaining in his sentence and the amount of accumulated credit (i. e., 730 minus 432) is less than a year (298 days), Year 9 is the last year he will spend in prison. (Year 10 has been completely offset by 365 of the 432 days of accumulated credit.) Further, Year 9 will be a partial year of 298 days (the other 67 days of the year being offset by the remainder of the accumulated credit). Here is where the elementary algebra comes in. We know that x, the good time, plus y, the remaining time served, must add up to 298. This gives us our first equation: x + y = 298.

Wé also know that the ratio of good time earned in the portion of the final year to the amount of time served in that year must equal the ratio of a full year’s good time credit to the amount of time served in a full year. The latter ratio is 54 -*■ 365 or 0.148. Thus, we know that x -*■ y = 0.148, or to put it another way, x = 0.148?/. Because we know the value of x in terms of y, we can make a substitution in our first equation to get 0.148?/ + y = 298. We then add the two y terms together (1.148?/ = 298), and we solve for y, which gives us y = 260.

Now we can plug that value into our first equation to solve for x (the good time credit). If we subtract 260 from 298, we find that x = 38. The offender will have to serve 260 days in prison in Year 9, and he will receive 38 days additional good time credit for that time served. The prisoner’s total good time is 470 days (432 + 38 = 470). His total time served is 3,180 days.

As a final matter, while we have described the foregoing as the method to calculate credit for the portion of the last year to more transparently track the relevant statutory language, we note that the mathematical formula can be used to calculate the amount of maximum available credit for an entire sentence. Using the equations supplied above, if we divide the total number of days in a sentence by 1.148, we get the minimum number of days that a defendant must serve in that sentence.

If we then subtract the number of days served from the total number of days in the sentence, we arrive at the maximum number of good time credit days the prisoner can earn. The statute, however, awards them on a yearly basis (but for the “last year or portion” thereof).