JOSÉ A. CABRANES, Circuit Judge:

This appeal arises out of a decision of the United States District Court for the Western District of New York (David G. Larimer, Judge), on a remand pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir.2005). On the Crosby remand, the District Court declined to order resentencing of two co-defendants who had been convicted of crimes arising out of their participation in a heroin trafficking conspiracy and who were sentenced to substantial terms of imprisonment.

On appeal, defendant Art Williams argues that the District Court used the wrong legal standard when determining whether to resentence him pursuant to Crosby, and that his 216-month sentence was unreasonable under the standard of appellate review set forth in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005) ( "Booker/Fanfan"). With respect to Williams's co-defendant, Roland Onaghinor, who had been indicted and convicted along with Williams, Onaghinor's counsel has submitted a brief pursuant to Anders v. California, 38( 5 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967), alleging that there are no non-frivolous grounds on which to appeal and asking to be relieved as counsel. The Government has filed a motion for summary affirmance as to Onaghinor. While Onaghinor's appeal was pending, he completed service of his term of imprisonment and was deported.

The parties' submissions require us to consider the scope of our review of a district court's decision not to resentence pursuant to Crosby. We conclude that we retain authority to review for reasonableness both the procedure whereby the District Court decided not to resentence and the substance of the undisturbed sentence. We clarify, however, that the law of the case doctrine forecloses reconsideration of issues that were decided — or that could have been decided — during prior proceedings.

In the matter of defendant Williams, we find no reversible error in the District Court's proceedings on the Crosby remand, and we conclude that the sentence imposed on Williams by the District Court was reasonable. We dismiss the appeal of Williams's co-defendant Onaghinor as moot.

BACKGROUND

I. Facts and Procedural History

In November 2001, defendants Art Williams and Roland Onaghinor were convicted by a jury for their participation in a conspiracy to possess with intent to distribute, and to distribute, one kilogram or more of heroin, in violation of 21 U.S.C. §§ 841(a)(1), 841(b)(1)(A), and 846. Defendant Williams was also convicted of thirteen counts of using a communication facility (the U.S. Mail) in committing, or in causing or facilitating the commission of, the heroin trafficking conspiracy, in violation of 21 U.S.C. § 843(b) and 18 U.S.C. § 2.

At their sentencings, which were conducted under the then-mandatory Sentencing Guidelines regime governing federal sentencing, the District Court made a number of rulings favorable to both Williams and Onaghinor, the net result of which was to reduce substantially the Guidelines range applicable to their offenses. For example, the District Court held that Williams could only be held responsible for conspiring to distribute between 700 grams and 1 kilogram of heroin, despite a jury finding that he was responsible for conspiring to distribute over 1 kilogram of heroin. This ruling, along with other favorable findings by the District Court, reduced Williams's potential sentence for the heroin trafficking conspiracy conviction from a mandatory sentence of life imprisonment without parole, see 21 U.S.C. § 841(b)(1)(A), to a Guidelines range of 188 to 235 months. The District Court also affirmed, over the Government's objection, a jury finding that Onaghinor could not be held responsible for conspiring to distribute more than 100 grams of heroin. The District Court did, however, impose a two-level enhancement for obstruction of justice pursuant to U.S. Sentencing Guidelines Manual ("U.S.S.G.") § 3C1.1 on both Williams and Onaghinor, and a three-level enhancement on Williams for his role in the offense pursuant to U.S.S.G. § 3B1.1(b).

The District Court sentenced Williams on March 5, 2003 to a term of imprisonment of 216 months on the heroin trafficking conspiracy count, and a term of imprisonment of 48 months on each of the remaining counts, each term of imprisonment to run concurrently with the others. He was also sentenced to three years of supervised release, a fine of $3,000 on count one, and a special assessment of $1,400. Onaghinor was sentenced on May 16, 2002 to a term of imprisonment of 78 months, a period of supervised release of three years, and a $100 special assessment.

On appeal, we affirmed defendants' convictions and rejected Williams's challenge to the District Court's imposition of the two-level obstruction of justice enhancement, see Peterson, 385 F.3d at 139-43, but held the mandate pending the decision of the Supreme Court in Booker/Fanfan, see id. at 143. Defendants did not challenge any of the District Court's other sentencing rulings on appeal, although Williams filed a supplemental brief challenging the imposition of the three-level role enhancement after his case was briefed and argued. See id. After the Supreme Court issued its decision in Booker/Fanfan, we remanded the cause to the District Court pursuant to our decision in Crosby for a determination of whether to resentence defendants. See Crosby, 397 F.3d at 117-20.

On remand, Williams asked the District Court to "reconsider . . . the application" of the Guidelines enhancements that it had imposed on him for obstruction of justice and his role in the offense. While Williams's sentencing memorandum sought to convince the District Court that Williams had not obstructed justice, it did not argue that any of the sentencing factors set forth in 18 U.S.C. § 3553(a) and given renewed vitality by Booker/Fanfan, see Crosby, 397 F.3d at 113 (discussing district court's obligation to "consider the Guidelines and all of the other factors listed in section 3553(a)" when imposing sentence after Booker/Fanfan), would support imposition of a non-Guidelines sentence. Onaghinor's sentencing memorandum on remand also challenged the District Court's previous imposition of the obstruction of justice enhancement, but offered no rationale for resentencing based on the § 3553(a) factors.

II. The District Court's Decision

In a published Decision and Order dated August 24, 2005, the District Court declined to resentence either defendant. See United States v. Williams, 383 F.Supp.2d 426 (W.D.N.Y.2005). The District Court began its discussion of the issues before it by stating that it was familiar with Booker/Fanfan, Crosby, and the proceedings in defendants' cases; that it had reviewed the memoranda submitted by counsel for defendants; and that it had considered the sentencing factors listed in § 3553(a). See id. at 427. It then proceeded to reject Williams's renewed attempt to challenge the imposition of Guidelines enhancements for his role in the offense and for obstruction of justice. In the course of this discussion, the District Court stated:

I understand that the Sentencing Guidelines are now advisory and that the Court must consider them and impose a reasonable sentence after considering all the factors listed at 18 U.S.C. § 3553(a). If the sentencing were to occur today in light of the new sentencing regime in effect since the Booker Supreme Court case, I would make the same findings as to the Guidelines and impose the same sentence. . . .

In sum, I see no reason to order a resentencing in this case since if we were do so [sic ], my sentence would be the same and would not be affected by the fact [that] the Sentencing Guidelines are now advisory and not mandatory.

Id. The District Court rejected Onaghinor's request for resentencing using similar language, concluding that "[w]hether the Guidelines were mandatory or advisory, it would make no difference in determining what the appropriate reasonable sentence should be. Therefore, I decline to resentence Roland Onaghinor and believe that the original sentence was proper and is a reasonable sentence under the Sentencing Guidelines and § 3553(a)." Id. at 428.

III. Arguments on Appeal and Subsequent Developments

Both defendants appealed the District Court's decision not to resentence pursuant to Crosby. Defendant Williams alleges on appeal that the District Court used the improper legal standard when determining whether to resentence, and that the sentence imposed by the District Court was unreasonable. Counsel for defendant Onaghinor moved to be relieved as counsel pursuant to Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967), submitting a brief in which he asserted that there were no non-frivolous grounds on which to appeal. The Government moved for summary affirmance of Onaghinor's sentence.

On July 10, 2006, Onaghinor completed his sentence of imprisonment and commenced service of his term of supervised release. In response to our inquiry at oral argument into Onaghinor's whereabouts, the Government informed us by supplemental letter dated January 16, 2007, that Onaghinor was deported to Nigeria on December 12, 2006.

DISCUSSION

I. Scope of Our Review of a Decision not to Resentence Pursuant to Crosby

Before adjudicating defendants' appeals, we clarify the scope of our review when a district court has declined to resentence a defendant upon a Crosby remand.

Pursuant to the Supreme Court's opinion in Booker/Fanfan, we review sentences for reasonableness. See Booker/Fanfan, 543 U.S. at 261-62, 125 S.Ct. 738; Crosby, 397 F.3d at 110, 114; see also United States v. Fernandez, 443 F.3d 19, 25-26 (2d Cir.2006) (declaring that sentences held to be unreasonable are "imposed in violation of law" (quoting 18 U.S.C. § 3742(a)(1))). The reasonableness review contemplated by Booker/Fanfan requires "consideration not only of the sentence itself, but also of the procedures employed in arriving at the sentence." Fernandez, 443 F.3d at 26 (citing Crosby, 397 F.3d at 114). Reasonableness review is "akin to review for abuse of discretion," under which we consider "whether the sentencing judge `exceeded the bounds of allowable discretion[,] . . . committed an error of law in the course of exercising discretion, or made a clearly erroneous finding of fact.'" Id. at 27 (quoting Crosby, 397 F.3d at 114) (alteration and omission in original).

We hold here that we review a sentence for reasonableness even after a District Court declines to resentence pursuant to Crosby. We do so because we are "obliged to apply Booker/Fanfan to this case . . . [which] is pending on direct review." Crosby, 397 F.3d at 116 n. 16. We implicitly adopted this approach in United States v. Park, 461 F.3d 245 (2d Cir.2006), in which we undertook a reasonableness review of a sentence imposed before the Supreme Court's decision in Booker/Fanfan that remained undisturbed after a Crosby remand. See id. at 246-47. We also alluded to our authority to review a sentence for reasonableness after a district court's decision not to resentence pursuant to Crosby in United States v. Garcia, 413 F.3d 201 (2d Cir.2005), in which we stated, in reviewing a pre-Booker sentence before ordering a Crosby remand, "[o]ur present task is not to review the defendants' sentences for reasonableness. Under the framework established by Crosby, that inquiry arises after the district court either has determined that the defendant does not need to be resentenced or has imposed a new sentence." Id. at 222.

Our approach also finds support from other Circuits that have followed Crosby. For example, in United States v. Paladino, 401 F.3d 471 (7th Cir.2005), the Seventh Circuit held that, where a district court declined to resentence; pursuant to a procedure modeled on Crosby, "we will affirm the original sentence against a plain-error challenge provided that the sentence is reasonable, the standard of appellate review prescribed by Booker, 125 S.Ct. at 765. The proviso is important; the mere reimposition of the original sentence does not insulate it from appellate review under the new standard." Id. at 484; see also United States v. Ameline, 409 F.3d 1073, 1074-75 (9th Cir.2005) (en banc) (providing that, if a district court declines to resentence upon a remand modeled on Crosby, "the original sentence will stand, subject to appellate review for reasonableness"). But see United States v. Combs, 470 F.3d 1294, 1297 (9th Cir.2006) (holding that scope of "reasonableness" review after a district court declines to resentence upon an Ameline remand is limited to consideration of "[w]hether the district judge properly understood the full scope of his discretion in a post-Sooner world").

We note, however, that by the time a district court's decision not to resentence pursuant to Crosby reaches us on appeal, at least two claims of error related to the sentencing will normally be foreclosed by prior proceedings. First, as we indicated in Crosby, any errors in the procedure for selecting the original sentence under the then-mandatory Guidelines regime "would be harmless, and not prejudicial under plain error analysis, if the judge decides on remand, in full compliance with now applicable requirements, that under the post-Booker/Fanfan regime the sentence would have been essentially the same as originally imposed." Crosby, 397 F.3d at 118. Thus, if a district court decides, pursuant to Crosby, that it would not "have imposed a materially different sentence . . . had [it] discharged [its] obligations under the post-Booker/Fanfan regime," id. at 117, a defendant will be unable to argue on appeal that the district court committed reversible error by failing to sentence under the advisory Guidelines regime created by Booker/Fanfan.

Second, the law of the case doctrine ordinarily will bar a defendant from renewing challenges to rulings made by the sentencing court that were adjudicated by this Court — or that could have been adjudicated by us had the defendant made them — during the initial appeal that led to the Crosby remand. See United States v. Quintieri, 306 F.3d 1217, 1229 (2d Cir. 2002) ("The law of the case ordinarily `forecloses relitigation of issues expressly or impliedly decided by the appellate court.' . . . [It] ordinarily prohibits a party, upon resentencing or an appeal from that resentencing, from raising issues that he or she waived by not litigating them at the time of the initial sentencing." (quoting United States v. Ben Zvi, 242 F.3d 89, 95 (2d Cir.2001))). For example, as in this very case, we have routinely resolved challenges to a district court's calculation of the Guidelines range applicable to a defendant before we remand pursuant to Crosby, see Peterson, 385 F.3d at 13913; see also, e.g., Garcia, 413 F.3d at 222-24 (ruling on challenges to Guideline calculations prior to Crosby remand); United States v. Maloney, 406 F.3d 149, 152-55 (2d Cir.2005) (same). But see United States v. Irving, 452 F.3d 110, 126 (2d Cir.2006) (declining to adjudicate challenges to Guidelines calculations prior to Crosby remand). In other words, when we have reached the Guidelines issues — or other sentencing issues — raised by defendants in their initial appeal, further challenges to our resolution of these issues after a district court has declined to resentence pursuant to Crosby will be foreclosed by the law of the case.

The law of the case doctrine will not, however, bar a defendant who is not resentenced after a Crosby remand from challenging the procedures used by the district court during the Crosby remand. This is so because the doctrine does not prevent a defendant from raising a sentencing issue "if it arises as a result of events that occur after the original sentence." Quintieri, 306 F.3d at 1230. A district court's decision not to resentence pursuant to Crosby occurs, by definition, after the original sentence and appeal; thus, the law of the case will not bar a defendant from challenging the manner in which the district court conducted the Crosby remand.

In addition, the law of the case usually will not prevent a defendant who appeals a district court's decision not to resentence pursuant to Crosby from obtaining reasonableness review of the length of his sentence. In remanding under Crosby, we generally decline to consider whether the sentence of a defendant is unreasonably long because of the possibility that a different sentence will be imposed after the Crosby remand. See Crosby, 397 F.3d at 120 ("Because a remand is warranted, we have no occasion on this appeal to consider whether Crosby's sentence is unreasonable solely because of its length. . . ."). Thus, a challenge to the reasonableness of the length of a sentence usually will only be ripe for review after the District Court has decided whether or not to resentence pursuant to Crosby. See Quintieri, 306 F.3d at 1229 (law of the case only bars relitigation of an issue that "was ripe for review at the time of an initial appeal" (quoting Ben Zvi 242 F.3d at 95)).

II. Analysis

Having clarified the standards guiding our review of a decision not to resentence made by a district court after a Crosby remand, we proceed to address defendants' appeals.

A. Williams's Appeal

Williams first argues that the District Court erred by failing to comply with the dictates of § 3553(a) in deciding not to resentence him. Specifically, Williams asserts that the District Court improperly stated that it was obligated to "impose a reasonable sentence after considering" the § 3553(a) factors, when in fact, the District Court's duty under § 3553(a) is to "impose a sentence sufficient, but not greater than necessary, to comply with the purposes set forth in" § 3553(a)(2). See note 3, ante (quoting 18 U.S.C. § 3553(a)). The "sufficient, but not greater than necessary" clause is known as the "parsimony clause" of § 3553(a). See United States v. Ministro-Tapia, 470 F.3d 137, 138 (2d Cir.2006) (discussing parsimony clause).

We have recognized that district courts are to impose sentences pursuant to the requirements of § 3553(a) — including the requirements of § 3553(a)'s parsimony clause — while appellate courts are to review the sentences actually imposed by district courts for reasonableness. See Ministro-Tapia, 470 F.3d at 141 (noting "our general agreement with this dichotomy"); see also United States v. Foreman, 436 F.3d 638, 644 n. 1 (6th Cir.2006) ("[A] district court's job is not to impose a `reasonable' sentence. Rather, a district court's mandate is to impose `a sentence sufficient, but not greater than necessary, to comply with the purposes' of section 3553(a)(2). Reasonableness is the appellate standard of review in judging whether a district court has accomplished its task.").

We nonetheless decline to order a second Crosby remand for two reasons. First, there is no indication that the District Court actually failed to consider the requirements of the parsimony clause when deciding whether to resentence Williams pursuant to Crosby. To the contrary, the District Court explicitly stated that it was considering all of the § 3553(a) factors in determining whether to resentence defendants, see Williams, 383 F.Supp.2d at 427 (stating, before declining to resentence, "I have also considered all the sentencing factors listed at 18 U.S.C. § 3553(a)"), and "we presume, in the absence of record evidence suggesting other-wise, that a sentencing judge has faithfully discharged [his] duty to consider the statutory factors" set out in 18 U.S.C. § 3553(a). Fernandez, 443 F.3d at 30. Here, on the Crosby remand Williams failed make any arguments to the District Court based on the parsimony clause; as we stated in Ministro-Tapia, "where . . . the defendant never argued the parsimony clause in the district court, we do not assume from the court's failure specifically to reference that clause that the court has ignored its mandate." 470 F.3d at 141.

Second, Williams has failed to demonstrate that the District Court's reference to the appellate standard of review when deciding whether to resentence him constituted reversible error. See Ministro-Tapia, 470 F.3d at 142 ("a `[district] court's reference to imposing a "reasonable" sentence under the § 3553(a) factors, as opposed to say an "appropriate," "sensible," or "fair" sentence under those factors, . . . does not invariably plant the seeds of reversible error'" (alteration in original) (quoting United States v. Cruz, 461 F.3d 752, 756 (6th Cir.2006))). There is no indication in the record that the District Court's reference to its duty to impose a sentence that was "reasonable" affected in any way its assessment of whether resentencing of Williams was warranted; the District Court did not, for example, indicate that while it might have imposed a different sentence under the advisory Guidelines regime created by Booker/Fanfan, it would not resentence because the initial sentence imposed was "reasonable." Instead, the District Court explicitly stated that even if it were to resentence Williams under the advisory Guidelines regime, the sentence it would impose "would be the same and would not be affected by the fact the Sentencing Guidelines are now advisory and not mandatory." Williams, 383 F.Supp.2d at 427. Accordingly, a second remand pursuant to Crosby — the remedy that Williams seeks for the District Court's alleged error — would not achieve any different result.

Williams also argues on appeal that the 216-month term of imprisonment imposed by the District Court was unreasonably long, primarily because his age (he is 56 years old) allegedly reduces the risk that he will be a repeat offender if he were released from prison. In addition, Williams contends that his sentence was overly long because of the impact that his sentence is having on his children, and because a shorter sentence would still permit him to pursue necessary educational or vocational training, medical care, and correctional treatment — including treatment for his drug addiction.

Although Williams's sentence was substantial, we conclude, upon consideration of the entire record, that his sentence was "well within the broad range of reasonable sentences that the District Court could have imposed in the circumstances presented." Fernandez, 443 F.3d at 34. Williams was convicted and sentenced for having a supervisory role in a substantial heroin trafficking conspiracy, and for thirteen separate counts of using the U.S. Mail to facilitate the conspiracy. At his sentencing hearing, the District Court found that Williams had obstructed justice in connection with the conspiracy, a conclusion that we affirmed on appeal. See Peterson, 385 F.3d at 139-43. Moreover, Williams had displayed a history of committing drug-related offenses, cutting against the argument that Williams posed a low risk of re-offending. Finally, the sentence imposed was well below the statutory maximum of life imprisonment that Williams faced for the heroin trafficking conspiracy, and also well below the sentence he could have faced had the District Court chosen to run the sentences on his multiple counts of conviction consecutively rather than concurrently. In sum, Williams's sentence was not unreasonably long.

B. Onaghinor's Appeal

Under the teaching of Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967), court-appointed appellate counsel may move to be relieved from his or her duties if "counsel is convinced, after conscientious investigation, that the appeal is frivolous." Id. at 741, 87 S.Ct. 1396 (quoting Ellis v. United States, 356 U.S. 674, 675, 78 S.Ct. 974, 2 L.Ed.2d 1060 (1958)). As we stated in United States v. Arrous, 320 F.3d 355, 358 (2d Cir.2003):

In support of the [Anders ] motion, defense counsel must supply a brief identifying by record references any issues that have at least arguable merit supported by legal authority, and explain why they are frivolous. See United States v. Burnett, 989 F.2d 100, 103 (2d Cir.1993). This Court will not grant a so-called Anders motion unless it is satisfied that (1) "counsel has diligently searched the record for any arguably meritorious issue in support of his client's appeal," and (2) "defense counsel's declaration that the appeal would be frivolous is, in fact, legally correct." Id. at 104.

While the brief accompanying Onaghinor's counsel's Anders motion fails to address whether there would be any non-frivolous basis for challenging the reasonableness of Onaghinor's sentence, we need not decide here whether the brief fails to comply with the requirements of Anders because Onaghinor's appeal was rendered moot by the completion of his term of incarceration.

"A case becomes moot when it no longer satisfies the `case-or-controversy' requirement of Article III, Section 2 of the Constitution. In order to satisfy the case or-controversy requirement, a party must, at all stages of the litigation, have an actual injury which is likely to be redressed by a favorable judicial decision." United States v. Mercurris, 192 F.3d 290, 293 (2d Cir.1999) (citing Spencer v. Kemna, 523 U.S. 1, 7, 118 S.Ct. 978, 140 L.Ed.2d 43 (1998)). Generally, "if an event occurs during the course of the proceedings or on appeal that makes it impossible for the court to grant any effectual relief whatever to a prevailing party, we must dismiss the case." United States v. Blackburn, 461 F.3d 259, 261 (2d Cir.2006) (internal quotation marks and citations omitted). While the Government has failed to argue that Onaghinor's appeal should be dismissed as moot, we have an independent obligation to ensure that developments in the case have not rendered the appeal moot. See In re Kurtzman, 194 F.3d 54, 58 (2d Cir.1999) ("We . . . have the obligation to consider whether this action is moot.").

In Blackburn, we noted that several other Circuits "have held that a challenge to a sentence by a criminal defendant who has completed his prison term but remains subject to supervised release is not moot because the possibility of the district court's reducing the term of supervised release on remand gives the defendant-appellant a continuing stake in the outcome." Blackburn, 461 F.3d at 262. We held that even if we were to adopt this rule, a defendant's sentencing appeal is nonetheless moot upon completion of the term of incarceration where "the possibility of the district court's imposing a reduced term of supervised release on remand is . . . remote and speculative." Id.

We conclude that Onaghinor's appeal was rendered moot upon his release from prison because there is no possibility that the district court could impose a reduced term of supervised release were we to remand for resentencing. Onaghinor was convicted of participation in a conspiracy to distribute heroin, a Schedule I substance, see 21 U.S.C. § 812, and the District Court was required to "impose a term of supervised release of at least 3 years," 21 U.S.C. § 841(b)(1)(C), on Onaghinor upon his conviction. See id. (establishing penalties for a person who is convicted of possessing with intent to distribute a "a controlled substance in schedule I or II"); 21 U.S.C. § 846 (making the penalties of 21 U.S.C. § 841(b)(1)(C) applicable to Onaghinor's conspiracy conviction). Onaghinor received the statutory minimum 3 years of supervised release. Were we to remand, the District Court could not impose a lesser term.

CONCLUSION

For the reasons stated above, we affirm defendant Williams's sentence, and we dismiss defendant Onaghinor's appeal.