
567 F.3d 40 (2009)
UNITED STATES of America, Appellee,
v.
Stephen Anthony Marc JOHNSON, Patrick Bowler, Defendants, *41 
Gregory Paul Timewell, Defendant-Appellant.
Docket No. 07-4587-cr.
United States Court of Appeals, Second Circuit.
Argued: November 18, 2008.
Decided: June 1, 2009.
*43 Burton T. Ryan Jr., Assistant United States Attorney (Benton J. Campbell, United States Attorney for the Eastern District of New York, Peter A. Norling, Assistant United States Attorney, on the brief), Brooklyn, New York, for Appellee.
Ivan S. Fisher (Lucas E. Andino, on the brief), New York, New York, for Defendant-Appellant.
Before: MINER, RAGGI, and LIVINGSTON, Circuit Judges.
MINER, Circuit Judge:
Defendant-appellant Gregory Timewell appeals from a Memorandum and Order entered on October 4, 2007, in the United States District Court for the Eastern District of New York (Platt, J.) denying his application to be resentenced following a remand for further proceedings in conformity with United States v. Crosby, 397 F.3d 103 (2d Cir.2005). United States v. Timewell, 124 Fed.Appx. 55 (2d Cir.2005). Timewell was convicted, upon a guilty plea, of conspiracy to import 1,000 kilograms or more of hashish and marijuana, in violation of 21 U.S.C. §§ 960(a)(1), (b)(1)(G), 963, and of making false statements to federal agents in violation of 18 U.S.C. § 1001. On March 5, 2004, he was sentenced principally to a prison term of 275 months and a 5-year term of supervised release. In the Memorandum and Order determining that it would adhere to the sentence originally imposed, the District Court took into account, inter alia, the government's customary practice of rescinding cooperation agreements breached by defendants. For the reasons that follow, we vacate the sentence *44 and once more remand for further proceedings.

BACKGROUND

I. Of the Events Leading to the Guilty Plea

Timewell, a native of New Zealand, was engaged as an international distributor and smuggler of drugs over a period of many years. He began his career as a local distributor of marijuana in Australia and New Zealand and expanded his interests to become a financier and organizer of worldwide smuggling operations. His successful efforts in distributing tons of hashish and marijuana in the United States and elsewhere enabled him to accumulate millions of dollars in personal assets.
The specific enterprise giving rise to the prosecution leading to this appeal was an undertaking by Timewell, along with co-defendants Patrick Bowler and Stephen Johnson, to smuggle 25 tons of hashish through New York for distribution in Upstate New York and Canada. Efforts to accomplish this goal occurred between 1993 and 1995, but the goal never was realized. The enterprise was infiltrated by undercover agents of the Drug Enforcement Administration ("DEA"). One undercover agent was recruited as a ship's captain to off-load the hashish from a "mother ship" in the Mid-Atlantic and to smuggle the drugs into Long Island, New York. The agent was to be paid $75,000 to cover his expenses for the trans-shipping, arrangements for payment having been made by Timewell through co-conspirator Johnson. Before the offloading could take place, the "mother ship," sailing from Pakistan under the direction of co-conspirator Bowler, sustained mechanical failure. The ship was rerouted, and its load of drugs ultimately was smuggled into Portugal and Ireland. Timewell and Johnson were arrested in Canada in 1995. Timewell subsequently waived extradition to the United States.
Timewell was indicted in the Eastern District of New York for operating a continuing criminal enterprise, conspiracy to import 1,000 kilograms or more of hashish and marijuana into the United States and conspiracy to distribute 1,000 kilograms or more of hashish and marijuana. The indictment included a demand for forfeiture of "[o]ne [h]undred [m]illion [d]ollars ($100,000,000) in United States currency and property constituting the proceeds of and derived from, directly and indirectly, the foregoing offenses." Timewell early on manifested a desire to cooperate with the government. Upon his arrival in the United States, he was extensively debriefed by agents of the DEA as well as officials of foreign governments. He provided information to them about his own criminal conduct and assets and shared with them his knowledge regarding the activities of the co-conspirators with whom he associated in the United States and throughout the world.
In a Cooperation Agreement dated February 5, 1998, Timewell agreed, inter alia, to plead guilty to conspiracy to import hashish into the United States and further agreed to provide truthful, complete, and accurate information to the Office of the United States Attorney for the Eastern District of New York. Timewell also agreed to testify at any proceedings, regardless of location, when requested to do so by the Office and to make full and complete financial disclosure. The Agreement identified numerous assets belonging to Timewell, consisting of bank accounts as well as real estate and currency in various countries throughout the world, all of which he agreed to forfeit to the government. For its part, the government agreed, inter alia, to "file a motion pursuant to Guidelines Manual § 5K1.1 and 18 *45 U.S.C. § 3553(e) with the sentencing [c]ourt setting forth the nature and extent of [Timewell's] cooperation," thereby enabling the court to impose a sentence below the Guidelines range and below any applicable mandatory sentence, and "not [to] oppose a downward adjustment of three levels for acceptance of responsibility under Guidelines Manual § 3E1.1." The Agreement provided that, as determined by the United States Attorney's Office, if Timewell "intentionally violated any provision of th[e] agreement, [he would] not be released from his plea of guilty but th[e] Office [would] be released from its obligation... (a) not to oppose a downward adjustment of three levels for acceptance of responsibility ..., and (b) to file the motion described" relating to the nature and extent of Timewell's cooperation. Timewell pleaded guilty to the conspiracy charge on February 5, 1998.
Timewell entered into a Supplemental Plea Agreement with the United States Attorney dated March 1, 2001, in which he agreed to waive indictment and plead guilty to a superseding information charging him with making a false statement to federal officers in violation of 18 U.S.C. § 1001. This charge was occasioned by the discovery that Timewell had misled agents regarding more than $4.8 million in Swiss francs that he had concealed in Switzerland. The discovery came about through continuing investigations relating to the arrests of Timewell's co-conspirators, including Bowler, who was arrested in Switzerland. Confronted with his failure to reveal these drug proceeds, Timewell arranged through his counsel to surrender to the government $2,089,000 in Swiss francs, that amount being the remainder of the proceeds. Timewell's story was that he originally believed that the funds in question had been removed by Bowler or those acting for Bowler. He later learned that Jim Wilson, a Canadian friend, had obtained the money and was sending monthly payments to Timewell's family. Timewell failed to notify the government of these developments and thereby violated the terms of his Cooperation Agreement. It is not contested by the government that Timewell otherwise provided extensive and substantial assistance to the government in identifying and describing the international narcotics operation of numerous individuals, including Bowler, Thomas Sherrett, and Michael Vondette, Timewell having testified as a witness at the trial of Vondette. See United States v. Vondette, 248 F.Supp.2d 149, 164 (E.D.N.Y.2001).

II. Of the Sentencing

The pre-sentence report recommended a total offense level of 41. Starting with the base level of 38, predicated upon 120,975 kilograms of marijuana, see U.S.S.G. § 2D1.1(a)(3), four levels were added for leadership role, see U.S.S.G. § 3B1.1(a), and two levels were added for obstruction of justice in the concealment of assets, see U.S.S.G. § 3C1.1. From the 44 levels thus arrived at was subtracted 3 levels for acceptance of responsibility, see U.S.S.G. § 3E1.1, with level 41 as the final result. Applying Criminal History Category I as recommended, the Guidelines Sentencing range was 324-405 months of incarceration. Prior to sentencing, the government submitted pursuant to U.S.S.G. § 5K1.1 a letter dated March 4, 2004, setting forth the basis for its recommendation that "the Court grant a significant downward departure in formulating Timewell's sentence." The letter, signed by an Assistant United States Attorney for the Eastern District of New York, described in detail Timewell's extensive cooperation with the authorities and noted that the information provided "was detailed, corroborated and consistently aided the agents in developing their *46 investigation." According to the letter, Timewell's substantial assistance "resulted in the arrest and conviction of major drug violators and the seizure of millions of dollars in drug proceeds."
Timewell was sentenced on March 5, 2004. During the sentencing proceeding, Timewell's counsel, urging a substantial Guidelines reduction, recounted at length Timewell's extensive cooperation, assistance to various law enforcement authorities, and testimony provided at the trial of Vondette. Before imposing sentence, the court noted that Timewell had not fully cooperated and therefore was in violation of the Cooperation Agreement. Counsel for Timewell pointed out that the pre-sentence calculation accounted for that by including a two-level upward adjustment for obstruction of justice. The court responded:
I saw that. But it doesn't affect the [G]uidelines as such, the [G]uideline computation.
As I said in 99 percent of the cases where this happens the government says you don't get any cooperation letter by breaching your opportunity to cooperate fully. And that's a fact I had to take into consideration in this case with respect to other features.
The court then observed that, according to the pre-sentence report,
information received from the government indicates that between January 1993 and May 1995 Timewell and others conspired to import and distribute 22,000 kilograms of hashish into the United States via Pakistan. This has been going on for many, many years.
....
The volume is staggering of what [Timewell] did. It's mind boggling, with the exception of Vondette. It is one of the biggest I have ever come across in my 30 years here.
The court further observed:
The money involved in addition to the drug quantities [is] mind boggling. It is to me, maybe not to other people: But it is an enormous amount of money involved.
Were it not for the government's letter I would have had no hesitancy in imposing 405 months, the upper end of the [G]uidelines and departing upward.
....
So I will depart down effectively from the 405 months, and that's to the minimum of 275 months.
The court also imposed a term of imprisonment of 60 months on the false statement count, to be served concurrently. A timely appeal followed.

III. Of the Initial Appeal

On his initial appeal, Timewell
assert[ed] that (1) his sentence [was] unconstitutional because it [was] premised on facts not proved beyond a reasonable doubt to the jury as required by the Sixth Amendment, see Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004); and (2) the district court erred in granting a § 5K1.1 departure from the guidelines because (a) it mistakenly thought defendant's guidelines were not affected by his § 1001 conviction, and (b) it was improperly influenced by the United States Attorney's Office's policy of not making specific sentencing recommendations in connection with its § 5K1.1 motions.
United States v. Timewell, 124 Fed.Appx. 55, 56 (2d Cir.2005). We rejected these arguments, holding that downward departure from the Sentencing Guidelines generally is not reviewable on appeal, id.; that even if the District Court erred in misapprehending *47 the effect of the § 1001 conviction on the Guidelines calculations (a fact of which we were not convinced), it was not mistaken that the false statements had obstructed justice and therefore properly considered that fact in determining the extent of departure, id. at 57; and that there was no abdication of judicial responsibility, since the District Court carefully considered the parties' submissions as well as the facts outlined in the pre-sentence report, id. As to Timewell's claim that the Guidelines-determined sentence was imposed in violation of his Sixth Amendment rights, we made the following determination: "In light of the Supreme Court's decision in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), and this court's decision in United States v. Crosby, 397 F.3d 103 (2d Cir. 2005), this case is remanded to the district court for further proceedings in conformity with Crosby." Id. at 57-58.

IV. Of the Proceedings on the Crosby Remand

Seeking on remand "a post-Booker sentence significantly lower than the 275-month term of imprisonment handed down on March 5, 2004," Timewell's attorney submitted to the court a letter dated July 11, 2005, arguing that Timewell's original sentence was "keyed to the mandatory Guidelines then in place" and urging a sentence taking into account "the factors... set out in 18 U.S.C. § 3553(a)." In the letter, Counsel recounted the extensive cooperation provided by his client to the authorities and again explained Timewell's failure to disclose his knowledge of the transfer of the $5 million Swiss bank account. Counsel took special note of the sentence imposed upon co-conspirator Sherrett, whose original sentence of 188 months (which took into account a three-level downward departure for assisting a prison guard attacked by inmates) was reduced to 120 months for cooperation, which included testimony at the trials of Vondette. Counsel's letter concluded as follows:
I urge Your Honor to reflect carefully about an error you may have made with regard to the Guidelines computation relating to the 18 U.S.C. § 1001 conduct, to consider the 10-year sentence you imposed on codefendant Thomas Sherrett, and to consider the government's functional equivalent of its highest recommendation of Timewell as the best of 146 cooperators in this case.
The government's submission on remand consisted of a letter dated July 7, 2005, signed by Assistant United States Attorney Burton T. Ryan Jr. The letter included a brief review of the history of the case and a description of the purpose of a Crosby remand as well as the procedure to be followed on such a remand. Noting that the government's 5K1.1 letter enabled the court to depart from the Guidelines and impose a sentence of 275 months, the letter concluded as follows:
[O]nly the Court can determine to what extent the then mandatory nature of the Guidelines [a]ffected the sentence the Court imposed. The question of whether the sentence would have ... been materially different if the guidelines were only advisory, we leave ... to the Court's discretion.
An additional submission came in the form of a letter dated July 1, 2005, from David S. Katz, President and CEO of Global Security Group, Inc. Katz was a former Special Agent of the Drug Enforcement Administration and was the Agent charged with debriefing Timewell. In his 8-page letter to the court, Katz detailed the extensive information he gleaned from Timewell's cooperation during the period 1996-1998. According to Katz, the overwhelming majority of information provided *48 by Timewell was previously unknown to the government and would never have been known without Timewell's cooperation. Katz characterized Timewell as "an extremely valuable source of information that furthered the investigation [he] had been conducting." Katz noted that the international drug trafficking information provided not only furthered his own investigation but "was also provided to the law enforcement authorities of Canada, Switzerland, Australia, Thailand, Belgium, Pakistan, Singapore, Spain, Portugal, the Netherlands, Ireland and the United Kingdom."
In a letter submission dated September 10, 2007, counsel for Timewell noted that Timewell's cooperation was much more extensive than that of Sherrett. Counsel also noted that Assistant United States Attorney Ryan had commented as follows in comparing the sentences of Timewell and Sherrett: "While their roles were similar, the amounts of the drugs Mr. [Sherrett] was held accountable for were much less." (alteration in original; emphasis omitted).
The proceedings on remand concluded with extensive arguments by counsel and colloquies with the court on September 20, 2007. Counsel for Timewell argued that co-conspirators more culpable than Timewell received more lenient sentences, with special references to co-conspirators Sherrett and Johnson. Although Johnson was sentenced after this Court ordered Timewell's Crosby remand, the government had consented to an adjournment of Timewell's Crosby hearing to permit consideration of Johnson's sentence, which was to a term of incarceration of fifteen years (180 months).
At the hearing, Assistant United States Attorney Charles Kelly advised the court that Timewell may have been put in a situation worse than Johnson because of his extensive disclosures. He noted that dealing with Johnson's proffers was like "pulling teeth" and that Johnson was in no way as forthcoming as Timewell. Johnson did not receive a letter recommending consideration for his cooperation. Kelly referred to the "good faith" of Timewell and made this statement: "And so we ask the [c]ourt to give serious consideration and weight to the argument that there should not be a significant disparity between Mr. Johnston [sic] and Mr. Timewell."
Despite the urging of the government, the District Court was concerned that Timewell failed to disclose the account in Switzerland and therefore, in accordance with past practices in the United States Attorney's Office, should not have had the benefit of the cooperation letter supplied by the government:
Well, mainly my understanding of ... this case, probably, and the principle that the U.S. Attorney's Office in this districtwhich is unique as far as any district is concerned in this country as far as I can determineif you didn't cooperate properly, and you violated your agreement with the government and didn't give full and accurate descriptions of everything, you lose all your benefits. Not just a partial, or not just some of it, but all benefits in the cooperation letter.
Now, when you hide 2 and-a-half million dollars in drug money in Switzerland, and it comes out through other sources than the defendantwhat happened to that rule?
Assistant United States Attorney Kelly, to whom the court's remarks were addressed, responded that his Office decided "to continue with the cooperation and penalize him by having him plead to the false statement charge." Mr. Kelly went on to emphasize the importance of Timewell's cooperation and the resultant benefit to the government, specifically pointing out the *49 disparity in sentences between Timewell and Johnson and the failure of Johnson, who did not receive a 5K1.1 letter, to make full disclosure. The court persisted in expressing its concern:
[I]n several prior cases, the moment a defendant has told the government a material falsehood, the [G]uidelines go like hard rock rules in those days. And there was no such thing as a reduction once he has taken that position. And I think there was a universal rule. I know it happened many times in this court.
Timewell's counsel then stated that in his experience "[t]here is no rule" that requires the government to "shred a cooperation agreement" for failure to disclose assets. The court responded: "There is no rule. But it has been invoked in this [c]ourt more times than you can imagine." In a later colloquy with Timewell's counsel in which counsel argued that the court had erroneously referred to the government's customary practice as a rule, the court responded: "[T]hey said to me it was a rule. And they have been representing that to me for years.... Not my rule. I certainly don't make up the rules."
The District Court also discussed with the government the sentencing range that would have applied to Timewell absent the submission of a 5K1.1 letter. Mr. Kelly indicated that Timewell "was at [an offense level of] 45 at one point," which carried a minimum sentence of life imprisonment. The District Court appeared to accept this summary of the applicable Guidelines calculation, suggesting that Timewell had benefitted substantially from his cooperation since he received a sentence of only 275 months. In fact, however, and as previously noted, Timewell's actual Guidelines sentencing range was 324 to 405 months, not life imprisonment as represented by the government.

V. Of the Decision on Remand

By Memorandum and Order entered on October 4, 2007, the District Court issued its decision on remand. Classifying the matter before it as a motion to reconsider its 275-month sentence, the court noted that counsel had advanced a claim of unwarranted disparities. According to the District Court, Timewell's counsel put forth the names of four defendants for comparison as similarly situated to Timewell: Michael Vondette, Mark Johnson, Patrick Bowler and Thomas Sherrett. The court reviewed the sentences imposed upon these co-defendants and the quantities of marijuana for which they were held responsible and found that Timewell was in a position different from the others:
The major factor in the difference between Timewell and three other defendantsJohnson, Bowler and Sherrett was and is the fact that Timewell violated his plea agreement with the government by failing to reveal five million dollars ($5,000,000) in drug proceeds that he had concealed in Europe. When confronted with this fact, he revealed only $2,890,000 [sic], i.e., leaving about $2,000,000 for which there has been no account.
In view of the foregoing facts, the court justified its disparate treatment of Timewell as follows:
In innumerable cases (notwithstanding counsel for Timewell's claim to the contrary) that have come before this [c]ourt, the Government has advised that when a defendant violates his plea agreement with the Government, the agreement is voided. This Court took that into account in substantially increasing Timewell's sentence from what it otherwise would have been.

(emphasis supplied). Accordingly, the court denied Timewell's motion and this *50 appeal followed. On appeal, Timewell argues that the District Court decision was procedurally as well as substantively unreasonable. He also requests that any remand of his case be to a different judge for sentencing.

ANALYSIS

A. Of the District Court's Mandate on Remand

Following the Supreme Court's determination in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), that the Sentencing Guidelines were to be considered advisory and not mandatory, this Court formulated the rule in Crosby for plain error review of pre-Booker sentences. See United States v. Garcia, 413 F.3d 201, 224-26 (2d Cir.2005) (discussing rationale and procedure for Crosby remand). Concluding that such a review requires a resolution of the issue of whether the sentence originally imposed is materially different from the sentence that would have been imposed under the Booker regime, we formulated the protocol now known as the Crosby remand to enable the District Court to decide the issue in the first instance. On such remand, District Judges are to re-examine sentences in light of the following:
[A]ny of the errors in the procedure for selecting the original sentence ... 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. Conversely, a district judge's decision that the original sentence would have differed in a nontrivial manner from that imposed will demonstrate that the error in imposing the original sentence was harmful and satisfies plain error analysis.
Crosby, 397 F.3d at 118.
Accordingly, the question to be resolved by the District Court is "whether the challenged sentence is materially different from the one that the district court would have imposed with a correct understanding of federal sentencing law as now explained by the Supreme Court." Garcia, 413 F.3d at 224. If the District Court decides not to resentence, it should explain that decision on the record; if it decides that the sentence should be vacated, it must resentence in accordance with Booker, with an explanation. Crosby, 397 F.3d at 120. The explanation referred to in Crosby is required by 18 U.S.C. § 3553(c), which provides in part that "[t]he court, at the time of sentencing, shall state in open court the reasons for its imposition of the particular sentence."
To sentence in compliance with Booker, the court is constrained to consider the sentencing factors set out in 18 U.S.C. § 3553(a):
(1) the nature and circumstances of the offense and the history and characteristics of the defendant;
(2) the need for the sentence imposed
(A) to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense;
(B) to afford adequate deterrence to criminal conduct;
(C) to protect the public from further crimes of the defendant; and
(D) to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner;
(3) the kinds of sentences available;

*51 (4) the kinds of sentence and the sentencing range established for
(A) the applicable category of offense committed by the applicable category of defendant as set forth in the guidelines... issued by the Sentencing Commission pursuant to [28 U.S.C. § 994(a)(1)] ...
....
(5) any pertinent policy statement(A) issued by the Sentencing Commission pursuant to [28 U.S.C. § 994(a)(2)] ...;
(6) the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct; and
(7) the need to provide restitution to any victims of the offense.
However, all sentencing proceedings must commence with the District Court's calculation of the applicable Guidelines range, with the Guidelines as "the starting point and the initial benchmark." Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 596, 169 L.Ed.2d 445 (2007). The court must then consider all the § 3553(a) factors and then undertake "an individualized assessment based on the facts presented." Id. at 597. If a non-Guidelines sentence is indicated, the court "must consider the extent of the deviation [from the Guidelines] and ensure that the justification is sufficiently compelling to support the degree of the variance." Id. Finally, "[a]fter settling on the appropriate sentence, [the District Court] must adequately explain the chosen sentence to allow for meaningful appellate review and to promote the perception of fair sentencing." Id. (citation omitted).

B. Of the Standards of Review

Following Booker, we are constrained to review sentences for reasonableness. See Booker, 543 U.S. at 260-61, 125 S.Ct. 738; see also United States v. Fernandez, 443 F.3d 19, 26-27 (2006). Reasonableness review requires an examination of the length of the sentence (substantive reasonableness) as well as the procedure employed in arriving at the sentence (procedural reasonableness). See United States v. Canova, 485 F.3d 674, 679 (2d Cir.2007). In our review of district court sentences, we are required to apply a "deferential abuse-of-discretion standard." Gall, 128 S.Ct. at 591. We recently stated that "[a]s to substance, we will not substitute our own judgment for the district court's on the question of what is sufficient to meet the § 3553(a) considerations in any particular case" and that the substantive determination of a District Court will be set aside only in those special cases where the range of permissible decisions does not encompass the District Court's determination. See United States v. Cavera, 550 F.3d 180, 189 (2d Cir.2008) (en banc). Accordingly, "when conducting substantive review, we take into account the totality of the circumstances, giving due deference to the sentencing judge's exercise of discretion, and bearing in mind the institutional advantages of district courts." Id. at 190.
However, the deference due the district court in sentencing requires that we first be satisfied that the procedural requirements for sentencing have been satisfied. Id. at 189. Procedural error occurs when the district court (1) fails to calculate the Guidelines range; (2) is mistaken in the Guidelines calculation; (3) treats the Guidelines as mandatory; (4) does not give proper consideration to the § 3553(a) factors; (5) makes clearly erroneous factual findings; (6) does not adequately explain the sentence imposed; or (7) deviates from the Guidelines range without explanation. Id. at 190. We have noted that a sentence is procedurally unreasonable if a district court "committed an error of law in the course of exercising *52 discretion," Crosby, 397 F.3d at 114 (emphasis supplied), erred "in determining the applicable Guideline range or the availability of departure authority," United States v. Selioutsky, 409 F.3d 114, 118 (2d Cir. 2005) (emphasis supplied), or misapprehended its ability to impose a non-Guidelines sentence, see United States v. Sanchez, 517 F.3d 651, 661-62 (2d Cir.2008). Our identification of significant procedural error may be a cause for remanding to the district court for explanation or correction. Cavera, 550 F.3d at 190.
We undertake a reasonableness review "even after a District Court declines to resentence pursuant to Crosby." United States v. Williams, 475 F.3d 468, 474 (2d Cir.2007). Such a review is precluded, however, where (1) the court determines that the discharge of its obligations under post-Booker procedures, treating the Guidelines as advisory only, would not result in a sentence materially different from the sentence imposed under the mandatory Guidelines procedure; or (2) the law of the case doctrine applies to bar challenges to sentencing rulings that were, or could have been, adjudicated in the initial appeal. Id. at 475. "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," and one not resentenced may therefore "challeng[e] the manner in which the district court conducted the Crosby remand." Id. at 476.

C. Of the District Court's Procedural Errors

On a Crosby remand, the district court must determine whether its sentence under the Booker regime would have been materially different from the sentence originally imposed; if the answer is "no," nothing further is required; if the answer is "yes," there must be a resentencing. See United States v. Ferrell, 485 F.3d 687, 688-89 (2d Cir.2007). The District Court here did not respond directly to the required inquiry. Indeed, the court and counsel immediately began to discuss whether a more lenient sentence should be imposed in light of the sentencing disparities identified by counsel. This was procedural error because "[o]nly if the district court answers the threshold [Crosby] determination in the affirmative does a resentencing occur." Id.
We are unable to conclude that the District Court's Crosby error was harmless. See United States v. Williams, 524 F.3d 209, 214 (2d Cir.2008) (recognizing that procedural error at sentencing can be reviewed for harmlessness). First, the District Court adhered to its original sentence after it "took ... into account" what the court perceived to be the government's customary practice of voiding plea agreements where a defendant violates the terms of the agreement. That such a customary practice exists is unsupported by the record before the District Court. See Cavera, 550 F.3d at 190 (noting that a district court commits procedural error when it "rests its sentence on a clearly erroneous finding of fact").
Second, although a district court alone may determine what effect to give to a 5K1.1 letter, in so doing may consider the extent of downward departures or variances received by other similarly situated defendants who have cooperated, and may even decline a reduction from the Guidelines altogether, the court here erred in the course of exercising its discretion by (1) "substantially increasing Timewell's sentence from what it otherwise would have been" and (2) giving as a reason for the increase the government's failure to comply with the purported customary prosecutorial practice of voiding cooperation *53 agreements upon breach by the defendant. The 5K1.1 letter, which the government saw fit not to revoke in Timewell's case despite his breach of the cooperation agreement, allows a downward departure from the Sentencing Guidelines in cases where a defendant provides substantial assistance to the government. Whether such a letter is merited is confided to the sole determination of the government, subject only to constitutional limitations. See Wade v. United States, 504 U.S. 181, 185-86, 112 S.Ct. 1840, 118 L.Ed.2d 524 (1992). That the government usually voids cooperation agreements upon a breach by the defendant should not be reason to constrain a district court from giving proper effect to a 5K1.1 letter if the government decides to submit a 5K1.1 letter notwithstanding the defendant's breach of the cooperation agreement.
In addition, the government indicated, and the District Court appeared to accept, that, absent a downward departure for substantial cooperation, the Guidelines would have recommended that Timewell serve a life sentence. As previously discussed, however, the pre-sentence report, to which the District Court adhered when calculating the Guidelines recommendation at Timewell's initial sentencing, established a total offense level of 41 carrying a sentencing range of only 324 to 405 months. The description of the sentencing range to which Timewell would have been subject absent his substantial cooperation therefore substantially overstated Timewell's actual Guidelines range. See Cavera, 550 F.3d at 190 (indicating that a District Court errs when it "makes a mistake in its Guidelines calculation").
Because we cannot determine the extent to which these errors affected the District Court's analysis, we are unable to discern how the District Court would have answered the threshold Crosby question in the absence of these errors. See Crosby, 397 F.3d at 115 (noting that procedural error is "cause for concern because, in many cases, it will be impossible to tell whether the judge would have imposed the same sentence had the judge not felt compelled to impose a Guidelines sentence").
The District Court also erred in its written opinion by mischaracterizing the unwarranted disparities argument made by defense counsel. The District Court wrote that counsel for Timewell argued that Timewell received a disparate sentence as compared to Michael Vondette, Stephen Johnson, Patrick Bowler, and Thomas Sherrett. However, Timewell's application listed only Sherrett and Johnson as comparators. Indeed, a determination of whether to be resentenced on a Crosby remand must be based only on the circumstances existing at the time of the original sentence. See Ferrell, 485 F.3d at 688; Crosby, 397 F.3d at 118, n. 19. Under this rule, the court could not, in the course of its threshold Crosby analysis, consider the sentence of Bowler or Johnson, both of which were imposed after Timewell's original sentence was pronounced. Notably, the District Court also erred in stating that Johnson "testified against Vondette in this Court."
Accordingly, we find that the District Court erred in neglecting to answer the question posed by the Crosby remand of Timewell's original sentence, namely, whether, based on the circumstances at the time of the original sentence, the District Court would have imposed a materially different sentence under the post-Booker sentencing regime, and that this error was not harmless. See Crosby, 397 F.3d at 118. The law of the case does not bar Timewell from challenging the manner in which the Crosby remand was conducted despite the Court's adherence to the original sentence. We are therefore constrained *54 to remand the case once more to enable the District Court to formulate a proper response to the Crosby inquiry. The District Court should state the reasons for the response without consideration of past practices of the government in regard to the rescission of cooperation agreements. Such consideration was error. Should the court determine to revisit its original sentence, we ask it to consider: (1) that a district court maybut is not required toconsider sentencing disparity among co-defendants under 18 U.S.C § 3553(a)(6); United States v. Frias, 521 F.3d 229, 236 n. 8 (2d Cir.2008); (2) that the United States Attorney's Office recommended a "substantial" departure from the Guidelines sentence in view of Timewell's excellent cooperation and asserted that a significant disparity in the sentences imposed upon Timewell, Johnson and Sherrett was not warranted; (3) that the appropriateness of any reduction of sentence below the Guidelines should be governed by the provisions set out in U.S.S.G. § 5K1.1:
(a) The appropriate reduction shall be determined by the court for reasons stated that may include, but are not limited to, consideration of the following:
(1) the court's evaluation of the significance and usefulness of the defendant's assistance, taking into consideration the government's evaluation of the assistance rendered;
(2) the truthfulness, completeness, and reliability of any information or testimony provided by the defendant;
(3) the nature and extent of the defendant's assistance;
(4) any injury suffered, or any danger or risk of injury to the defendant or his family resulting from his assistance;
(5) the timeliness of the defendant's assistance.
In the absence of a showing of any unfairness or the appearance of any unfairness on the part of the District Judge, we reject Timewell's claim that the case should be reassigned to another judge on remand. See United States v. Bradley, 812 F.2d 774, 782 n. 9 (2d Cir.1987).

CONCLUSION
This case is remanded to the District Court for further proceedings consistent with the foregoing.
