
557 F.3d 93 (2009)
UNITED STATES of America, Appellee,
v.
Sean CARR, Defendant-Appellant.
Docket No. 06-5490-cr.
United States Court of Appeals, Second Circuit.
Argued: October 22, 2008.
Final Briefs Submitted October 29, 2008.
Decided: February 19, 2009.
*96 Jessica Roth, Assistant United States Attorney, New York, NY, (Michael J. Garcia, United States Attorney for the Southern District of New York, Helen V. Cantwell, Celeste L. Koeleveld, Assistant United States Attorneys, New York, NY, on the brief), for Appellee.
Tina Schneider, Portland, ME, for Defendant-Appellant.
Before: KEARSE, SACK, and KATZMANN, Circuit Judges.
KEARSE, Circuit Judge:
This case returns to us on the appeal of defendant Sean Carr from an amended judgment of the United States District Court for the Southern District of New York, Thomas P. Griesa, Judge, resentencing him after a decision of this Court, United States v. Carr, 424 F.3d 213 (2d Cir.2005) ("Carr I"), cert, denied, 546 U.S. 1221, 126 S.Ct. 1447, 164 L.Ed.2d 145 (2006), which upheld Carr's convictions and the district court's various calculations under the 2002 version of the Sentencing Guidelines ("Guidelines") and remanded to the district court pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir. 2005) ("Crosby"), cert, denied, 549 U.S. 915, 127 S.Ct. 260, 166 L.Ed.2d 202 (2006), for consideration of resentencing in light of the ruling in United States v. Booker, 543 U.S. 220, 245, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), that application of the Guidelines is not mandatory. Carr was convicted, following a jury trial, on one count of *97 participating in a racketeering enterprise, in violation of 18 U.S.C. § 1962(c) (Count 1); one count of racketeering conspiracy, in violation of id. § 1962(d) (Count 2); one count of conspiracy to distribute cocaine base (or "crack"), in violation of 21 U.S.C. § 846 (Count 3); one count of possession with intent to distribute cocaine base, in violation of id. §§ 812, 841(a)(1), and 841(b)(1)(C) (Count 5); and one count of using and carrying a firearm during and in relation to a drug trafficking crime, in violation of 18 U.S.C. § 924(c) (Count 4). Carr was originally sentenced principally to life imprisonment. On the Crosby remand, the court resentenced Carr principally to 40 years' imprisonment, comprising two 35-year terms for Counts 1 and 2 (the racketeering (or "RICO") counts) to be served concurrently; two 20-year terms for Counts 3 and 5 (the narcotics counts), to be served concurrently with each other and with the terms imposed for the racketeering counts; and a five-year term for Count 4, the firearm count, to be served consecutively to the 35-year terms imposed for the racketeering counts; his 40-year total prison term was to be followed by a five-year period of supervised release.
On this appeal, Carr asks this Court principally (1) to revisit the Carr I decisions that affirmed his conviction and upheld the district court's Guidelines calculations, arguing that the law-of-the-case doctrine should not be applied where the district court imposes a new sentence following a Crosby remand, and (2) to vacate his sentence on the ground that a 40-year term of imprisonment is unreasonable. In addition, Carr urges us to remand for further resentencing in light of Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), and Kimbrough v. United States, ___ U.S. ___, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007). For the reasons that follow, we reject all of Carr's arguments in support of this appeal and affirm his new sentence; we remand, however, for correction of the amended judgment to reflect accurately the sentence imposed.

I. BACKGROUND
The present prosecution centered on the operation of a street gang called Sex Money and Murder ("SMM") that sold narcotics in the Soundview section of the Bronx, New York. The trial evidence leading to Carr's convictions on the five counts listed above included videotapes, an audiotape, and testimony from former SMM members who were cooperating with the government. The evidence was summarized in Carr I, 424 F.3d at 217-18, familiarity with which is assumed.

A. The Trial and Carr's First Appeal

Briefly, the evidence at trial showed that Carr was a member of the SMM narcotics distribution enterprise. Carr himself, though denying that he was a member of SMM, testified that he had been a drug dealer nearly all of his adult life and had sold crack all over the Soundview area. As to his membership in SMM, the government introduced an audiotape of an SMM meeting at which Carr was present, and former SMM members "testified as to Carr's participation in crack sales and robberies, acts of intimidation, and other acts of violence," Carr I, 424 F.3d at 217.
With respect to the RICO counts, three predicate acts of racketeering activity were alleged: (1) the 1994 murder of one Tony Morton, (2) a 1996 armed robbery to which Carr had pleaded guilty in state court, and (3) narcotics conspiracy. The evidence as to the murder was that Morton, who was unarmed, had been dragged from his automobile by armed SMM members other than Carr; that while Morton *98 was being physically restrained, Carr went up to Morton and, from inches away, shot him in the neck; and that while Morton then lay on the ground, Carr shot him in the head. (See Trial Transcript 150, 159, 282-83, 286, 374-75.) Morton's wounds were fatal.
The jury found that Carr had committed all three of the alleged acts of racketeering activity, and it found him guilty on all of the counts against him.
The Guidelines applicable to racketeering offenses provided that the base offense level should be the greater of 19 or "the offense level applicable to the underlying racketeering activity," Guidelines § 2E1.1, and that "[i]f the underlying conduct violates state law, the offense level corresponding to the most analogous federal offense is to be used," id. Application Note 2. The district court concluded that Carr's base offense level was 43 as prescribed by Guidelines § 2A1.1 ("First Degree Murder") because the murder of Morton, a racketeering act that the jury found proven, was conduct that the court concluded was most analogous to the federal offense of first-degree murder, see 18 U.S.C. § 1111(a) ("Murder is the unlawful killing of a human being with malice aforethought. Every murder perpetrated by. . . any . . . kind of willful, deliberate, malicious, and premeditated killing ... is murder in the first degree."). For an offense level of 43, the Guidelines recommended life imprisonment. The district courtstating that "[i]f the murder were not in the picture the sentence would be somewhere between 20 and 30 years" concluded,
based on the jury's verdict and their specific findings, it is my duty to impose a sentence of life imprisonment on Count One and on Count Two.
(Transcript of Original Sentencing, January 14, 2004 ("Original S.Tr."), at 16, 17.) Accordingly, Carr was sentenced principally to life imprisonment for the racketeering counts, with shorter sentences imposed for the narcotics counts to be served concurrently with the sentences on the racketeering counts, and a five-year term for Count 4, the firearm count, to be served consecutively to the life imprisonment terms imposed for the racketeering counts, see 18 U.S.C. § 924(c)(1)(D)(ii) ("Notwithstanding any other provision of law ... no term of imprisonment imposed on a person under this subsection shall run concurrently with any other term of imprisonment imposed on the person....").
Carr appealed, challenging both his conviction and his sentence. As to his conviction, Carr contended principally that certain of the trial court's instructions to the jury were erroneous and that the government, in summation, had improperly vouched for the credibility of its witnesses. As to his sentence, Carr contended, inter alia, that because the indictment alleged that the killing of Morton constituted the state-law crime of second-degree murder, the district court should not have calculated Carr's offense level using Guidelines § 2A1.1, which applies to the federal crime of first-degree murder and prescribed an offense level of 43, but should instead have used Guidelines § 2A1.2, which governs the federal crime of second-degree murder and prescribed an offense level of 33. He also challenged the district court's Guidelines enhancements based on drug quantity, brandishing of a firearm, and criminal history.
While Carr's appeal was pending, the Supreme Court decided Booker, holding that the Guidelines are advisory rather than mandatory. Accordingly, we concluded that a remand pursuant to our post-Booker decision in Crosby was required in order to permit the district court to determine whether it would have imposed a *99 nontrivially different sentence on Carr if it had known that the Guidelines are merely advisory. Prior to remanding, however, we considered and rejected Carr's challenges to his conviction, see Carr I, 424 F.3d at 218-30, and his challenges to the district court's Guidelines calculations, see id. at 230-31. In rejecting Carr's "conten[tion] that the district court erred in applying the base offense level for the federal offense of first degree murder," id., we stated that
as we made clear in considering a virtually identical challenge in United States v. Minicone, 960 F.2d 1099 (2d Cir.), cert. denied, 503 U.S. 950, 112 S.Ct. 1511, 117 L.Ed.2d 648 (1992), "the district court did not err in concluding that the most analogous federal offense [to the New York offense of second degree murder] was first degree murder under [18 U.S.C] § 1111," id. at 1110. "[T]he absence of reference to premeditation or malice aforethought [in the state law] does not mean that federal first degree murder is not the most analogous federal offense." United States v. Diaz, 176 F.3d 52, 123 (2d Cir.), cert. denied sub nom. Rivera v. United States, 528 U.S. 875, 120 S.Ct. 181, 145 L.Ed.2d 153 (1999). We therefore conclude that Carr's argument in this regard is without merit.
Carr I, 424 F.3d at 231; see also United States v. Diaz, 176 F.3d 52, 123 (2d Cir.) ("Diaz") (noting that there was "no error, much less clear error, in the district court's conclusion that federal first degree murder was the most analogous federal offense" even though there was no reference to "premeditation or malice aforethought" in the state statute), cert, denied, 528 U.S. 875, 120 S.Ct. 181 (1999).

B. The Proceedings on Remand

On remand, both sides made written submissions to the district court. The government pressed for adherence to the sentence of life imprisonment; Carr urged that his prison term be only 30 years. The court held two hearings in order to determine whether to resentence Carr and, if so, to determine what prison term would be appropriate. At the hearings, most of the discussion as to Carr's offenses centered on the circumstances of the Morton murder, which would most impact his sentence on the RICO counts. At the first hearing, the court noted that under New York law, "this would be a second degree murder" and that such a murder is by definition intentional, though not premeditated (Hearing Transcript, August 25, 2006 ("August 2006 Hearing Transcript" or "Aug. Tr."), at 20.). The court agreed with the government that the Guidelines offense level for the federal offense of first-degree murder was applicable (see id. at 20-21); the court stated that it was "not really terribly concerned about what [degree] the state law would regard [Morton's murder] as"; rather, it was concerned with "the degree of [Carr's] culpability" (id. at 21). The court announced that it would resentence Carr and that the only remaining issue was what the new sentence should be, an issue that the parties should address in additional submissions. (See id. at 26-27.) The court pointed out that
[t]he degree of culpability is important. Under the guidelines, we almost forgot that, but under the statute that is applicable and under any common sense view of things, the degree of culpability is important, and this is not something that is listed in some numerical list in the guidelines. And both sides should give serious thought to this. It is important.
I do not understand, even a mitigating factor in this shooting, even if Mr. Morton drove by and was suspected in being in some hostile group, by the time of the *100 shooting, I believe, and you can consider the evidence in the record and maybe what I'm saying is not completely accurate,. . . but I believe, subject to correction, that Mr. Morton was no longer a menace to anyone, even if he possibl[y] was before he had been pulled out of the car.
So the question before me is whether the shooting of Mr. Morton was simply an act of sheer cruelty, even if it was impulsive and on the spot, someone who has a gun in the situation of Mr. Carr here, had the opportunity to decide whether to shoot or not to shoot, and he decided to shoot under circumstances that are quite impossible for me to understand in any rational way, except that this was perhaps what I said.
(Id. at 27.)
At the sentencing hearing some three months thereafter, the court again focused principally on the prison term to be imposed for Carr's RICO offenses. It stated, inter alia, as follows:
[T]he sentence has been considered in view of the current state of the law. The guidelines are now advisory and the court can apply the guidelines or take a different course if there's a reasonable ground[ ] to do so. The court is also obliged to give specific attention to the factors listed in 18 United States Code Section 3553(a). There has been some debate about exactly what guideline applies to the RICO counts in which the charge of murder is contained but that debate has been settled and the . . . level is a level 43 and the guidelines range is simply life.
There are other counts involving narcotics and the weapons but the crucial thing here for this sentence is what the sentence will be on the two RICO counts, that's Counts 1 and 2, and the sentence that was imposed before was a life sentence on each of those counts.
The defense has recommended that there be a substantial sentence but a definite term instead of life, a definite term of years, and the recommendation was 30 years. The suggestion was to use level 42 of the guidelines. And the range there would be 360 months to life or 30 years to life. And if that were done, the court could follow that guideline range and impose a sentence of 30 years.
(Sentencing Transcript, November 15, 2006 ("S.Tr."), at 17-18.)
The court then reviewed the trial evidence as to the killing of Morton. It stated that after other SMM members had pulled Morton from his car and an SMM member was talking to him at the trunk of the car, Carr
walks ... to the back of the car. He shoots Tony Morton once in the head. Tony Morton falls down. And [Carr] shoots Tony Morton again in the neck while Tony Morton is down.
There's conversation within the gang afterwards, and the other gang members were convinced that this was an unnecessary shooting, had nothing to do with any need to protect or defend the Sex, Money and Murder people. Exactly how it appeared to Sean Carr, I really don't know. I will give him a little of a benefit of the doubt that he may have thought there was still some menace. But the others in the gang really didn't think so. And he showed no remorse at the time at all.
(Id. at 19-20.)
The court determined that, in light of the sentencing factors set out in 18 U.S.C. § 3553(a), the appropriate total prison term for Carr's offenses was 40 years:

*101 Mr. Carr was 24 years old at the time of this murder. He is about 34 now. He's been in prison about five years. I believe that there can be a sentence which justly and fairly takes into account the gravity of the killing that Mr. Carr perpetrated. I think there could be a sentence which protects society sufficiently, and I'm now referring to the factors in Section 3553, although I might not go down them doggedly, each one, but I certainly have them in mind, and the principal one is the seriousness of the offense and to have an appropriate punishment of that offense and also protect society from any occurrence of criminal behavior by Mr. Carr. Those are the two main factorsalso to be a deterrent to other criminal activity because that gang apparently still goes its way up there. And a serious punishment is necessary for the protection of the community and the deterrent effect onthat we hope that criminal sentences have....
I'm sure that Mr. Carr and his family came in hoping that I could accept the recommendation of his lawyer and make the sentence 30 years. . . . I do not think that that is sufficient. . . . [T]he problem is that this was a crime[] that . . . involve[d] killing an innocent person. It involved firing a shot into his head and firing another shot into his neck when he was down. That is very serious. What I have decided to doand I know this is not the degree of change that he hoped for, but I am imposing a sentence of 40 years in prison. I feel that I cannot do less and be fair to the community andthere is a community out there that we have to consider. So I'm imposing a sentence of 40 years in prison
(S.Tr. 21-22.) The 40-year prison term was ultimately constructed as follows:
Counts 1 and 2, 35 years. Those are to be served concurrently.
Count 3, 20 years.
Count 5, 20 years.
All those sentences are to be served concurrently.
Count 4 is 5 years to run consecutively to all the other counts.
And that means a total of 40.
(Id. at 23.)
This appeal followed.

II. DISCUSSION
On this appeal, Carr principally challenges his sentence, (1) arguing chiefly, now as he did in Carr I, that the district court erred in calculating his Guidelines offense level by reference to the guideline for the federal offense of first-degree murder, and (2) contending that the 40-year prison term imposed on him is unreasonable. The government contends that Carr's challenges to the calculation of the Guidelines-recommended range of imprisonment, having been rejected by this Court in Carr I, are barred by the law of the case; and it contends that the sentence imposed is reasonable.
Carr also suggests that his conviction should be overturned because of certain of the court's instructions to the jury and statements by the government in summation, contentions that were also rejected in Carr I. Carr appears to acknowledge that his renewal of the challenges to his conviction is barred by the law-of-the-case doctrine but states that he renews them here in order to "preserv[e] these issues for presentation in a Petition for Writ of Certiorari" (Carr brief on appeal at 13). We agree that these challenges are foreclosed by the law-of-the-case doctrine and we do not address them. We reject Carr's challenges to his sentence for the reasons that follow.


*102 A. Application of the Law-of-the-Case Doctrine to Carr's Sentencing Challenges

The law-of-the-case doctrine has two facets. First, when a court has ruled on an issue, "that decision should generally be adhered to by that court in subsequent stages in the same case." United States v. Quintieri, 306 F.3d 1217, 1225 (2d Cir. 2002) ("Quintieri") (internal quotation marks omitted), cert, denied, 539 U.S. 902, 123 S.Ct. 2246, 156 L.Ed.2d 110 (2003); see, e.g., United States v. Williams, 475 F.3d 468, 475 (2d Cir.2007) ("Williams"), cert, denied, ___ U.S. ___, 128 S.Ct. 881, 169 L.Ed.2d 739 (2008); United States v. Minicone, 26 F.3d 297, 300 (2d Cir.) ("Minicone"), cert, denied, 513 U.S. 940, 115 S.Ct. 344, 130 L.Ed.2d 300 (1994); United States v. Fernandez, 506 F.2d 1200, 1203 (2d Cir.1974). Second, when the court of appeals has ruled on an issue and has remanded the case to the district court, the district court on remand is required to follow that ruling. See, e.g., Quintieri, 306 F.3d at 1225; Minicone, 26 F.3d at 300. Both facets of the law-of-the-case doctrine are driven by considerations of fairness to the parties, judicial economy, and the societal interest in finality. See generally County of Suffolk v. Stone & Webster Engineering Corp., 106 F.3d 1112, 1117 (2d Cir.1997); United States v. Stanley, 54 F.3d 103, 107 (2d Cir.), cert, denied, 516 U.S. 891, 116 S.Ct. 238, 133 L.Ed.2d 166 (1995).
A court's reconsideration of its own earlier decision in a case may, however, be justified in compelling circumstances, consisting principally of (1) an intervening change in controlling law, (2) new evidence, or (3) the need to correct a clear error of law or to prevent manifest injustice. See, e.g., Quintieri, 306 F.3d at 1230; Minicone, 26 F.3d at 300; United States v. Fernandez, 506 F.2d at 1203-04 & n. 7. For example, a defendant who has obtained a remand on his first appeal will not be barred from raising sentencing issues if they "arise[] as a result of events that occur[red] after the original sentence," Quintieri, 306 F.3d at 1230.
Applying these principles in the context of an appeal following a Crosby remand on which the district court has concluded that it will not resentence the defendant, we have held that the parties are free to challenge the procedures used by the district court on remand in reaching its conclusion and are free to challenge the reasonableness of the sentence originally imposed. See, e.g., Williams, 475 F.3d at 476. But "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" are ordinarily barred. Id. at 475; see, e.g., United States v. Negron, 524 F.3d 358, 360 (2d Cir.), cert. denied, ___ U.S. ___, 129 S.Ct. 252, 172 L.Ed.2d 190 (2008).
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.
Williams, 475 F.3d at 476.
In addition, we have applied the law-of-the-case doctrine to foreclose renewal of challenges to jury instructions and Guidelines calculations that had been adjudicated on the defendant's first appeal where, on the Crosby remand, the district court conducted sentencing proceedings anew but reimposed the same sentence. See United States v. Frias, 521 F.3d 229, 231, 235 (2d Cir.), cert, denied, ___ U.S. ___, *103 129 S.Ct. 289, 172 L.Ed.2d 212 (2008). However, we have not heretofore determined "what effect the law of the case doctrine might have on a defendant who is resentenced pursuant to Crosby" and given a different sentence. Williams, 475 F.3d at 476 n. 4. Carr argues that a defendant who is given a different sentence following a Crosby remand is entitled to challenge all components of the sentencing decision, arguing that the sentencing proceedings conducted on such a remand are de novo.
If this Court in the prior appeal declined to adjudicate the sentencing challenges before remanding, see, e.g., United States v. Irving, 452 F.3d 110, 126 (2d Cir.2006), we agree that the parties are entitled to raise any properly preserved challenges to the sentencewhether or not the district court on remand imposed a new sentence. But to the extent that this Court has, on the prior appeal, adjudicated challenges to the district court's Guidelines calculations, we disagree. Although a district court, in the wake of Booker and its progeny, is not required to impose the now-advisory Guidelines-recommended sentence, the court is nonetheless normally required to calculate the sentencing range that the Guidelines recommend. See, e.g., Gall, 128 S.Ct. at 596 ("a district court should begin all sentencing proceedings by correctly calculating the applicable Guidelines range" (emphasis added)); Crosby, 397 F.3d at 111 ("In order to fulfill this statutory duty to `consider' the Guidelines, a sentencing judge will normally have to determine the applicable Guidelines range."); id. at 115 ("a sentencing judge would commit a statutory error in violation of section 3553(a) if the judge failed to `consider' the applicable Guidelines range (or arguably applicable ranges)"). And this Court, on reviewing a sentence, is required to determine whether the district court's calculations under the Guidelines are correct: "[T]he appellate court," which is to review the sentence under an abuse-of-discretion standard, "must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range . . . ." Gall, 128 S.Ct. at 597 (emphasis added). "The abuse-of-discretion standard incorporates de novo review of questions of law (including interpretation of the Guidelines). . . ." United States v. Legros, 529 F.3d 470, 474 (2d Cir.2008). As "the interpretation of a sentencing guideline is a question of law," United States v. Vasquez, 389 F.3d 65, 68 (2d Cir.2004), when a party contends in the initial appeal that Guidelines calculations made by the district court were erroneous, this Court will usually, in the interests of judicial efficiency and economy, address those contentions prior to remanding, in order that the district court either have the assurance that its prior calculations were correct or be sufficiently informed so that it will not repeat an error. See, e.g., United States v. Gonzalez, 407 F.3d 118, 124 (2d Cir.2005) (determining a Guidelines application issue previously decided by the district court, because that issue might be raised again in the district court in the course of the Crosby remand). Thus, in Carr I itself, we addressed Carr's challenge to the calculation of his offense level precisely because
[t]his [wa]s a question the district court w[ould] again be required to decide on remand because, post-Booker, it must still consider the appropriate Guidelines sentence along with the other section 3553(a) factors in arriving at the correct sentence.
424 F.3d at 230.
Accordingly, given (a) that the sentencing court, regardless of its ultimate sentence, must first calculate the Guidelines-recommended *104 sentence, (b) that interpretations of guidelines are questions of law, and (c) that such questions are addressed by this Court prior to remand in the interests of judicial efficiency and economy, we conclude that, in the absence of compelling circumstances such as those mentioned above that could warrant exceptions to application of the law-of-the-case doctrine, the doctrine bars the district court on remand from revisiting issues that were adjudicated on the prior appeal, and it forecloses the parties from renewing their previously adjudicated challenges on a subsequent appeal, even if the district court has imposed a new sentence on the Crosby remand.
In a letter brief submitted subsequent to oral argument of this appealat which this Court solicited briefing with respect to the effects, if any, of Gall and Kimbrough on this appealCarr in effect contends that Kimbrough represents a change in the law that should prevent application of the law-of-the-case doctrine to his renewed challenge to the use of the first-degree murder guideline to calculate his offense level (see Carr letter brief dated October 29, 2008 ("Carr supplemental brief on appeal") at 1-2, 4-7). Carr argues that in light of Kimbrough, the district court has "authority to fashion a sentence based in part on its disagreement with this Court's interpretation of a Guideline." (Id. at 1.) Elaborating, he states as follows:
At issue in this case is the district court's authority to deviate from the Guidelines because of disagreements with this Court's interpretation of those Guidelines. In the original appeal of conviction and sentence that lead [sic] to the Crosby remand here, Carr challenged the use of the first degree murder guideline in calculating his sentence. This Court held that the most analogous federal offense to New York second degree murder is first degree murder under 18 U.S.C. sec. 1111. United States v. Carr, 424 F.3d 213, 231 (2d Cir.2005), citing United States v. Minicone, 960 F.2d 1099, 1110 (2d Cir. 1992).
On resentencing, Carr again challenged the use of the first degree murder guideline. . . . The district court did not revisit the issue, because the "debate about exactly what guideline applies to the RICO counts in which the charge of murder is contained ... has been settled and the guideline range is forthe level is a level 43 and the guideline range is simply life." [S.Tr. 17.]
However, the district court's comments and questions at the resentencing hearing (which took place over two days) show that the court was concerned that federal first degree murder was not the most analogous federal offense in the circumstances of this case.
(Carr supplemental brief on appeal at 2-3 (footnote omitted) (emphasis in original).) Pointing out that in imposing sentence originally "in 2004, the court stated `because of the guideline calculations, based on the jury's verdict and their specific findings, it is my duty to impose a sentence of life imprisonment on Count One and on Count Two'" (id. at 3 n. 1 (quoting Original S.Tr. 17)), Carr states that the district court on remand
inquired extensively and repeatedly about Carr's culpability for the murder. [Aug. Tr.] at 16 ("Let's talk about the question of culpability.); [Aug. Tr.] at 16-17 (court notes that this murder was not premeditated); [Aug. Tr.] at 21 (court finds that killing was "on the spot"); [Aug. Tr.] at 27 ("[T]he degree of culpability is important, and this is not something that is listed in some numerical list in the guidelines."); [S.Tr. 18] ("I have been very concerned to *105 assess the degree of culpability in the shooting.").
The court's inquiries and statements at the sentencing hearing suggest that it disagreed with this Court's interpretation of the Guidelines, but felt itself boundas it was at that point by this Court's jurisprudenceto use the first degree murder guideline as its baseline for determining sentence. However, in light of Kimbrough, disagreement with the Commission's policy judgment (as interpreted by this Court in Minicone and Carr[I]) is a permissible reason to deviate from the guideline.
(Carr supplemental brief on appeal at 3-4 (emphasis in original).) In support of this argument, Carr cites United States v. Boardman, 528 F.3d 86 (1st Cir.2008) ("Boardman"), stating that "[t]he First Circuit . . . held that Kimbrough allows district judges to deviate from the Guidelines on the basis of categorical policy-disagreements, including disagreements with the Court's interpretation of those Guidelines." (Carr supplemental brief on appeal at 4 (emphases added).)
We disagree with Carr's interpretations of both Kimbrough and Boardman. Preliminarily, however, we note our disagreement as well with his description of the district court as "disagree[ing] with this Court's interpretation of [the pertinent] Guidelines" (Carr supplemental brief on appeal at 2, 4), and as being "concerned that federal first degree murder was not the most analogous federal offense in the circumstances of this case" (id. at 3 (emphasis in original)). Although the district court indicatedentirely properlythat the propriety of its application of the federal first-degree murder guideline was no longer in question, it did not express any disagreement with the appropriateness of that guideline as the analog for Carr's murder of Morton. Indeed, that was the guideline originally applied by the district court; in Carr I, we held that the district court's ruling was correct. The transcripts of the hearings held on remand do not indicate that the district court disagreed with this Court's jurisprudence; rather, they reveal clearly that the district court was concerned simply with assessing the degree of Carr's culpability for a callous murder that seemed senseless even to his fellow gang members.
Even had the district court disagreed, however, with this Court's jurisprudence reflected in Carr I, Minicone, and Diaz as to the propriety of using the federal first-degree murder guideline as the most appropriate analog for a RICO-related murder such as that committed here, we reject Carr's contention that the district court would have been free to disregard that jurisprudence after Kimbrough. Kimbrough, which concerned the Guidelines recommendations for severe sentencing of defendants convicted of offenses involving cocaine in the form of crack, as contrasted with cocaine in powder form, held that "under Booker, the cocaine Guidelines, like all other Guidelines, are advisory only," 128 S.Ct. at 564, and that "a district court may consider arguments that `the Guidelines sentence itself fails properly to reflect § 3553(a) considerations,'" id. at 570 (quoting Rita v. United States, 551 U.S. 338, 127 S.Ct. 2456, 2465, 168 L.Ed.2d 203 (2007)). The Kimbrough Court discussed the fact that in adopting Guidelines provisions which, as they then stood, equated one gram of crack with 100 grams of powder cocaine, the Sentencing Commission had looked to certain statutory mandatory minimum prison terms, rather than to empirical evidence as was its general practice, see id. at 567, and that numerous reports of the Commission revealed that the 100 to 1 ratio did not reflect the view of the Commission itself as to appropriate proportionality, see id. at *106 568. The Kimbrough Court held that "[g]iven all this, it would not be an abuse of discretion for a district court to conclude when sentencing a particular defendant that the crack/powder disparity yields a sentence `greater than necessary' to achieve § 3553(a)'s purposes, even in a mine-run case." Id. at 575. See also id. (questioning, but not deciding, whether "closer review may be in order when the sentencing judge varies from the Guidelines based solely on the judge's view that the Guidelines range fails properly to reflect § 3553(a) considerations even in a mine-run case" as to which the Commission formulated the Guidelines range based on its institutional strengths, taking into account "empirical data and national experience" (internal quotation marks omitted)).
Thus, Kimbrough stands for the proposition that the sentencing court has discretion to deviate from the Guidelines-recommended range based on the court's disagreement with the policy judgments evinced in a particular guideline. Kimbrough did not suggest that the district court may simply disregard the relevant guidelines; to the contrary, the Kimbrough Court noted that, "[a]s explained in Rita and Gall, district courts must treat the Guidelines as the `starting point and the initial benchmark,'" 128 S.Ct. at 574 (quoting Gall, 128 S.Ct. at 596). And we see nothing in Kimbrough that suggests, as Carr would have it, that a district court is free to disregard its circuit court's interpretation of a particular guideline, which is a ruling on a question of law.
Nor do we interpret the First Circuit's decision in United States v. Boardman, 528 F.3d 86, as authorizing its district courts, in light of Kimbrough, to "deviate from the Guidelines on the basis of categorical policy disagreements ... with the Court[ of Appeals'] interpretation of those Guidelines" (Carr supplemental brief on appeal at 4). The Boardman court, in addressing a Guidelines calculation for burglary of a nonresidential building, noted the interpretation it had given the pertinent guideline in a prior case ("Flore") and observed that the sentencing court in Boardman had indicated that it would have imposed a lower sentence if it had had discretion to do so. See Boardman, 528 F.3d at 86-87. The First Circuit in Boardman remanded to the district court, reasoning that a sentencing court "has broader freedom tha[n] it did before Kimbrough" to deviate from the Guidelines based on the sentencing judge's "disagreement with the Commission's policy judgment (as expressed in the guideline as we interpreted it in Fiore)." Id. at 87 (emphasis added). But nothing in Boardman stated that the district court was free to deviate from the Court of Appeals' interpretation of the relevant guideline itself. Indeed, the First Circuit preceded its discussion of the effect of Kimbrough by pointing out that "the district court [wa]s still required to calculate and consider the guidelines range," and that "[t]he district court properly recognized that it was bound by Fiore to treat the guideline as we had interpreted it," id.
Finally, Carr argues that the law-of-the-case doctrine should not be applied to his sentencing challenges because of a change in circumstances, to wit, that his "first sentencing" had "t[aken] place under the mandatory guidelines scheme." (Carr brief on appeal at 12.) He concedes, however, his convictions having been upheld, that "the constellation of offenses for which he was sentenced remained the same." (Id. (internal quotation marks omitted).) And it is indisputable that the change consisting of the Guidelines' being advisory rather than mandatory was dealt with by the remand itself. The remand *107 instructed the district court to resentence Carr if it determined that it would have imposed a nontrivially different sentence had it known the Guidelines were not mandatory; and on remand the district court acknowledged its understanding that "[t]he guidelines are now advisory and the court can apply the guidelines or take a different course if there's a reasonable ground[] to do so" (S.Tr. 17). We see no change in circumstances that would warrant nonapplication of the law-of-the-case doctrine here. Certainly there was no change in the circumstances surrounding the Morton murder.
In sum, we conclude that there was no relevant change in the law or the circumstances, nor any interest of justice that would indicate that the law-of-the-case doctrine should not be applied to foreclose Carr's present challenges to the Guidelines calculations that were approved in Carr I. We accordingly decline to revisit those issues.

B. The Reasonableness of the Sentence Imposed

In reviewing a sentence post-Booker, the court of appeals is required to determine whether the sentence is "reasonable." Gall, 128 S.Ct. at 594 (internal quotation marks omitted); Booker, 543 U.S. at 261-62, 125 S.Ct. 738. As adverted to in the preceding section, in making that determination, we use "the familiar abuse-of-discretion standard of review," Gall, 128 S.Ct. at 594, regardless of whether the sentence was within or outside the Guidelines-recommended range, see id. at 591; United States v. Jones, 531 F.3d 163, 170 (2d Cir.2008). This standard of review applies as well to our review of a sentence imposed after a Crosby remand. See Williams, 475 F.3d at 474.
Reasonableness review has both a procedural and a substantive component. See, e.g., United States v. Irving, 554 F.3d 64, 71-72 (2d Cir.2009); United States v. Jones, 531 F.3d at 170; United States v. Canova, 485 F.3d 674, 679 (2d Cir.2007). Review for procedural reasonableness requires us to
ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence.
Gall, 128 S.Ct. at 597. In determining whether the district court has considered the appropriate factors, we do not require "robotic incantations" by the sentencing judge. United States v. Brown, 514 F.3d 256, 270 (2d Cir.2008); United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.), cert, denied, 549 U.S. 882, 127 S.Ct. 192, 166 L.Ed.2d 143 (2006); Crosby, 397 F.3d at 113. In the absence of record evidence suggesting otherwise, we presume that the district court has faithfully discharged its duty to consider the § 3553(a) factors. See, e.g., United States v. Brown, 514 F.3d at 264; United States v. Fernandez, 443 F.3d at 30. In reviewing a sentence for substantive reasonableness, we are guided by the § 3553(a) factors that the sentencing court is required to apply. See, e.g., Booker, 543 U.S. at 261, 125 S.Ct. 738; Crosby, 397 F.3d at 114-15 & n. 13.
In the present case, Carr contends that his sentence is unreasonable, arguing principally that the district court "unjustifiably relied on certain sec. 3553 factors, while not giving due weight to others," and that it committed an error of law in
characteriz[ing] subsection (2) of that statute (setting forth the goals of sentencing) as "the principal one." ... As a matter of law, no single factor in sec. *108 3553(a) is controlling, and no single factor is "the principal one."
(Carr brief on appeal at 16 (quoting (S.Tr. 21)).) He also argues that his new sentence is "greater than necessary to accomplish the statutory sentencing goals." (Id.)
The record belies these contentions. The statute directs the sentencing court to "impose a sentence sufficient, but not greater than necessary, to comply with the purposes set forth in paragraph (2) of this subsection." 18 U.S.C. § 3553(a). Other than concerns for training and treatment, see id. § 3553(a)(2)(D), which Carr has not suggested have any relevance whatever here, the sentencing purposes spelled out in paragraph (2) of § 3553(a) are
(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; [and]
(C) to protect the public from further crimes of the defendant[.]
18 U.S.C. § 3553(a)(2). The district court clearly considered these factors. The issue that received the most attention from the court and the parties in this case was the degree of Carr's culpability in killing Morton, as the court sought to arrive at "a sentence which justly and fairly takes into account the gravity of the killing that Mr. Carr perpetrated" (S.Tr. 21)an act that the court found "impossible ... to understand" except as "an act of sheer cruelty" (Aug. Tr. 27). But while using the phrases "the principal one," or "the two main factors," the court in fact expressly cited four of the above § 3553(a)(2) factors, stating that
the principal one is the seriousness of the offense and to have an appropriate punishment of that offense and also protect society from any occurrence of criminal behavior by Mr. Carr. Those are the two main factorsalso to be a deterrent to other criminal activity ....
(S.Tr. 21 (emphases added).) And, as set forth in detail in Part I.B. above, the district court expressly noted its "oblig[ation] to give specific attention to the factors listed in 18 United States Code Section 3553(a)" (S.Tr. 17), and stated "although I might not go down them doggedly" one by one, "I certainly have them in mind" (id. at 21). Thus, the record does not support Carr's contention that the district court ignored any of the § 3553(a) factors.
Nor is there merit in Carr's suggestion that the district court lost sight of its obligation to impose a sentence no "greater than necessary to accomplish the statutory sentencing goals" (Carr brief on appeal at 16). Having mentioned the above factors (see S. Tr. 21), the court noted that Carr had proposed that he be given a 30-year prison term, but the court stated "I do not think that that is sufficient" (id.); it stated, however, that "a very substantial penalty does not need to be endless" (id.); and in concluding that Carr's prison term should be 40 years, the court stated, "I cannot do less and be fair to the community" (id. at 22). The court plainly followed the statutory mandate to impose a sentence that it deemed sufficient, but not greater than necessary, to accomplish the purposes set forth in § 3553(a)(2).
In sum, it is abundantly clear in this case that the court considered the appropriate factors and rendered a thoughtful judgment that complied with the requirements of § 3553(a). We see no basis for concluding that the district court abused its discretion or that the sentence it imposed is unreasonable.

C. The Request for a Remand With Respect to Sentencing for Crack

Lastly, in his postargument supplemental brief, Carr argues that this *109 Court should remand to the district court for resentencing in light of (a) Kimbrough's holding that a sentencing court has discretion to deviate from the harsh sentences for defendants convicted of trafficking in crack as recommended in the version of the Guidelines applicable to Carr, and (b) amendments to the crack-related guidelines, adopted subsequent to his resentencing. We disagree.
Carr's contention that he should be resentenced because of the harshness of the crack-related guidelines that were applied to him is subject to plain-error analysis because he made no challenge to those guidelines on harshness grounds in the district court. See, e.g., United States v. Regalado, 518 F.3d 143, 147 (2d Cir.2008). To receive relief under plain-error analysis, "`a defendant must show (1) error, (2) that is plain at the time of appellate review, and (3) that affects substantial rights. Where these conditions are met, we have the discretion to notice a forfeited error if (4) it seriously affects the fairness, integrity, or public reputation of judicial proceedings.'" Id. (quoting United States v. Quinones, 511 F.3d 289, 316 (2d Cir. 2007), cert, denied, ___ U.S. ___, 129 S.Ct. 252, 172 L.Ed.2d 190 (2008)). Carr cannot meet this test, for if there was error it did not affect his substantial rights. He was sentenced to two concurrent terms of 35 years' imprisonment on the RICO counts. His sentences on the narcotics counts were 20 years, to be served concurrently with the sentences on the RICO counts. There is no indication in the record that the district court believed these 20-year sentences were inappropriate for Carr's admitted dealing in narcotics throughout virtually his entire adult life. Rather, at the sentencing hearing, the district court noted that "[t]here are other counts involving narcotics and the weapons but the crucial thing here for this sentence is what the sentence will be on the two RICO counts. . . ." (S.Tr. 17.) We cannot see that Kimbrough warrants a remand with respect to Carr's sentence on the narcotics counts.
As to Carr's contention that he should be resentenced anew in light of amendments to the Guidelines adopted after his resentencing on the Crosby remand, that contention is not properly before us. Defendants who seek relief based on Guidelines amendments "should move for modification of their sentences pursuant to 18 U.S.C. § 3582(c)(2) in the district courts." United States v. Regalado, 518 F.3d at 151.

D. Correction of the Amended Judgment

Finally, we note that the amended judgment entered in this case does not accurately reflect the judgment imposed on Carr at his sentencing hearing. The written amended judgment states that the concurrent prison terms imposed for Counts 1 and 2 are 30 years. Yet the sentencing transcript revealsand the parties' briefs on appeal reflectthat the court orally announced a 40-year total prison term that included imprisonment for 35 years on Counts 1 and 2 (see S.Tr. 23, quoted in Part I. B. above).
"[W]here there is a direct conflict between an unambiguous oral pronouncement of sentence and the written judgment. . . the oral pronouncement, as correctly reported, must control." United States v. Marquez, 506 F.2d 620, 622 (2d Cir.1974) (internal quotation marks omitted). See, e.g., United States v. DeMartino, 112 F.3d 75, 78-79 (2d Cir. 1997); United States v. Werber, 51 F.3d 342, 347 (2d Cir. 1995); United States v. Pagan, 785 F.2d 378, 380 (2d Cir.), cert. denied, 479 U.S. 1017, 107 S.Ct. 667, 93 L.Ed.2d 719 (1986); United States v. Moyles, 724 F.2d 29, 30 (2d Cir.1983).
*110 Accordingly, we remand for entry of a corrected amended judgment, reflecting the sentence actually imposed.

CONCLUSION
We have considered all of Carr's arguments on this appeal and have found in them no basis for reversal. The amended judgment, as announced orally, is affirmed. The matter is remanded for the entry of a corrected written amended judgment to reflect that Carr has been sentenced to concurrent prison terms of 35 years on Counts 1 and 2.
