
583 F.3d 108 (2009)
UNITED STATES of America, Appellee,
v.
John J. RIGAS and Timothy J. Rigas, Defendants-Appellants.
Docket Nos. 08-3485-cr (L), 08-3500-cr (CON), 08-3592-cr (CON), 08-3597-cr (CON).
United States Court of Appeals, Second Circuit.
Argued: May 5, 2009.
Decided: October 5, 2009.
*111 Stephen R. McAllister, Thompson Ramsdell & Qualseth, P.A., Lawrence, KS (Neal K. Katyal, Morgan Legal Consulting, Washington, D.C., and Lawrence G. McMichael, Dilworth Paxson, LLP, Philadelphia, PA, on the brief), for Defendants-Appellants.
William F. Johnson, Assistant United States Attorney (Michael J. Garcia, United States Attorney for the Southern District of New York, and Katherine Polk Failla, Assistant United States Attorney, on the brief), United States Attorney's Office for the Southern District of New York, New York, NY, for Appellee.
Douglas A. Berman, Stephanos Bibas, Marc Miller, Michael O'Hear, Mark Osler, Sandra Guerra Thompson, Amicus Curiae in support of Defendants-Appellants.
Before: FEINBERG, WINTER, and CABRANES, Circuit Judges.
JOSÉ A. CABRANES, Circuit Judge:
We consider several challenges to the trial and sentencing of John J. Rigas, the former CEO of Adelphia Communications Corp. ("Adelphia"), and his son Timothy J. Rigas, Adelphia's former CFO (together, the "Rigases"), including the Rigases' claims that their sentences were procedurally and substantively unreasonable.

BACKGROUND
The history of massive corporate fraud that forms the background of these proceedings has been set forth exhaustively in United States v. Rigas, 490 F.3d 208, 212-19 (2d Cir.2007). We supply here only a brief summary of the relevant procedural history.

Trial and Sentencing
In September 2002, the Rigases were indictedalong with Michael Rigas, James Brown, and Michael Mulcahey, who were *112 also executives at Adelphiaon multiple counts of securities fraud, wire fraud, bank fraud, and criminal conspiracy. In June 2004, following a trial in the United States District Court for the Southern District of New York (Leonard B. Sand, Judge), a jury convicted the Rigases of conspiracy, bank fraud, and securities fraud but acquitted them of wire fraud. Michael Rigas was acquitted of conspiracy and wire fraud, with the jury remaining deadlocked on the other counts; he later pleaded guilty to a charge of making a false entry in the books and records of Adelphia in violation of 47 U.S.C. § 220(e). Brown pleaded guilty prior to trial and testified as a government witness. Mulcahey was acquitted of all charges. See Rigas, 490 F.3d at 219.
For each of the Rigases, the initial Presentence Investigation Reports ("PSR"), prepared by the United States Probation Office ("Probation Office"), calculated, under the United States Sentencing Guidelines ("Guidelines"), a base offense level of six and recommended multiple sentencing enhancements: (1) twenty-six levels because the loss exceeded $100 million; (2) four levels because the offense involved more than fifty victims; (3) two levels because the offense involved sophisticated means; (4) two levels because defendants derived more than $1 million in gross receipts from financial institutions as a result of their offenses; (5) two levels because defendants abused the public trust; and (6) four levels because appellants were leaders of criminal activity that involve five or more participants. Based on these calculations, the PSRs concluded that the total offense level for each of the Rigases was 46, their Criminal History Category was I, and the resulting sentencing range under the Guidelines was life imprisonment. However, the Probation Office recommended a term of ten years' imprisonment and five years' supervised release for John Rigas, and twenty years' imprisonment and five years' supervised release for Timothy Rigas.
At a sentencing hearing on June 20, 2004, the District Court announced that it would consider the Guidelines and the factors in 18 U.S.C. § 3553(a), and stated that, in its view, the PSR calculations were accurate. After hearing argument from counsel, the District Court imposed sentences that were more severe than those recommended in the PSR, but which nonetheless fell significantly below the recommended Guidelines ranges of life imprisonment. Specifically, the District Court sentenced John Rigas principally to an aggregate term of fifteen years' imprisonment. The Court divided his sentence as follows:
 15 years on each of two counts of bank fraud, the sentences to run concurrently with each other;
 5 years on one count of conspiracy and 10 years on one count of securities fraud, the sentences to run consecutively to each other and concurrently with the bank fraud sentence; and
 10 years on one count of securities fraud, the sentences to run concurrently with each other and the other sentences.
The District Court sentenced Timothy Rigas principally to an aggregate term of twenty years' imprisonment, according to the following criteria:
 20 years on each of two counts of bank fraud, the sentences to run concurrently with each other;
 5 years on one count of conspiracy, 10 years on one count of securities fraud, and 5 years on another count of conspiracy, the sentences to run consecutively to each other and concurrently with the bank fraud sentence; and

*113  10 years on each of the other securities fraud counts, the sentences to run concurrently with each other and the other sentences.
In addition, the Rigas family and the government reached a settlement of other matters, under which the Rigases forfeited over $1 billion in assets to Adelphia. The liquidated value of these assets was $715 million.

Appeal and Resentencing
The Rigases appealed their convictions, and on May 24, 2007, another panel of our Court affirmed the convictions on all counts except one count of bank fraud  "Count 23"for which it found insufficient evidence. See Rigas, 490 F.3d at 236, 239. However, the panel concluded that there was sufficient evidence to support a related count of bank fraud"Count 22." Id. at 235-36. The panel remanded the cause for resentencing. Id. at 239.
No new PSR was prepared for resentencing, but at the District Court's request, the Probation Office informed the District Court by letter that the appropriate sentence under the Guidelines was still life imprisonment because the "aggregate of the statutory maximum terms of the [remaining] counts of conviction" was 185 years, reduced from 215 years. Special App. 17. The District Court conducted a resentencing hearing on May 22, 2008 and issued a written opinion and order on June 24, 2008. The District Court held that it was not required to resentence defendants de novo because Count 23 was a small part of the overall conviction and ran concurrently with Count 22, which this Court upheld. Accordingly, the District Court concluded that the reversal was akin to a "sentencing" error rather than a "conviction" error, and that only a "limited" resentencing was required. Special App. 18-19. The District Court expressly rejected the Rigases' argument that under United States v. Quintieri, 306 F.3d 1217 (2d Cir. 2002), resentencing had to be de novo because the reversal was based on a "conviction" error, not a "sentencing" error, and characterized this distinction as a "mechanical" test. Id.
Nevertheless, the District Court concluded in an alternative holding that even under de novo or "holistic" resentencing, there was "no basis for a reduction of [a] sentence which is broader than the relatively minor adjustment occasioned by the reversal of Count 23. Indeed, ... the sentence previously imposed was fully justified under all of the circumstances." Special App. 23. In reaching this conclusion, the District Court addressed and rejected the Rigases' challenges to the twenty-six level sentencing enhancement for loss in excess of $100 million. The Court also observed that the Rigases "made no claim that the reversal of [the conviction on] Count 23 ... [affects] the strength or substance of the convictions on the 17 other counts as to which the Court of Appeals noted there was ample evidence." Special App. 23-24. Indeed, the District Court concluded that the reversal on Count 23 altered neither the applicable Guidelines range, nor "the seriousness of the[ir] ... crimes, nor the suffering which their conduct inflicted on so many people." Special App. 24.
Despite observing that there was "no basis for a reduction" in the Rigases' sentences, Special App. 23, the District Court in fact applied a "minimal adjustment," reducing each sentence by three years, to 12 and 17 years for John and Timothy Rigas, respectively. Special App. 24.

Motion for a New Trial
On July 5, 2007prior to resentencingdefendants filed a motion for a new trial pursuant to Rule 33 of the Federal Rules of Criminal Procedure on the basis *114 of alleged "newly discovered evidence" of perjury by their former co-defendant James Brown, who had testified at the criminal trial as a government witness and later allegedly provided contradictory testimony in a civil proceeding. On November 20, 2007, the District Court denied the motion on the grounds that (1) Brown did not commit perjury, see United States v. Rigas, No. 02-CR-1236, 2007 WL 4145282, at *1-5, 2007 U.S. Dist. LEXIS 85590, at *4-11 (S.D.N.Y. Nov. 20, 2007); (2) the post-trial depositions of Brown and other witnesses in a civil proceeding were newly available, not newly discovered, since defendants could have pursued their testimony before or during the criminal trial, but did not do so, see id. at *5, 2007 U.S. Dist. LEXIS 85590, at *11-15; and (3) even if Brown's testimony were perjured or newly discovered, it would not have affected the outcome of the criminal trial, see id. at *5-6, 2007 U.S. Dist. LEXIS 85590, at *15-16.

Motion to Compel Discovery
On December 4, 2007, defendants filed a motion to compel the government to produce its notes from interviews with Carl Rothenberger, Adelphia's former lead outside counsel, and other witnesses not called by either party at trial. Defendants argued that the notes should have been disclosed to them pursuant to Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). The District Court denied the motion on January 15, 2008, reasoning that, inter alia, the government had no obligation to produce notes of witnesses who did not testify at trial, and the defendants knew or should have known of Rothenberger's existence as a possible witness and the relevance of his testimony. See United States v. Rigas, No. 02-CR-1236, 2008 WL 144824, at *1-2, 2008 U.S. Dist. LEXIS 2827, at *2-6 (S.D.N.Y. Jan. 15, 2008).

* * *
In this appeal, defendants challenge all three of the decisions of the District Court outlined above: (1) the June 24, 2008 resentencing order, (2) the November 20, 2007 opinion and order denying the Rigases' motion for a new trial, and (3) the January 15, 2008 memorandum and order denying the Rigases' motion to compel discovery.

DISCUSSION

A. Reasonableness of the Sentences
Following United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), a district court has broad latitude to "impose either a Guidelines sentence or a non-Guidelines sentence." United States v. Sanchez, 517 F.3d 651, 660 (2d Cir.2008); see also United States v. Cavera, 550 F.3d 180, 190 (2d Cir.2008) (en banc). Accordingly, the role of the Court of Appeals is limited to examining a sentence for reasonableness, which is akin to review under an "abuse-of-discretion" standard. See Cavera, 550 F.3d at 190; see also Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 591, 169 L.Ed.2d 445 (2007) (holding that "courts of appeals must review all sentenceswhether inside, just outside, or significantly outside the Guidelines rangeunder a deferential abuse-of-discretion standard"); cf. Sims v. Blot, 534 F.3d 117, 132 (2d Cir.2008) ("A district court has abused its discretion if it based its ruling on an erroneous view of the law or on a clearly erroneous assessment of the evidence, or rendered a decision that cannot be located within the range of permissible decisions." (alteration, citations, and quotation marks omitted)). This standard applies "both to the [substantive reasonableness of the] sentence itself and to the procedures employed in arriving at the sentence." United States *115 v. Verkhoglyad, 516 F.3d 122, 127 (2d Cir. 2008).
The Rigases allege that their sentences were procedurally unreasonable in several ways. Principally, the Rigases contend that the District Court did not resentence them de novo but instead conducted only a limited resentencing hearing. Alternatively, the Rigases argue that even under the District Court's alternative holdingfor which the scope of resentencing was de novothe Court committed several procedural errors, including failures to (1) conduct the individualized assessment required by 18 U.S.C. § 3553(a); (2) make an appropriate calculation of loss to justify a twenty-six-point sentencing enhancement; (3) exclude an enhancement for bank fraud; (4) find facts in support of a sentencing enhancement for leading a conspiracy; and (5) specify who exactly was harmed before imposing a "fifty victim" sentencing enhancement. Defendants also argue that their sentences were substantively unreasonable because people convicted of "more serious" crimes, such as murder and terrorism, have been sentenced to only a few years more than the Rigases.

1. Scope of Resentencing
The Rigases argue principally that, following our decision in Quintieri, 306 F.3d at 1227-28, we have held that defendants must be resentenced de novo where a portion of a conviction has been reversed on appeal. The government asks us to affirm on the basis of the District Court's limited resentencing because (1) defendants did not challenge their sentences on the initial appeal, thereby waiving any arguments that the sentences were unreasonable, and (2) "the sentencing considerations relating to Count Twenty-Three were entirely severable from the considerations on the other counts," Appellee's Br. 35.
In Quintieri, we distinguished between conviction errors, for which de novo resentencing was the "default rule," and sentencing errors, for which limited resentencing was the default rule. We held:
When the conviction on one or more charges is overturned on appeal and the case is remanded for resentencing, the constellation of offenses of conviction has been changed and the factual mosaic related to those offenses that the district court must consult to determine the appropriate sentence is likely altered. For the district court to sentence the defendant accurately and appropriately, it must confront the offenses of conviction and facts anew.
306 F.3d at 1227-28; see also id. at 1228 ("[R]esentencing usually should be de novo when a Court of Appeals reverses one or more convictions and remands for resentencing...."). Quintieri created a "default rule" that de novo resentencing is required where a conviction is reversed in part on appeal. Quintieri, 306 F.3d at 1229 n. 6 ("Today we conclude that when a resentencing results from a vacatur of a conviction, we in effect adhere to the de novo default rule ... because multiple convictions are `inextricably linked' in calculating the sentencing range under the guidelines." (emphasis added)).
Moreover, we recognized in Quintieri that "when a case is remanded for de novo resentencing, the defendant may raise in the district court and, if properly preserved there, on appeal to the court of appeals, issues that he or she had previously waived by failing to raise them." Id. at 1225. In clear contrast, we stated that limited resentencing was the default rule where there was a sentencing error; de novo resentencing was required for a sentencing error only where "one or more *116 specific sentencing errors ... would undo the sentencing calculation as a whole or the `spirit of the mandate' otherwise requires de novo resentencing." Id. at 1228 n. 6 (emphasis added).
Accordingly, Quintieri supplies two pertinent rules: (1) where a count of a conviction is overturnedas opposed to an aspect of a sentenceresentencing must be de novo; and (2) de novo means "anew," id. at 1228, so that a defendant may raise issues even if they would otherwise have been waived.
Here, an experienced and respected judge expressed the view that these rules are unduly "mechanical." Special App. 19. It is nevertheless true that on more than one occasion since Quintieri, our Court has adhered to the "de novo default rule," however characterized, in successive cases where a portion of a defendant's conviction was overturned on appeal, even though the portion of the conviction that was overturned was unlikely to alter the ultimate sentence in any significant way. For example, in United States v. Hertular we explained that,
although our reversal of [the defendant's] § 111 conviction changes the "constellation of offenses" relevant to sentencing, the "factual mosaic" may be little altered. Nevertheless, mindful that the law entrusts district courts, not courts of appeals, with the primary responsibility for weighing the totality of circumstances relevant to sentencing, we conclude that, even in these circumstances, we must vacate the defendant's sentence and remand the case to the district court so that it may decide, in the first instance, whether a conviction on three rather than four counts affects its assessment of the sentencing factors detailed in 18 U.S.C. § 3553(a).
562 F.3d 433, 446 (2d Cir.2009) (quoting Quintieri, 306 F.3d at 1228); see also United States v. Draper, 553 F.3d 174, 175-76, 184 (2d Cir.2009) (concluding, where defendants were convicted of "witness retaliation, witness tampering, narcotics, and firearm charges," that "because we are reversing the witness retaliation convictions, de novo resentencing is required and we are compelled to remand this matter to the district court in any event." (emphases added)). Indeed, we have also observed that Quintieri has particular salience in the post-Booker regime, under which a District Court must make an individualized assessment based on all the sentencing factors in § 3553(a). See Hertular, 562 F.3d at 446; Gall, 552 U.S. 38, 128 S.Ct. 586 at 591, 169 L.Ed.2d 445; see also 18 U.S.C. § 3553(a)(1) (requiring an assessment of "the nature and circumstances of the offense"); id. at § 3553(a)(2) (requiring an assessment of the "seriousness of the offense," "adequate deterrence," and "just punishment").
In this case, the District Court concluded that a de novo resentencing was not required because our Court's reversal of the conviction on Count 23 was more akin to a "sentencing error" than a "conviction error." To reach this conclusion, the District Court decided first that Counts 22 and 23 were "quite different" from the remainder of the indictment, such that it was unlikely that the reversal of Count 23 would alter the appropriate sentence.[1]*117 Special App. 19. Accordingly, the District Court ruled that it could, consistent with Quintieri, conduct only a limited resentencing. See, e.g., Quintieri, 306 F.3d at 1225 ("We conclude that in this case, because we identified a particular sentencing issue necessitating remandwhether [the defendant's] total offense level on the conspiracy count was improperly enhanced as a result of `double counting'the remand was limited, not de novo. Because the remand was limited, [the defendant] may not now raise arguments that he had an incentive and an opportunity to raise previously but did not raise, absent a cogent and compelling reason for permitting him to do so." (emphasis added)); United States v. Stanley, 54 F.3d 103, 108 (2d Cir.1995) (concluding that de novo resentencing is unnecessary when the remanding court identifies a only sentencing error and does not explicitly limit the scope of resentencing).
We disagree with the premise of the District Court's analysis. Quintieri expressly created a "default rule" that resentencing is required where part of a conviction is reversed on appeal. Quintieri, 306 F.3d at 1228 n. 6 (holding that "when a resentencing results from a vacatur of a conviction, we in effect adhere to the de novo default rule of the Sixth, Eighth, Ninth, and Eleventh Circuit[s], because multiple convictions are `inextricably linked' in calculating the sentencing range under the guidelines." (emphasis added)); see also Draper, 553 F.3d at 184 (stating that "because we are reversing the witness retaliation convictions, de novo resentencing is required" (emphasis added)). In Quintieri, we created a rule, not a guideline. To the extent that any language in Quintieri or cases that pre-date Quintieri suggest otherwisesee, e.g., Quintieri, 306 F.3d at 1228 ("[R]esentencing usually should be de novo when a Court of Appeals reverses one or more convictions and remands for resentencing." (emphasis added)); United States v. Atehortva, 69 F.3d 679, 685-86 (2d Cir.1995) ("When a defendant challenges convictions on particular counts that are inextricably tied to other counts in determining the sentencing range under the guidelines, the defendant assumes the risk of undoing the intricate knot of calculations should he succeed." (emphasis added))we resolve any ambiguity today. In Quintieri, the Court of Appeals identified a conviction error, not a mere sentencing error, when it reversed the convictions on Count 23. See Rigas, 490 F.3d at 239. Accordingly, the Rigases were entitled to be resentenced de novo at a plenary sentencing rehearing.
We also disagree with the government's proposed interpretation of Quintieri. According to the government, if a challenge to a sentence has been waived, the "law of the case" doctrine and Quintieri require resentencing de novo only where (1) the "spirit of the mandate" requires as much (such as when the reversed portion of the *118 conviction is "inextricably linked" to the remainder of the conviction), (2) an issue became relevant only after appellate review, or (3) there is a "cogent" or "compelling" reason for resentencing de novo, such as a change in controlling law. Otherwise, the government argues, resentencing should be limited, not de novo.
The government assumes that these three considerations apply where an appellate court has reversed a conviction. However, it is clear from Quintieri that the three considerations identified by the government apply only where an appellate court has reversed part of a sentence, not part of a conviction. See 306 F.3d at 1229 (discussing these exceptions under the heading "Implications of a Limited Remand"). The "spirit of the mandate" and other considerations identified by the government are exceptions to limited resentencing following reversal of a sentence:
That resentencing usually should be de novo when a Court of Appeals reverses one or more convictions and remands for resentencing, then, does not deviate from the rule ... that absent explicit language in the mandate to the contrary, resentencing should be limited when the Court of Appeals upholds the underlying convictions but determines that a sentence has been erroneously imposed and remands to correct that [sentencing] error. To be sure, there may be circumstances when we reverse a sentence in which the "spirit of the mandate" requires de novo sentencing, for example when the reversal effectively undoes the entire "knot of calculation," but this is not such a case.
Quintieri, 306 F.3d at 1228 (final emphasis added); see also id. at 1229 n. 6 ("But when a resentencing is necessitated by one or more specific sentencing errors, unless correction of those errors would undo the sentencing calculation as a whole or the `spirit of the mandate' otherwise requires de novo resentencing, we in effect adhere to the ... default rule of limited resentencing." (emphasis added)); id. at 1230 ("[E]ven when a remand is limited, an issue may be raised if it arises as a result of events that occur after the original sentence.").
In Quintieri, we determined that the basis for the prior reversal was the defendant's sentencespecifically, "double counting," see id. at 1229not the defendant's conviction. Accordingly, we held that there was a presumption that resentencing would be limited, not de novo, but that the defendant would be entitled to de novo review if he could show that (1) the "spirit of the mandate" requires de novo sentencing, (2) an issue became relevant only after the initial appellate review, or (3) there is a "cogent" or "compelling" reason for resentencing de novo, such as a change in controlling law. By contrast, the prior appeal in the instant case reversed a portion of the defendants' conviction, and so defendants were entitled to be resentenced de novo and, as noted, to "raise in the district court and, if properly preserved there, on appeal to the court of appeals, issues that he or she had previously waived by failing to raise them." Id. at 1225.
To reiterate, on remand, a district court that is required to resentence de novo must reconsider the sentences imposed on each count, as well as the aggregate sentence. In such circumstances, the court should determine whether the "change[ ]" in the "constellation of offenses of conviction" has "altered" the "factual mosaic related to those offenses." Quintieri, 306 F.3d at 1227-28. If so, the court must reconsider the sentence imposed on the count or counts affected by the vacatur of the conviction of another count, as well as on the aggregate sentence, in light of *119 the sentencing factors in § 3553(a). If the court determines that the "factual mosaic" related to a count of conviction has not been altered, no further proceeding as to that count is necessary, except to the extent it affects the aggregate sentence.

2. "Procedural Reasonableness"
We turn now to the District Court's alternative holding, in which the Court imposed a new sentence on the assumption that it was resentencing de novo. As noted above, the Rigases offer multiple arguments in support of their contention that the District Court's de novo resentencing was procedurally flawedto wit, they argue that the District Court failed to (1) conduct the individualized assessment required by 18 U.S.C. § 3553(a); (2) make an appropriate calculation of loss to justify a twenty-six-level sentencing enhancement; (3) exclude an enhancement for bank fraud; (4) find facts in support of a sentencing enhancement for leading a conspiracy; and (5) specify who exactly was harmed before imposing a "fifty victim" sentencing enhancement. Although the Rigases have offered additional reasons why their sentences were procedurally unreasonable, we confine our discussion to these arguments, which consumed the bulk of the briefing on procedural reasonableness.
Regarding the statutory requirement of an individualized assessment of wrongdoing and appropriate punishment, see 18 U.S.C. § 3553(a), we observe that prior to the May 22, 2008 resentencing hearing, the District Court solicited from the Probation Office revisions to the original PSR. See Special App. 17. At the resentencing hearing, the District Court stated on the record that it had also read the Rigases' sentencing memoranda and would consider the factors in 18 U.S.C. § 3553(a). In our view, the Court's written ruling reflects its informed consideration of these factors. See Cavera, 550 F.3d at 189-190 (stating that our review for procedural reasonableness "requires that we be confident that the sentence resulted from the district court's considered judgment as to what was necessary to address the various, often conflicting, purposes of sentencing"). In addition to specifically mentioning "the § 3553 sentencing considerations," Special App. 19, the District Court discussed the applicable Guidelines range (devoting considerable discussion to the twenty-six level additur for loss causation); the Rigases' continued argument that they "engaged in no criminal conduct but were themselves victims"; the seriousness of their offenses; and the suffering caused by the Rigases' crimes. Special App. 17, 19-24. That the District Court did not parse every sentencing factor individually or address in writing each of defendants' sentencing arguments does not render the ultimate sentence procedurally unreasonable. See United States v. Fernandez, 443 F.3d 19, 29 (2d Cir.2006) ("We have imposed no ... requirement that a sentencing judge precisely identify either the factors set forth in § 3553(a) or specific arguments bearing on the implementation of those factors in order to comply with her duty to consider all the § 3553(a) factors along with the Guidelines applicable range."). As we have previously stated, "we presume, in the absence of record evidence suggesting otherwise, that a sentencing judge has faithfully discharged her duty to consider the statutory factors." Id. at 30.
With respect to loss causation, the Rigases argue at length that the losses in this case, including most notably the bankruptcy of Adelphia, "`may reflect, not the [Rigases'] misrepresentation[s], but changed economic circumstances, changed investor expectations, new industry-specific *120 or firm-specific facts, conditions, or other events.'" Appellant's Br. 32 (quoting Dura Pharm. v. Broudo, 544 U.S. 336, 343, 125 S.Ct. 1627, 161 L.Ed.2d 577 (2005)). The government argues that the amount of loss attributable to the Rigases' fraud may be measured in billions, not millions, and so even if "the entire decline in Adelphia's market capitalization" was caused by a number of factors, the evidence presented at trial "was sufficient to demonstrate, by a preponderance standard, that substantially all of the decline was a `reasonable estimate' of the loss." Appellee's Br. 48.
In calculating the amount of loss under the Guidelines, a sentencing court "need only make a reasonable estimate of the loss." U.S.S.G. § 2B1.1 cmt. n. 3(C). Although "[d]etermining this amount is no easy task[,] ... some estimate must be made for Guidelines' [calculation] purposes, or perpetrators of fraud would get a windfall." United States v. Ebbers, 458 F.3d 110, 127 (2d Cir.2006). Although it is true that "[t]he loss must be the result of the fraud," id. at 128, as opposed to other, non-fraudulent occurrences, we agree with the District Court and the government that, regardless of the precise amount of the loss attributable to the Rigases' fraud, that figure easily exceeds $100 million. For example, as we noted in our previous opinion in this case,
[t]he evidence at trial showed that throughout the period of the conspiracy, Defendants took over $200 million dollars from Adelphia's Cash Management System for personal expenses ranging from $200 to purchase 100 pairs of bedroom slippers for Timothy Rigas, to over $3 million to produce a film by Ellen Rigas, to $200 million to pay off Rigas family margin loans. The missing money was obscured by the commingling of cash between Adelphia and [privately-held companies owned by the Rigases].
Rigas, 490 F.3d at 218. In any event, the District Court reasoned that even if a loss of only $0.50 per share were attributable to the Rigases' fraudulent conduct, that would still satisfy the $100 million threshold for the sentencing adjustment applied to the count. See Special App. 22; see also Rigas, 490 F.3d at 212 (noting that on the day that Adelphia's $2.2 billion in previously unrecorded liabilities were disclosed, the company's stock price dropped "about twenty-five percent to $20.39," and that Adelphia filed for bankruptcy within months). Accordingly, we have no trouble affirming the District Court's estimate of loss caused by the Rigases' fraud.[2]
It is undisputed that, at resentencing, the government did not seek a two-level enhancement for bank fraud in excess of $1 million in gross receipts. The Rigases contend that the District Court considered it anyway, based on the District Court's comment in a footnote that the Rigases' arguments about the bank fraud enhancement were "totally without merit." *121 Special App. 20 n. 3. On this basis alone, we cannot conclude that the District Court erroneously considered an abandoned sentencing enhancement for bank fraud. On resentencing, the District Court agreed with the Probation Office that the Rigases' offense levels surpassed what was required under the Guidelines for a recommended sentence of life imprisonmentthe maximum aggregate sentence allowableand then imposed sentences that were substantially below the applicable Guidelines range. As a practical matter, even without the two-level enhancement for bank fraud, the Guidelines would call for life imprisonment. Accordingly, whatever ambiguity exists in the record with respect to the District Court's consideration of the bank fraud enhancement is de minimis, and certainly does not render the sentence procedurally unreasonable.
We further disagree with the Rigases that the District Court erred in not making the necessary factual findings before adopting the PSR recommendation that the Rigases' roles in defrauding Adelphia warranted a four-level sentencing enhancement. See U.S.S.G. § 3B1.1 (authorizing a four-level additur for organizing or leading a criminal activity). The thrust of the Rigases' argument here is that the District Court failed to make adequate factual findings to support this enhancement. According to the Rigases, had the District Court scrutinized the record, it would have realized that the Rigases merely oversaw employees who committed fraud and were not themselves "criminally responsible" for any misconduct. Appellant's Br. 58.[3] We detect no error in the District Court's conclusion, which "expressly adopt[ed] the position set forth by the government [at the] sentencing hearings, ... [and] satisfied its obligation to make factual findings." United States v. Eyman, 313 F.3d 741, 745 (2d Cir.2002). For the same reason, we also reject the Rigases' argument that the District Court failed to specify who exactly was harmed before imposing a "fifty victim" sentencing enhancement.

3. "Substantive Reasonableness"
The Rigases also argue that their sentences were substantively unreasonablethat is, the sentences of twelve and seventeen years for John and Timothy Rigas, respectively, were "`greater than necessary'" to accomplish the purposes of sentencing (just punishment, deterrence, rehabilitation, etc.). Appellant's Br. 72 (quoting 18 U.S.C. § 3553(a)). In particular, the Rigases observe that their sentences for "white-collar" crimes are only slightly shorter than the sentences of some admitted or convicted terrorists. See Appellant's Br. 74. When, at oral argument, we inquired what a "substantively reasonable" sentence might be, counsel for the Rigases replied that it was unclear but that any sentence must take account of the Rigases culpability.
Where, as here, we have identified "`no significant procedural error'..., a reviewing court then `considers the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard,' taking `into account the totality of the circumstances, including the extent of any variance from the Guidelines range.'" *122 Cavera, 550 F.3d at 200 (Raggi, J., concurring) (brackets omitted) (quoting Gall, 128 S.Ct. at 597). As the en banc court observed in Cavera, "[w]e will ... set aside a district court's substantive determination only in exceptional cases where the trial court's decision `cannot be located within the range of permissible decisions.'" 550 F.3d at 189 (quoting Rigas, 490 F.3d at 238 (summarizing the abuse-of-discretion standard)). For example,
[a]t the substantive stage of reasonableness review, an appellate court may consider whether a factor relied on by a sentencing court can bear the weight assigned to it. To be sure, this review is deferential. As a result, we do not consider what weight we would ourselves have given a particular factor. Rather, we consider whether the factor, as explained by the district court, can bear the weight assigned it under the totality of circumstances in the case.
Cavera, 550 F.3d at 191 (citations omitted).[4] Accordingly, our role in sentencing appeals is to "patrol the boundaries of reasonableness, while heeding the Supreme Court's renewed message that responsibility for sentencing is placed largely in the precincts of the district courts." Id.
Our decisions addressing substantive reasonableness have focused more on the process of sentencing than on actually defining the boundaries of substantive reasonableness. Insofar as we have defined as "unreasonable" a sentence that cannot be "`cannot be located within the range of permissible decisions,'" Id. at 189 (quoting Rigas, 490 F.3d at 238), that definition is obviously circularwhat is reasonable or unreasonable is what other cases have deemed reasonable or unreasonable. It is therefore unsurprising that several courts, including our own, have cautioned against converting review for substantive reasonableness into a "rubber stamp." United States v. Rattoballi, 452 F.3d 127, 132 (2d Cir.2006) ("Our review for reasonableness, though deferential, will not equate to a `rubber stamp.'"); see also United States v. Pinson, 542 F.3d 822, 836-37 (10th Cir. 2008) ("[U]ntil the Supreme Court tells us otherwise[,] appellate review continues to have an important role to play and must not be regarded as a rubber stamp."); United States v. Moreland, 437 F.3d 424, 433 (4th Cir.2006) ("Although [a reasonableness] standard clearly requires us to afford a degree of deference to the sentencing decisions of the district court, `reasonableness' is not a code-word for `rubber stamp.'").
In other areas of the law, we employ various concepts that seek to capture the same idea represented in the phrase "substantive reasonableness." For example, we held that in considering a motion for a new trial in a criminal case following a jury verdict, the essential inquiry is whether a guilty verdict is manifestly unjust. See, e.g., United States v. Josephberg, 562 F.3d 478, 488 (2d Cir.2009) ("In deciding ... a motion [for a new trial], the district court must take care not to usurp the role of the jury, and the ultimate consideration is whether letting a guilty verdict stand would be a manifest injustice."). We examine intentional torts by state actors under a similarly imprecise "shocks-the-conscience" standard. See, e.g., O'Connor v. Pierson, 426 F.3d 187, 203 (2d Cir.2005) (observing that "`the measure of what is conscience-shocking is no calibrated yard *123 stick'" and that "the test `points clearly away from liability, or clearly toward it, only at the ends of the ... spectrum'") (quoting County of Sacramento v. Lewis, 523 U.S. 833, 847-48, 118 S.Ct. 1708, 140 L.Ed.2d 1043 (1998)).
The manifest-injustice, shocks-the-conscience, and substantive unreasonableness standards in appellate review share several common factors. First, they are deferential to district courts and provide relief only in the proverbial "rare case." Second, they are highly contextual and do not permit easy repetition in successive cases. Third, they are dependent on the informed intuition of the appellate panel that applies these standards. In sum, these standards provide a backstop for those few cases that, although procedurally correct, would nonetheless damage the administration of justice because the sentence imposed was shockingly high, shockingly low, or otherwise unsupportable as a matter of law.[5]See Rita v. United States, 551 U.S. 338, 365, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) (Stevens, J., concurring) ("[A] district judge who gives harsh sentences to Yankees fans and lenient sentences to Red Sox fans would not be acting reasonably even if her procedural rulings were impeccable."). Of course, an "intuitive" review cannot be an invitation to mischief by tinkering with any sentence that appellate judges simply do not like. See Gall, 128 S.Ct. at 597 ("The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court."); Cavera, 550 F.3d at 191 (same). Responsible appellate review of sentences necessarily places great trust in sentencing courts while still recognizing the responsibility to examine the actual sentence itself (quite apart from the procedures employed in arriving at the sentence).
Applying these general principles of "substantive reasonableness" to the instant case, we have no trouble concluding that, in the circumstances presented, the sentences imposed on the Rigases were reasonable. Indeed, we confronted many of the same arguments in reviewing the sentence of Bernard Ebbers, the former Chief Executive Officer of WorldCom, Inc. See Ebbers, 458 F.3d at 112, 129. Ebbers was convicted by a jury on multiple counts of conspiracy and securities fraud and received a sentence consisting principally of 25 years' imprisonment. Id. at 112. On appeal, Ebbers argued, among other things, that his sentence was unreasonably long, even though it was shorter than the recommend Guidelines sentence in that case (thirty years to life). See id. at 129 & n. 4. We recognized the potential shortcomings of the Guidelines sentences for "white-collar" offenses, including the apparent disparity between sentences for non-violent, corporate crimes and violent crimes punishable under state law:
Twenty-five years is a long sentence for a white collar crime, longer than the sentences routinely imposed by many states for violent crimes, including murder, or other serious crimes such as serial child molestation. However, Congress has directed that the Guidelines be a key component of sentence determination. *124 Under the Guidelines, it may well be that all but the most trivial frauds in publicly traded companies may trigger sentences amounting to life imprisonmentEbbers' 25-year sentence is actually below the Guidelines level. Even the threat of indictment on wafer-thin evidence of fraud may therefore compel a plea. For example, a [$ 0.15] decline in share price in a firm with only half the number of outstanding shares that WorldCom had would constitute a loss of $ 200 million. No matter how many reasons other than the fraud may arguably account for the decline, a potential defendant would face an enormous jeopardy, given the present loss table, and enhancements for more than 250 victims, for being a leader of a criminal activity involving 5 or more participants, and for being an officer of the company.
Id. at 129. Nonetheless, we concluded in Ebbers that, in the circumstances presented, stiff Guidelines sentences for "white-collar" crimes "reflect[ed] Congress' judgment as to the appropriate national policy for such crimes." Id. We also noted that Ebbers' fraud, like the Rigases' crimes, "were specifically intended to create a false picture of profitability even for professional analysts" and were "motivated by... personal financial circumstances." Id. at 130; see also Rigas, 490 F.3d at 214 (observing that in order to fulfill certain obligations to purchase Adelphia stock, the Rigases "borrowed funds to pay Adelphia, but then caused Adelphia to use that cash to pay off other family debts"); id. at 215 ("The government argued, and the jury apparently agreed, that [general] ledger entries [regarding co-borrowed debt] were fraudulent and intended to mislead stockholders and analysts about the debt the Rigas family and [their privately-held companies] owed to Adelphia."); id. at 215-17 (explaining how the Rigases were personally responsible for manipulating and approving publicly-filed earnings information and other data); id. at 237 n. 42 (noting that the jury heard "evidence of acts that occurred during the period charged in the indictment," including "evidence that Adelphia paid more than $500,000 for antiques in John Rigas's possession" and that the Rigases "used Adelphia funds and other assets for their personal benefit, and that of other members of the Rigas family").
Accordingly, we cannot conclude that this is the "rare case" that "`cannot be located within the range of permissible decisions.'" Cavera, 550 F.3d at 189 (quoting Rigas, 490 F.3d at 238). In light of the circumstances of the fraud perpetrated by the Rigases, the sentences imposed by the District Court on resentencing, which "reflect Congress' judgment as to the appropriate national policy for such crimes," Ebbers, 458 F.3d at 129, do not constitute a "manifest injustice" or "shock the conscience," and do not otherwise compel a conclusion that they are substantively unreasonable.

B. Motion for a New Trial
The Rigases also appeal the District Court's denial, in an opinion filed on November 20, 2007, of their Rule 33 motion for a new trial on the basis of "newly discovered evidence."[6]See Rigas, 2007 WL 4145282, at *5, 2007 U.S. Dist. LEXIS 85590, at *16. They argue, as they did before the District Court, that former co-defendant who testified as a government witnessJames Brown, the former Vice *125 President of Finance at Adelphiagave testimony in subsequent civil proceedings that contradicted his testimony at trial.
We review motions for a new trial under an "abuse-of-discretion" standard. See, e.g., United States v. Owen, 500 F.3d 83, 87 (2d Cir.2007); cf. Sims, 534 F.3d at 132 (explaining the "abuse-of-discretion" standard).
In a comprehensive opinion, the District Court compared Brown's testimony in a civil case to his testimony in the criminal case and found that they were largely consistent and did not indicate any perjury. Specifically, the Court found that Brown admitted to lying to Adelphia's auditors in a "variety of formats," Rigas, 2007 WL 4145282, at *2, 2007 U.S. Dist. LEXIS 85590, at *6, some of which were explored in greater detail in a subsequent civil enforcement proceeding conducted by the United States Securities and Exchange Commission ("SEC"). The District Court also concluded that Brown's testimony was not newly discovered, but was simply newly available. Id. at *6, 2007 U.S. Dist. LEXIS 85590, at *15 ("Because the testimony that [the Rigases] cite could have been available if [they] had subpoenaed these witnesses at the time of [the criminal] trial, there is no newly discovered evidence within the meaning of Rule 33."); see also Owen, 500 F.3d at 89 ("[W]e now join the majority of circuits to have addressed the issue and hold that Rule 33 does not authorize district courts to grant new trials on the basis of ... evidence [that] is not newly discovered, but merely newly available."). Finally, the District Court determined that Brown's civil testimony would have had no effect on the outcome of the criminal prosecution of the Rigases. Rigas, 2007 WL 4145282, at *6, 2007 U.S. Dist. LEXIS 85590, at *15-16
The District Court's November 20, 2007 opinion and order does not contain an error of law, is not based on any clearly erroneous assessment of facts, and is not outside the scope of permissible decisions. Accordingly, we affirm the denial of defendants' Rule 33 motion for a new trial.

C. Motion to Compel Production of Interview Notes
Finally, the Rigases argue that the District Court erred in not ordering the government to produce notes from interviews with various witnessesprincipally notes from interviews with Carl Rothenberger, Adelphia's former lead outside counsel. The Rigases further contend that the government was constitutionally compelled to disclose the notes pursuant to the rule of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).
We review a district court's ruling on a motion to compel discovery under an "abuse-of-discretion" standard. See, e.g., OSRecovery, Inc. v. One Groupe Int'l, Inc., 462 F.3d 87, 94 (2d Cir.2006); cf. Sims, 534 F.3d at 132 (explaining the "abuse-of-discretion" standard).
In this case, the District Court concluded that the government had no obligation under Brady or the Jencks Act, 18 U.S.C. § 3500the statute codifying the government's disclosure obligations during criminal proceedingsto disclose its interview notes with Rothenberger because he did not testify at the trial. See Rigas, 2008 WL 144824, at *1, 2008 U.S. Dist. LEXIS 2827, at *2; see also 18 U.S.C. § 3500(a) ("In any criminal prosecution brought by the United States, no statement or report in the possession of the United States which was made by a Government witness or prospective Government witness (other than the defendant) shall be the subject of subpoena, discovery, or inspection until said witness has testified on direct examination in the trial of the case." (emphasis *126 added)). In addition, the District Court found that the government was not in exclusive possession of any exculpatory information, since defendants knew of Rothenberger's role at Adelphia and the facts about which he could testify; accordingly, Brady did not compel disclosure of the government's interview notes with Rothenberger. See United States v. Paulino, 445 F.3d 211, 224 (2d Cir.2006) ("To establish a Brady violation, a defendant must show [inter alia, that] ... the evidence must have been suppressed by the State, either willfully or inadvertently...." (internal quotation marks omitted)); United States v. Gaggi, 811 F.2d 47, 59 (2d Cir.1987) ("[N]o Brady violation occurs if the defendant knew or should have known the essential facts permitting him to take advantage of any exculpatory evidence."). See generally United States v. Coppa, 267 F.3d 132, 140 (2d Cir.2001) ("Although the government's obligations under Brady may be thought of as a constitutional duty arising before or during the trial of a defendant, the scope of the government's constitutional dutyand, concomitantly, the scope of the defendant's constitutional rightis defined retroactively, by reference to the likely effect that the suppression of evidence had on the outcome of the trial.") Finally, the District Court found that the United States Attorney's Office was not in possession of notes from SEC interviews with Rothenberger or other witnesses, and did not have an obligation to disclose what they did not possess. See Rigas, 2008 WL 144824, at *2, 2008 U.S. Dist. LEXIS 2827, at *5-6.
We detect no error in the District Court's January 15, 2008 Order denying defendants' motion to compel discovery. Accordingly, we affirm.

CONCLUSION
To summarize:
(1) The District Court was required to resentence defendants de novo following the reversal of a portion of defendants' convictions by another panel of this Court.
(2) Based on the District Court's alternative ruling in its June 24, 2008 resentencing order, in which the Court resentenced defendants de novo, we conclude that the new sentences imposed on the Rigases were procedurally and substantively reasonable.
(3) We detect no error in the District Court's November 20, 2007 opinion and order denying the Rigases' motion for a new trial.
(4) We detect no error in the District Court's January 15, 2008 memorandum and order denying the Rigases' motion to compel discovery.
We have considered all of the Rigases arguments on this appeal. For the reasons stated above, we AFFIRM the judgment of the District Court.
NOTES
[1]  Our earlier decision in this case compels a conclusion that the consequences of the convictions on Count 23 were far from de minimis. As we observed, the alleged bank fraud "related to two of the three Co-Borrowing Agreements," Rigas, 490 F.3d at 217-18, which were required to "mask[ ] ... debts that the Rigas family [and their privately-held companies] owed to Adelphia." id. at 215. Masking the Rigases' private debt as Adelphia's debt was a cardinal goal of their scheme to defraud Adelphia. Id.; see also id. at 232-33 (outlining the specific proof that would be required to sustain the bank fraud convictions and the mechanism of alleged fraud); but see id. at 234-35 (explaining that, under the circumstances, defendants' misrepresentations to the banks were not "material" and could not support the conviction for bank fraud on Count 23). In addition, John Rigas was originally sentenced to an aggregate term of 15 years' imprisonment and received 15-year terms on each of two counts of bank fraud. The most he received on any other count was 10 years (for securities fraud). Timothy Rigas was originally sentenced to an aggregate term of 20 years' imprisonment, and he was sentenced to a term of 20 years on each of two counts of bank fraud. The most he received on any other count was 10 years (for securities fraud). Under these circumstances, Count 23 was part of the "constellation of offenses" and "factual mosaic" of this case, Quintieri, 306 F.3d at 1228, and, sentencing on that count cannot be considered de minimis.
[2]  The Rigases further contend that the District Court erred in calculating loss by not discounting the loss by the $715 million in liquidated private assets that the Rigas family pledged as collateral to several banks that underwrote co-borrowing agreements. Appellant's Br. 52 (citing U.S.S.G. § 2B1.1 cmt. n. 2(E)(ii) (providing that, "[i]n a case involving collateral pledged or otherwise provided by the defendant, [loss shall be reduced by] the amount the victim has recovered at the time of sentencing from disposition of the collateral")); see generally Rigas, 490 F.3d at 213-18 (describing the central role of co-borrowing agreementsbank loans for which Adelphia and private companies owned by the Rigases were jointly and severally liable for the debtsin the Rigases' fraud). We agree with the District Court that, even if the $715 million were considered, that amount was pledged only to banks to satisfy Adelphia's debts. The collateral could not compensate equity holders for their substantial losses. See Special App. 23.
[3]  This argument brings to mind the words of Judge Learned Hand, who confronted similar circumstances decades ago:

As is usual in such cases, we are urged incidentally in a brief whose length and prolixity only serves to confuse the reader to substitute ourselves for the jury and try the merits over again. We shall not labor the point that this we cannot do; but we do wish to emphasize that the established character of the scheme was alone enough to condemn it.
United States v. Bronson, 145 F.2d 939, 942 (2d Cir.1944) (L. Hand, J.).
[4]  The Rigases do not argue that any particular sentencing factor in 18 U.S.C. § 3553(a) "can[not] bear the weight assigned it under the totality of circumstances," Cavera, 550 F.3d at 191. Instead, they argue that the District Court "gave no specific consideration to any § 3553 factors," Appellant's Br. 72, and ultimately "impose[d] punishment far greater than necessary and betray[ed] the balance struck by § 3553," id. at 75.
[5]  To say that a sentence is "substantively unreasonable" is not to say that "no reasonable person" would have imposed such a sentence. We may generally assume that federal judges are "reasonable" people in the commonsense definition of the term. Nonetheless, even reasonable individuals can make unreasonable decisions on occasion. The Supreme Court recognizes this and has charged the Courts of Appeals with reviewing the substance of sentences for reasonableness, and we cannot employ a definition of "substantive unreasonableness" that would render the required review a dead letter.
[6]  Rule 33(a) of the Federal Rules of Criminal Procedure provides that "[u]pon the defendant's motion, the court may vacate any judgment and grant an new trial if the interest of justice so requires." Rule 33(b)(1) establishes a three-year window for "motion[s] for a new trial grounded on newly discovered evidence."
