
557 F.3d 15 (2009)
UNITED STATES of America, Appellee,
v.
Kevin HALL, Defendant, Appellant.
No. 07-1858.
United States Court of Appeals, First Circuit.
Heard April 9, 2008.
Decided February 19, 2009.
*16 Edward S. MacColl, with whom Thompson, Bull, Furey, Bass & MacColl, LLC, P.A. was on brief, for appellant.
Margaret D. McGaughey, Appellate Chief, with whom Paula D. Silsby, United States Attorney was on brief, for appellee.
Before LYNCH, Chief Judge, *17 MERRITT[*] and HOWARD, Circuit Judges.
HOWARD, Circuit Judge.
Kevin Hall was convicted of conspiring to distribute marijuana, money laundering, and tax evasion. 21 U.S.C. §§ 841(a)(1) & 846; 18 U.S.C. § 1956(a)(1)(B)(i); 26 U.S.C. § 7201.[1] For the second time, Hall appeals his conviction and sentence. In Hall's first appeal, we rejected his Brady challenge and affirmed his conviction. United States v. Hall, 434 F.3d 42 (1st Cir.2006). Ultimately, however, we remanded for resentencing because of the Supreme Court's intervening decision in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). In this appeal, Hall argues that on remand the district court erroneously denied his new trial motion, which was based on a renewed Brady challenge, and also erroneously denied his various requests for hearings. He also claims that the sentence imposed by the district court is unreasonable. After review, we affirm Hall's conviction and sentence.

I.
In United States v. Hall, we presented the background facts of this case in detail. 434 F.3d at 48-54 ("Hall I"). In discussing this appeal, we presume acquaintance with that opinion.
In his first appeal, Hall argued that the government committed a Brady violation by failing to disclose the full extent of the criminal history of one of its witnesses. This witness, John Redihan, testified against Hall pursuant to a plea agreement.
Before Hall's trial began, the government disclosed to the defense that Redihan had been convicted in Maine in 1998 of terrorizing, theft by extortion, and unlawful trafficking in marijuana. It also informed the defense that Redihan had been convicted in Rhode Island in 1998 of possessing a firearm and trafficking in steroids and Percodan. Redihan admitted these convictions at Hall's trial.
Following Hall's conviction, but prior to his sentencing, the probation office discovered additional details about Redihan's 1998 Rhode Island convictions. As it turned out, Redihan also had been convicted of conspiring to distribute marijuana and pled no contest to a charge that he possessed marijuana with intent to distribute.
In Hall I, we concluded that the government's failure to disclose additional details regarding Redihan's 1998 Rhode Island convictions did not amount to a remediable Brady violation. We explained in part:
[E]ven assuming the government had to disclose the details of Redihan's Rhode Island conviction, Hall has not shown sufficient prejudice to warrant relief. Brady prejudice exists where "there is a reasonable probability that the suppressed evidence would have produced a different verdict." Hall elicited from Redihan, on cross-examination, that he was a convicted drug dealer and that he had distributed drugs in Rhode Island. Additional detail about the Rhode Island conviction would have been mostly cumulative.
Hall I, 434 F.3d at 55 (internal citation omitted).
*18 Nevertheless, we remanded the case. The Supreme Court had issued Booker after Hall's initial sentencing. Because the district court had expressed some reservation when sentencing Hall, based on its uncertainty about the drug quantities involved in Hall's crimes and about Hall's personal circumstances, we remanded for resentencing in light of Booker.
While the case was on remand, Hall moved for a new trial based on the government's alleged Brady violation. Hall argued that his further research of both Redihan's 1998 Rhode Island convictions, and the investigation underlying them, produced additional evidence he characterized as material. This evidence consisted of an affidavit from a government informant which provided support for a warrant to search Redihan's house and police reports and witness statements describing the execution of that search. In the affidavit, the informant stated that Redihan was a large-scale marijuana trafficker who supplied others with marijuana from Redihan's house. The police reports and witness statements described how government agents seized a small amount of cocaine, Percodan, steroids, a twelve-gauge shotgun, and three large plastic storage bags containing 1004 grams of marijuana from Redihan's home. Primarily on the basis of this evidence, Hall requested an evidentiary hearing on his new trial motion.
The district court did not hold an evidentiary hearing on Hall's new trial motion and ultimately denied the motion. The district court interpreted our Brady decision in Hall I as constituting the "law of the case," concluding that our ruling in Hall I that there was no Brady prejudice, meant that there could be no remediable Brady violation. The court concluded that our prejudice ruling was based largely on the premise that the impeachment value of any additional information about Redihan's Rhode Island convictions would be diminished. Although Hall argued to the court that he had unearthed "new evidence" not presented in his first appeal, specifically, further details regarding Redihan's Rhode Island convictions and the investigation underlying them, the court considered the prejudice issue foreclosed.
In anticipation of resentencing, Hall filed two motions. The first was for the preparation of a new presentence report. In this motion, Hall outlined what he claimed was the government's disparate treatment of non-cooperating and cooperating defendants when disclosing evidence to the sentencing court. Specifically, Hall described the government's practice in the District of Maine of "piling on" speculative evidence of drug quantity for non-cooperating defendants but only introducing irrefutable evidence of drug quantity for cooperating defendants. This, Hall alleged, led to broad-based sentencing disparities between cooperating and non-cooperating defendants. His motion requested an evidentiary hearing.
Hall's second motion sought to compel the government to file a substantial assistance motion under either U.S.S.G. § 5K1.1 or 18 U.S.C. § 3553(e). Hall requested an evidentiary hearing on this motion as well, alleging that the government failed to file a substantial assistance motion because he had exercised his right to trial.
The district court rejected Hall's motions and his requests for hearings. The court explained that Hall's allegation regarding the government's disparate treatment of non-cooperating and cooperating defendants had been "fully ventilated" at his first sentencing. It also, alternatively, noted that the issue was beyond the scope of the remand. As for Hall's request for a hearing on the government's failure to file *19 a substantial assistance motion, the court explained that Hall had failed to make a substantial threshold showing of a constitutional violation by the government. It also considered this issue to be beyond the scope of the remand.
The district court ultimately sentenced Hall to 120 months imprisonment.[2] This appeal followed, in which Hall presents myriad challenges to both his conviction and sentence.

II.
Hall first challenges the district court's denial of both his new trial motion and his request for a hearing on that motion. We review both rulings for an abuse of discretion. United States v. Connolly, 504 F.3d 206, 211, 220 (1st Cir.2007).
To cut to the chase, no new trial was warranted. Regardless of whether the district court correctly concluded that our original decision in Hall I foreclosed Hall's renewed Brady claim, the claim fails in all events. To justify a new trial, Hall must show that the government's failure to disclose evidence caused him prejudice. Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999); see also United States v. Morales-Rodriguez, 467 F.3d 1, 14 (1st Cir.2006). Prejudice occurs where withheld evidence is "material." Morales-Rodriguez, 467 F.3d at 15. Evidence is "material" if there is "a reasonable probability that had [it] been disclosed to the defense, the result of the proceeding would have been different." Id.
The evidence Hall identifies  Redihan's 1998 Rhode Island convictions for conspiracy to traffic marijuana and possession of marijuana with intent to distribute and information about the government's underlying investigation of these convictions  is not material. It is merely cumulative of the impeachment evidence adduced at Hall's trial. United States v. Garcia-Torres, 341 F.3d 61, 70 (1st Cir. 2003) ("Impeachment evidence that is merely cumulative ... is insufficient to establish prejudice under Brady.") (citations omitted). For example, at Hall's trial Redihan admitted that in 1998 he had been convicted in Maine for marijuana trafficking and that, in the same year, he had been convicted in Rhode Island for trafficking in Percodan and steroids. Put simply, the jury was well aware that Redihan dealt drugs, including marijuana. See Connolly, 504 F.3d at 217 ("Given [the government witness's] extensive criminal history, it would not have been an abuse of discretion for the district court to find that the absence of additional cross-examination on essentially the same well-developed theme would not undermine confidence in the jury's verdict.").
Moreover, the government presented evidence sufficient to convict Hall on all counts. This evidence is discussed at length in our first decision, and we will not rehash it here. Hall I, 434 F.3d at 49-56. Although the evidence included testimony from Redihan, other witnesses corroborated his testimony in large part and none of the testimony from these witnesses was inconsistent with Redihan's in any material way. See Connolly, 504 F.3d at 217 n. 6 (noting that the value of impeachment evidence is reduced "when the witness's testimony is supported by substantial corroborating evidence") (citing United States v. Gonzalez-Gonzalez, 258 F.3d 16, 22-23 (1st Cir.2001)). Accordingly, the court acted within its discretion in denying Hall's new trial motion.
*20 The court also acted within its discretion in denying Hall's request for a hearing on his new trial motion. Hall requested a hearing on his new trial motion for two reasons: (1) to find out what the government knew about Redihan's 1998 Rhode Island convictions prior to Hall's trial; and (2) to learn more about Redihan's marijuana dealing in general.
In determining whether an evidentiary hearing is needed, a district court must make a "practical, commonsense evaluation." Connolly, 504 F.3d at 219. Here, the court could have validly concluded that, regardless of what the government knew or did not know about Redihan's criminal history, an evidentiary hearing would be fruitless because additional impeachment evidence regarding Redihan would be cumulative. Such a conclusion would not have been baseless. In declining Hall's request for a hearing, the court had access to documents detailing the investigation that led to Redihan's Rhode Island convictions. These documents, which were attached to Hall's new trial motion, allowed the court to assess the need for a full-blown evidentiary hearing regarding Redihan's various marijuana dealing. See Connolly, 504 F.3d at 220 (recognizing that new trial motions are ordinarily decided on paper records). As we have said, "evidentiary hearings on new trial motions in criminal cases are the exception rather than the rule." Id. at 206. The court acted within its discretion in concluding this case fell within the rule.[3]
Next, Hall challenges the court's refusal to receive evidence on the government's alleged practice of inappropriately treating cooperating and non-cooperating defendants differently and to hold a hearing on the government's failure to file a substantial assistance motion pursuant to either U.S.S.G. § 5K1.1 or 18 U.S.C. § 3553(e). We address each challenge in turn. Our review, again, is for an abuse of discretion. Owens v. United States, 483 F.3d 48, 57 (1st Cir.2007).
At Hall's first sentencing, his counsel described the government's alleged practice of selectively withholding or piling on drug quantity evidence for sentencing purposes, referring, somewhat colloquially, to a practice known generally as "fact-bargaining." On remand, and prior to Hall's second sentencing, Hall's counsel renewed the argument, requesting an opportunity to present evidence regarding the practice.
The district court denied the request in part because it concluded that Hall's claim that the government inappropriately treated cooperating and non-cooperating defendants disparately had been "fully ventilated" at the first sentencing. At that first sentencing, the court observed that prosecutors could offer what the court characterized as "extraordinary" inducements to people who cooperate, including inducements concerning the presentation of evidence. The court acted within its discretion in declining to entertain evidence on this issue that had been addressed previously.
*21 Although Hall trains this particular challenge on the court's decision not to entertain evidence on the government's sentencing practices in Maine, to the extent he is challenging fact-bargaining in general, its lack of transparency in certain cases, or both, these arguments also fail. We have upheld the practice generally. See United States v. Yeje-Cabrera, 430 F.3d 1, 20-30 (1st Cir.2005) (providing an extensive discussion on practice of fact-bargaining and its constitutionality). Inherent in many forms of fact-bargaining is the withholding of certain evidence from the court such as, for example, speculative evidence on drug quantity. See William L. Gardner & David S. Rifkind, A Basic Guide to Plea Bargaining Under the Federal Sentencing Guidelines, 7 Crim. Just. 14, 16 (Summer 1992) ("Where facts are unclear or unascertainable, the parties may agree on some form of them without further justification or explanation to the court."); see also Cabrera, 430 F.3d at 28 ("Even if the prosecutor knew and could prove a gun enhancement at the time of the plea bargain, that fact would not make a difference to our analysis. No misrepresentation was made; rather, there was an omission, helpful to the defendant, which was an implicit part of the bargain."); Thore v. Howe, 466 F.3d 173, 183 (1st Cir.2006) ("[G]uilty pleas do not necessarily establish absolute historic facts; what is stated in a plea agreement is an agreed-upon version of the facts that, while it avoids misrepresentation, is sufficient to support the entry of the plea.").[4]
We also conclude that the court acted within its discretion in denying Hall's request for a hearing regarding the government's decision not to file a substantial assistance motion. To be entitled to an evidentiary hearing on the government's refusal to file such a motion, Hall had to make a "substantial" threshold showing of a constitutional violation. Wade v. United States, 504 U.S. 181, 186, 112 S.Ct. 1840, 118 L.Ed.2d 524 (1992); United States v. Alegria, 192 F.3d 179, 187 (1st Cir.1999). In his request for a hearing, Hall emphasized that he had provided the government with information that it used against Redihan, and observed that Redihan received a significant downward departure for providing information used against Hall. Hall claimed that the government refused to file a substantial assistance motion on his behalf because of his decision to go to trial. He did not assert racial, religious, or other invidious discrimination.
The district court was well within its bounds in concluding that Hall had not made a substantial showing of a constitutional violation. See Wade, 504 U.S. at 186, 112 S.Ct. 1840 ("[A] claim that a defendant merely provided substantial assistance will not entitle a defendant to a remedy or even to discovery or an evidentiary hearing."); Alegria, 192 F.3d at 189 (upholding district court's denial of evidentiary hearing where defendant offered "conclusory assertions" of bad faith but no *22 persuasive evidence). We further note that, when denying Hall's request for a hearing, the district court observed that the government's refusal to file a substantial assistance motion was justified for a host of reasons. Hall lost his composure in a proffer session, obstructed justice by attempting to influence another witness's testimony, and admitted at his first sentencing that he had not cooperated truthfully with the government at all times.[5]
We turn, finally, to Hall's challenge to his sentence. In line with his requests for evidentiary hearings, Hall argues that his sentence is unreasonable because: (1) he was denied an opportunity to present evidence of a broad-based sentencing disparity between pleading defendants and those who go to trial; and (2) his sentence is more severe than the sentence imposed on Redihan.
In reviewing a sentence, we look at whether the sentence is both procedurally sound and substantively reasonable, taking into account the totality of the circumstances when considering reasonableness. Gall v. United States, ____, U.S. ____, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007); see also United States v. Martin, 520 F.3d 87, 92 (1st Cir.2008). Review for substantive reasonableness amounts to review for an abuse of discretion. Gall, 128 S.Ct. at 591.
We have already explained why the court was not required to take evidence on sentencing disparities between defendants who plead guilty and those who do not. As for Hall's complaint based on Redihan's sentence, the differences between the sentence given to Redihan, a cooperating defendant who pled guilty, and to Hall, a non-cooperating defendant who went to trial, are significant but not unjustifiable. Redihan and Hall were not "similarly situated" for sentencing purposes. See United States v. Brandao, 539 F.3d 44, 65 (1st Cir.2008). Unlike Redihan, Hall obstructed justice, changed his account of his role in the crime, and failed to accept responsibility. Hall's sentence reflects these differences and is not substantively unreasonable.[6]

III.
For the reasons provided above, we affirm.
NOTES
[*]  Of the Sixth Circuit, sitting by designation.
[1]  Altogether, he was convicted on 168 counts: one count of conspiring to distribute marijuana, 163 counts of money laundering, and four counts of tax evasion.
[2]  Hall was sentenced to 151 months imprisonment at his first sentencing.
[3]  Hall also argues that the district court erred in not granting his request for an evidentiary hearing because of its erroneous understanding that the law of the case doctrine precluded it from doing so. This argument is made for the first time in Hall's reply brief and is therefore waived. United States v. Eirby, 515 F.3d 31, 37 n. 4 (1st Cir.2008) ("[I]ssues ... advanced for the first time in an appellant's reply brief are deemed to have been waived.") (citation omitted). But, in any event, the argument appears inaccurate. In resolving Hall's motion for a new trial, which was based on the allegedly new evidence Hall had unearthed, the court did not rely on the law of the case doctrine. See United States v. Hall, 434 F.Supp.2d 19, 24-25 (D.Me.2006).
[4]  Differing treatment of defendants who plea bargain and those who go to trial does not render unconstitutional the practice of plea bargaining in general, or fact-bargaining in particular. See Cabrera, 430 F.3d at 25 ("The fact that the defendant who pleads gets a benefit over those who go to trial and are convicted is a necessary artifact of any plea bargaining regime. The law long ago determined there was nothing unconstitutional about any `burden on trial rights' caused by such a differential."). Of course, the government must refrain from acting vindictively "in retaliation against the exercise of rights by a defendant." Cabrera, 430 F.3d at 25. But vindictiveness concerns arise in a discrete set of circumstances not present here. Id. at 26 (citing North Carolina v. Pearce, 395 U.S. 711, 725, 89 S.Ct. 2089, 23 L.Ed.2d 656 (1969)).
[5]  We note that Hall also contends that the court failed to directly address his disparate treatment and substantial assistance claims based on the erroneous belief that those issues were beyond the scope of the remand in Hall I. Although the court did observe in a written procedural order that the scope of the remand was limited, the court nevertheless offered alternative reasonswhich we have limned abovefor rejecting each of Hall's challenges.
[6]  In a last gasp effort, Hall urges us to break with the Supreme Court's precedent in Booker. We decline to do so.
