
617 F.3d 452 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Glenn Lee BACON, Defendant-Appellant.
No. 09-1793.
United States Court of Appeals, Sixth Circuit.
Argued: July 28, 2010.
Decided and Filed: August 19, 2010.
*454 ARGUED: Jeffrey J. O'Hara, Grand Rapids, Michigan, for Appellant. Jennifer L. McManus, Assistant United States Attorney, Grand Rapids, Michigan, for Appellee. ON BRIEF: Jeffrey J. O'Hara, Grand Rapids, Michigan, for Appellant. Julie Ann Woods, Assistant United States Attorney, Grand Rapids, Michigan, for Appellee.
Before: GILMAN and COOK, Circuit Judges; and OLIVER, Chief District Judge.[*]

OPINION
RONALD LEE GILMAN, Circuit Judge.
Pursuant to a plea agreement, Glenn Lee Bacon pled guilty to one count of bank fraud. The agreement provided that the government would not oppose Bacon's request for a reduction under the U.S. Sentencing Guidelines for his acceptance of responsibility, but the Presentence Report (PSR) recommended only "reservedly" that Bacon receive this reduction. At Bacon's sentencing hearing, the district court denied Bacon the acceptance-of-responsibility reduction, citing the PSR and a letter that Bacon had written after his guilty plea that deflected responsibility for the crime. As a result, the district court placed Bacon in a higher Guidelines range than Bacon had anticipated, and utilized that range to impose a within-Guidelines sentence of 34 months' imprisonment. Bacon now appeals. For the reasons set forth below, we AFFIRM the judgment of the district court.

I. BACKGROUND
Bacon was charged in an information with one count of bank fraud, in violation of 18 U.S.C. § 1344(2). Roughly six weeks later, Bacon reached a plea agreement with the government. In essence, the agreement called for Bacon's consent to waive being indicted and to plead guilty to the bank-fraud charge in exchange for the government agreeing not to oppose his request to reduce his offense level under the Guidelines based upon the acceptance of responsibility. The government also agreed that, if Bacon received the acceptance-of-responsibility reduction, it would move for an additional one-level reduction because of Bacon's timely notification to the government of his intent to plead guilty. See U.S.S.G. § 3E1.1(b). Finally, the government agreed that it would not *455 charge Bacon with any additional crimes relating to the underlying bank fraud.
A month after their initial plea agreement, the parties filed an amended plea agreement. The amended agreement reiterated the terms described above, but added a requirement that Bacon cooperate with the government, and it discussed the possibility of the government filing a motion to reduce his sentence under either § 5K1.1 of the Guidelines or Rule 35(b) of the Federal Rules of Criminal Procedure, depending on his level of cooperation. Bacon pled guilty to one count of bank fraud shortly after the parties entered into the amended agreement.
Bacon's sentencing hearing occurred seven months later. As the district court explained at sentencing, Bacon's crime consisted of "defraud[ing] a credit union by falsifying information about his income and employment on loan applications on which the credit union relied in granting him loans." Specifically, Bacon was involved in a convoluted real-estate and mortgage-fraud scheme with at least two other peopleRonald Tran, who served as the credit union's manager, and David Walker, another customer of the credit unionin which he fraudulently applied for multiple loans with the credit union. Both Tran and Walker pled guilty to related crimes and were sentenced prior to Bacon's sentencing hearing.
When calculating Bacon's Guidelines range at his sentencing hearing, the district court initially stated that Bacon's offense level under the Guidelines was 16. This was "based on the Court's acceptance of the defendant's acceptance of responsibility reduction of two points." At this point, the court was relying on the PSR's calculation of Bacon's offense level, which included both the two-level acceptance-of-responsibility reduction and the one-level reduction for timely notification. This offense level, when combined with Bacon's criminal history category of II, equated to a Guidelines range of 24 to 30 months' imprisonment.
The district court then explained that "I have some reservations which I shared with the probation officer about the issue of acceptance of responsibility in this case, and I'm referring specifically to Paragraph 36 of the [PSR] in which Mr. Bacon submitted a written statement ... which in my view is considerably short of acceptance of responsibility." In this letter, which Bacon wrote and sent to the U.S. Probation Office, he blamed the offense in large part on Tran. Bacon claimed that he had not known that his actionsthe submission of loan applications and a forged employment-verification letter, all of which falsely stated that Bacon was employed and making a healthy salarywere wrong at the time of the offense. The letter stated, in particular, that when Bacon applied for the loans, he had "started work as the manager of a small store and was promised a salary of $52,000.00 a year." According to the PSR, this claim is demonstrably false.
Because of its stated reservations, the district court ultimately rejected Bacon's request for an acceptance-of-responsibility reduction. The court found Bacon's applicable offense level to be 18 without this reduction, and used this level to calculate a Guidelines range of 30 to 37 months' imprisonment.
After hearing arguments from both sides and considering Bacon's allocution, the district court discussed the sentencing factors contained within 18 U.S.C. § 3553(a). The court noted that the bank fraud committed by Bacon had nearly ruined the credit union from which he had acquired the loans, and that Tran and Walker had received sentences of 46 and 12 months' imprisonment, respectively. It *456 also explained that, even if it had granted Bacon's acceptance-of-responsibility reduction, the court likely would have varied upward in order to impose a sentence that reflected the seriousness of Bacon's offense. The court then sentenced Bacon to a term of 34 months' imprisonment, in the middle of its calculated Guidelines range.
Neither the parties nor the district court took into account that, under the Guidelines, the court's rejection of the acceptance-of-responsibility reduction also prevented Bacon from receiving the one-level reduction for timely notification of his willingness to plead guilty. See U.S.S.G. § 3E1.1(b). If the court had realized this and correctly reworked its calculations, Bacon's offense level would have been 19 instead of 18, with a corresponding Guidelines range of 33 to 41 months of imprisonment.
Bacon now appeals, contending that the district court erred in denying his request for an acceptance-of-responsibility reduction, and that his sentence is both procedurally and substantively unreasonable. The government responds by arguing that the court properly denied Bacon's request for an acceptance-of-responsibility reduction, and that his sentence is reasonable. Neither party has raised the argument that the district court's failure to eliminate the reduction for timely notification, and thus its failure to correctly calculate Bacon's actual Guidelines range, made Bacon's sentence procedurally unreasonable.

II. ANALYSIS

A. Standard of review
We review the district court's determination of whether to apply a Guidelines reduction under the clear-error standard. See United States v. Paulette, 457 F.3d 601, 608 (6th Cir.2006) (applying that standard in reviewing the district court's denial of an acceptance-of-responsibility reduction). In addition, we review a defendant's sentence for both procedural and substantive reasonableness. United States v. Thomas, 498 F.3d 336, 339 (6th Cir. 2007).

B. Procedural reasonableness
As the government explains in its brief, the district court erred in computing Bacon's Guidelines range. This occurred when the court denied Bacon's two-level acceptance-of-responsibility reduction, but failed to also rescind his one-level reduction for timely notifying the government of his intent to plead guilty. In other words, the reduction for timely notification depended on Bacon first receiving the acceptance-of-responsibility reduction. See U.S.S.G. § 3E1.1(b). The court therefore wrongly concluded that Bacon's offense level was 18. It was in fact 19.
Generally, where the district court commits an error in computing the Guidelines' recommended sentencing range, a defendant's sentence will be held to be procedurally unreasonable and a remand will be warranted. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007) (holding that an appellate court "must ... ensure that the district court committed no significant procedural error" in sentencing a defendant); United States v. Hazelwood, 398 F.3d 792, 801 (6th Cir.2005) (concluding that a remand for resentencing was needed due to the improperly imposed Guidelines enhancement). Because the district court in the present case erred in computing Bacon's Guidelines range, it committed a "significant procedural error." See Gall, 552 U.S. at 51, 128 S.Ct. 586.
Remand is not necessarily required, however, because such errors may be deemed harmless where we are "certain that ... any such error `did not affect the *457 district court's selection of the sentence imposed.'" Hazelwood, 398 F.3d at 801 (quoting Williams v. United States, 503 U.S. 193, 203, 112 S.Ct. 1112, 117 L.Ed.2d 341 (1992)). We determine whether the error is harmless by evaluating the extent of the error and considering whether the district court "adequately explained" the sentence "by reference to the 18 U.S.C. § 3553(a) factors." United States v. O'Georgia, 569 F.3d 281, 296 (6th Cir. 2009).
As explained in Part II.D. below, the district court thoroughly addressed the § 3553(a) factors. Moreover, the error in the Guidelines calculation was marginal because Bacon's sentence is within the properly calculated Guidelines range as well as within the erroneously calculated range. We therefore conclude that this error was harmless. Both parties apparently agree. The government conceded at oral argument that it wants to avoid the time and expense of another sentencing hearing, and Bacon did not pursue this issue on appeal, perhaps not wishing to take the risk of being resentenced at a higher offense level.
Bacon makes other arguments in support of his contention that his sentence was procedurally unreasonable, but these are wholly without merit. One such argument is that the district court's reference to a hypothetical "24-to-40-month" Guidelines range in its discussion of the § 3553(a) factors was a serious procedural error. Bacon fails to acknowledge, however, that the court in that instance was not referring to the actual Guidelines range, but rather to what the range would have been had it granted the acceptance-of-responsibility reduction. The fact that the court misspoke by saying "40" instead of "30" when discussing the high end of a hypothetical Guidelines range does not make Bacon's sentence procedurally unreasonable, particularly where the court had accurately described that range earlier in the proceedings.
Bacon also claims that the district court failed to give him a proper opportunity to respond to its concerns regarding the letter that he sent to the Probation Office. But the record belies this argument. Bacon's counsel asked for, and was granted, the opportunity to respond to the court's suggestion that Bacon had failed to accept responsibility for his crime. The court then invited Bacon to speak on his own behalf, noting that this was "one of the very important factors" that went into the court's sentencing decision. Bacon took that opportunity by speaking to the court for what appears from the transcript to be several minutes. When Bacon became emotional, the court gave him the opportunity to take a break or speak while sitting down. Eventually, Bacon told the court that "I've ... I can't talk. Thank you for the time, though." The record thus indicates that the court gave Bacon a reasonable opportunity to address the court's concerns about his failure to accept responsibility for his actions.
In addition, Bacon argues that the district court failed to explain its rejection of his motion for a downward variance, which was based on his record of "volunteering and helping others." He correctly asserts that a sentence may be deemed procedurally unreasonable if the court fails to explain why it rejected a nonfrivolous request for a different sentence. See United States v. Peters, 512 F.3d 787, 789 (6th Cir.2008) (citing Rita v. United States, 551 U.S. 338, 357, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007)).
Although the district court did not explicitly deny Bacon's motion, it did address his record of volunteering, noting that Bacon "self-reports lots of volunteer activities, *458 and he mentioned those [again] in his allocution here today." The court explained that it viewed these contentions skeptically, saying that "it's all self-reported for the most part without substantiation." In this way, the court in fact addressed the grounds for Bacon's motion and stated why it was not inclined to grant the same. Given that "[s]ometimes the circumstances will call for [only] a brief explanation" of why a district court "has rejected [a defendant's] arguments," Rita, 551 U.S. at 357, 127 S.Ct. 2456, the court's rather summary discussion of why it disfavored Bacon's motion for a downward variance does not make his sentence procedurally unreasonable.

C. The district court's denial of Bacon's acceptance-of-responsibility reduction
Bacon's primary argument on appeal is that the district court erred in denying his request for an acceptance-of-responsibility reduction under the Guidelines. In order to merit this reduction, Bacon bore the burden of proving his acceptance of responsibility by a preponderance of the evidence. See United States v. Roberts, 243 F.3d 235, 241 (6th Cir.2001).
According to the commentary to the applicable guideline, Bacon's entitlement to an acceptance-of-responsibility reduction depended on his "truthfully admitting the conduct comprising the offense(s) of conviction, and truthfully admitting or not falsely denying any additional relevant conduct for which [he] is accountable under § 1B1.3 (Relevant Conduct)." See U.S.S.G. § 3E1.1 cmt. n. 1(a). This same commentary explains that "a defendant who falsely denies, or frivolously contests, relevant conduct that the court determines to be true has acted in a manner inconsistent with acceptance of responsibility." Id.
At his plea hearing, Bacon appeared to accept responsibility for the crime of bank fraud. But in the months between his plea and the sentencing hearing, he drafted and submitted a letter to the U.S. Probation Office that portrayed himself as a victim, not as a person who recognized that he had committed a criminal act. The letter stated that, after he had submitted various fraudulent loan applications, he "learned that the process of which I was guided was improper." This claim is disingenuous because Bacon had previously admitted at his plea hearing that his loan applications contained information that he knew was false when he submitted them. Bacon's knowledge of the falsity, in other words, was not acquired later; he knew it at the time.
His letter also claimed that he simply submitted a "blank loan application" that he unwisely allowed Tran to fill in, and that he was betrayed by Tran. The letter therefore never acknowledged that Bacon knowingly submitted false information to the credit union. Even Bacon's brief concedes that the letter "puts way too much emphasis on Mr. Tran and too little emphasis on [Bacon's] own criminal acts."
Furthermore, Bacon continued to lie about certain details of his fraud in the letter. The letter stated, for example, that when he applied for the loans at issue, he was employed as the manager of a small store and had been promised a salary of $52,000. But the PSR reports that Bacon never worked at this store and, at oral argument, Bacon's counsel admitted that the PSR was correct on this point. Moreover, the owner of the store stated that the employment-verification letter that Bacon had submitted as part of his loan application was a forgery. And the felony information to which Bacon pled guilty charged him with giving the credit union "a false employment verification document," i.e., *459 the forged employment-verification letter. But in Bacon's letter to the Probation Office, he claimed that this suspect letter was "signed by the current owner of the store."
In addition, Bacon made equivocal statements at sentencing that further indicated his failure to accept responsibility for his actions. He told the district court, for example, that, "[a]s soon as I learned I had done something wrong, I absolutely took responsibility." But Bacon must have known that applying for loans using false information was wrong when he did it. Bacon also attempted to minimize his participation in the offense by telling the court that "[m]y role in this was simply using my name, using my signature." And Bacon made these statements after the district court stated that it had reservations about the acceptance-of-responsibility reduction. Bacon thus knew that the court was skeptical about his acceptance of responsibility, and he had the opportunity to make clear that he was admitting his culpability. But he chose not to take advantage of that opportunity.
Given this equivocation at sentencing and the statements in Bacon's post-plea letter that repeated falsehoods and blamed others for the fraud, the district court's rejection of Bacon's request for an acceptance-of-responsibility reduction was not clearly erroneous. See U.S.S.G. § 3E1.1 cmt. n. 1(a) (explaining that "a defendant who falsely denies, or frivolously contests, relevant conduct that the court determines to be true has acted in a manner inconsistent with acceptance of responsibility"); see also United States v. Wilson, 239 Fed. Appx. 260, 267 (6th Cir.2007) (upholding a district court's denial of a request for an acceptance-of-responsibility reduction because of the defendant's "evasive" and "illogical" description of his criminal activity).

D. Substantive reasonableness
Bacon's final claim is that his sentence is substantively unreasonable. The district court calculated the applicable Guidelines range as 30 to 37 months (without the acceptance-of-responsibility reduction) and imposed a sentence of 34 months' imprisonment. But the actual Guidelines range was 33 to 41 months' imprisonment without the reductions for both acceptance of responsibility and timely notification. Despite the district court's error, Bacon's 34-month sentence is still within the proper Guidelines range. Where such is the case, the sentence is viewed as presumptively reasonable on appeal. See United States v. Vonner, 516 F.3d 382, 389-90 (6th Cir.2008) (holding that a defendant had not rebutted the presumption that his within-Guidelines sentence was reasonable); see also United States v. Bolds, 511 F.3d 568, 581 (6th Cir.2007) (acknowledging that a within-Guidelines sentence is presumed to be reasonable on appeal, and noting that the substantive reasonableness of a sentence is evaluated under the abuse-of-discretion standard).
Bacon seeks to rebut this presumption by arguing that his sentence is substantively unreasonable because there is a disparity between the sentence he received and the sentences given to his two codefendants, Tran and Walker, who both pled guilty and were sentenced before Bacon. As shown below, however, this argument is contradicted by Bacon's own brief and is not supported by controlling law.
Bacon admits that "Mr. Tran [the manager of the credit union] was the most culpable of the three," while "Mr. Walker was the least culpable ... and [Bacon] was in the middle." He was sentenced accordingly, with Tran receiving a 46-month sentence, Walker a 12-month sentence, and Bacon a 34-month sentence. Bacon argues, *460 however, that his sentence was too close to Tran's, whereas he contends that it should have been closer to Walker's. But this argument hardly demonstrates an abuse of discretion. Furthermore, "the need to avoid unwarranted sentence disparities" mentioned in 18 U.S.C. § 3553(a)(6) refers to "national disparities among the many defendants with similar criminal backgrounds convicted of similar criminal conduct," not to "disparities between one individual's sentence and another individual's sentence, despite the fact that the two are co-defendants." United States v. Simmons, 501 F.3d 620, 623 (6th Cir.2007). Yet Bacon's disparity argument is based precisely on this latter comparison.
Bacon's argument also ignores the district court's thorough consideration of the various § 3553(a) factors. The court first discussed "the nature and circumstances of the offense," see 18 U.S.C. § 3553(a)(1), including the amount of money that Bacon never repaid the credit union, the type of loan transactions, and the long duration of his fraud. Next, the court reviewed Bacon's "history and characteristics," see id., including his age, educational background, employment record, and mental health. The court then addressed the issues of "just punishment" and "promot[ing] respect for the law." See id. § 3553(a)(2)(A).
These issues were viewed by the district court as particularly important in Bacon's case because, where a person "engage[s] in a series of transactions which you almost certainly have to know were not legitimate, there has to be a recognition that punishment must follow." The court also compared the fraud to a robbery, explaining that, "even when you don't use a gun to hold up a credit union, but you do it from the inside with phony information and phony loans, that kind of theft, which is really what it is at the bottom of it all, suggests a lack of respect for the law."
Moving on to other factors, the district court stated its belief that the issues of deterrence and protection of the public from further crimes by Bacon were not "particularly pertinent in this case." The court related that it also did not view Bacon's need for "rehabilitation via medical, educational, and correctional treatment" to be as important as the need for "punishment and promotion of respect for the law." Considering the need to avoid "unwarranted [sentencing] disparities," the court also discussed the sentences and restitution orders imposed on Tran and Walker.
The district court then noted its belief that the advisory Guidelines range "properly reflect[s] the statutory factors" in Bacon's case, explaining that it did not "think there's anything extraordinary about this case that would place it outside the heartland, and the [G]uidelines as I scored them." It reasoned that, even if the applicable Guidelines range was "as scored by the probation officer" (meaning with the acceptance-of-responsibility reduction and thus lower), the court "would vary upward from that because I don't think that is adequate to meet the requirements of the statute given ... the seriousness of the offense and the need for punishment." The court then sentenced Bacon to a term of 34 months' imprisonment.
In sum, the district court considered all of the applicable sentencing factors and reached a sentence within what it believed (and, ultimately, what is) the applicable Guidelines range. Bacon has thus failed to rebut the presumption that the court's decision was substantively reasonable. See Vonner, 516 F.3d at 389-90; see also United States v. Tristan-Madrigal, 601 F.3d 629, 636 (6th Cir.2010) (holding that a district court's sentence was substantively *461 reasonable where it "extensively" explained its reasoning and "analyzed each of the § 3553(a) factors in determining what constituted an appropriate sentence").
Furthermore, the district court's discussion of why the § 3553(a) factors called for a sentence of 34 months' imprisonment constituted a sufficient explanation of the sentencing decision to excuse its slight miscalculation of the Guidelines range, see United States v. O'Georgia, 569 F.3d 281, 296 (6th Cir.2009) (noting that a miscalculation of the Guidelines range may be excused where the district court adequately addressed the § 3553(a) factors), particularly given that the 34-month sentence was within the properly calculated Guidelines range and that neither party has complained about this miscalculation. See Part II.B. above.

III. CONCLUSION
For all of the reasons set forth above, we AFFIRM the judgment of the district court.
NOTES
[*]  The Honorable Solomon Oliver, Jr., Chief United States District Judge for the Northern District of Ohio, sitting by designation.
