ORDER AND JUDGMENT*
MICHAEL W. McCONNELL, Circuit Judge.Beginning in the late 1980s and continuing until 2004, Randy McArthur embezzled millions of dollars from the Bank of Ephraim in Ephraim, Utah. When he was finally caught, the unreconciled balance in the account over which he had responsibility was nearly $5 million. Mr. McArthur pleaded guilty to bank fraud but disputed what portion of that $5 million imbalance was traceable to his crime. Based on the evidence the government presented at Mr. McArthur’s sentencing hearing, the district court found that he stole between $3 million and $4 million of that $5 million imbalance and sentenced him accordingly. And because the government was forced to expend resources to prove the total amount of money Mr. McArthur stole, it refused to move for an acceptance of responsibility reduction under § 3El.l(b) of the United States Sentencing Guidelines.
Mr. McArthur now appeals from the district court’s loss finding and the government’s failure to move for a § 3El.l(b) reduction. We find no error in the proceedings below and therefore affirm.1
*834I. FACTS
Beginning in the 1980s, Mr. McArthur began a series of fraudulent transactions that enabled him to steal, for the better part of two decades, millions of dollars from the Bank of Ephraim (“Bank”), a community bank in the central Utah town from which it took its name. As the Bank’s cashier, Mr. McArthur was responsible for reconciling the Bank’s accounts with Zions Bank and Far West Bank. He perpetrated the fraud by writing cashier’s checks payable from the Bank to the Far West Bank; cashing the check at Far West, informing the Far West teller that the Bank needed cash on hand; and then keeping the cash for himself instead of returning it to the Bank. He concealed those fraudulent transactions by altering statements to make it appear as if the cashier’s check proceeds were deposited in the Bank’s account at Zions. Mr. McArthur reported that “it was easy to hide the embezzlement” during the 1980s and early 1990s because “there were no internal controls” at the Bank “and outside audits were ‘lax.’ ” R. Vol. VI, at 5.
The ruse became more difficult in the mid-1990s because of the advent of computer-generated bank statements and greater internal controls at the Bank. Around this time, Mr. McArthur’s longtime friend and subsequent codefendant Dean Johnson began helping Mr. McArthur perpetrate the fraud by falsifying various computer statements. Their joint venture continued until 2004, when an anonymous tip led to the discovery of the embezzlement scheme and the fact that the Bank’s accounts were out of balance by nearly $5 million. This, in turn, caused the Bank to collapse and be placed in receivership with the Federal Deposit Insurance Corporation.
Mr. McArthur pleaded guilty to bank fraud and aiding and abetting in violation of 18 U.S.C. §§ 1344 and 2. Following a lengthy evidentiary hearing, the district court found that Mr. McArthur caused a loss of between $3 million and $4 million to the Bank. After applying several enhancements and an acceptance of responsibility reduction, the district court found that Mr. McArthur’s Guidelines offense level was 29 and his criminal history category was I, resulting in an advisory Guidelines range of 87 to 108 months. It then heard argument relating to the 18 U.S.C. § 3553(a) sentencing factors before sentencing Mr. McArthur to 87 months imprisonment. He now appeals, challenging the district court’s loss calculation and its failure to deduct one additional level from his Guidelines offense level for timely notifying the government of his intention to accept responsibility. He also alleges that the government breached his plea agreement by refusing to recommend a § 3El.l(b) reduction. We have jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a).
II. DISCUSSION
A. Burden of Proof for Sentencing Facts
Mr. McArthur first argues that the district court should have required the government to prove sentencing facts beyond a reasonable doubt. He acknowledges, however, that our precedent forecloses this argument, see United States v. Magallanes, 408 F.3d 672, 684-85 (10th Cir.2005), and that he raises it merely to preserve it, see Appellant’s Br. 7-8. We therefore affirm.
B. The Government Proved by a Preponderance of the Evidence that Mr. McArthur Caused a Loss of at Least $2.5 Million.
In calculating Mr. McArthur’s Guidelines offense level, the district court *835applied an 18-level enhancement under § 2Bl.l(b)(l) after finding that McArthur caused a loss to the Bank of “between 4 million and 3 million,” but “certainly ... more than $2,500,000.” R. Vol. IV, at 160. Mr. McArthur challenges this finding, arguing that there is no factual basis in the record for valuing the actual loss, and that the district court’s range of $3 million to $4 million is an unreasonable estimate. We disagree.
“When evaluating sentence enhancements under the Sentencing Guidelines, we review the district court’s factual findings for clear error and questions of law denovo. We will not disturb a factual finding unless it has no basis in the record.” United States v. Mozee, 405 F.3d 1082, 1088 (10th Cir.2005) (citations omitted) (emphasis added). And when, as here, we review a district court’s “decision to apply an enhancement, we view the evidence and inferences therefrom in the light most favorable to the district court’s determination.” Id.
The record is replete with evidence that, together with inferences from it, prove by a preponderance of the evidence, see United States v. Swanson, 360 F.3d 1155, 1168 (10th Cir.2004), that the loss amount was at least $2.5 million. For example, during Mr. McArthur’s sentencing hearing, the government presented testimony from, among others, Keith Church, the former Bank president; Gary Myers, the accountant the Bank hired to audit its books after Mr. McArthur’s scheme collapsed; and Todd Argyle, the FBI special agent who investigated the crime. All three witnesses testified that Mr. McArthur admitted to stealing at least $4 million from the Bank. See R. Vol. IV, at 35, 91-92, 127. Mr. McArthur attempts to discredit his admission by calling it “mathematically impossible” and “not credible,” ultimately arguing that he “was simply wrong about how much money he stole.” Appellant’s Br. 11. “[T]he credibility of the witnesses and the weight to be given the evidence,” however, “together with the inferences, deductions and conclusions to be drawn from the evidence, are all matters most appropriate for resolution by the district court.” United States v. Guerrero, 472 F.3d 784, 789 (10th Cir.2007) (internal quotation marks omitted). We see no reason to reverse the district court’s finding on credibility.
And even if Mr. McArthur is correct that it is mathematically impossible for him to have stolen $4 million, the relevant numbers for purposes of appeal are $2.5 million — the amount at which, under § 2Bl.l(b)(l)(J), his 18-level Guidelines enhancement applies — and $3 million, the amount of his restitution order. Mr. McArthur’s brief does not argue that the latter two numbers are mathematically impossible. To the contrary, he states in his brief “that the amount of loss was at least $1.6 million but no greater than $3.8 million.” Appellant’s Br. 14. Because both the relevant loss amounts are within that range, Mr. McArthur’s mathematical impossibility argument is without merit, and any error the district court made by including $4 million in the range of possible loss was harmless.
The district court also heard testimony that the amounts Mr. McArthur stole were “pretty consistent” from the 1980s until 2004. Id. at 93. At the time of the sentencing hearing, data from the earlier years of the scheme was either unavailable or as-yet undiscovered, but the existing evidence from the later years showed that Mr. McArthur stole $1,154,500 between 1999 and 2004. Appellant’s Br., Attach. B, at 1. That period of time was, by McArthur’s own admission, a more difficult operating environment due to the increased internal controls and change in bank state*836ment format. Given this admission, it was not unreasonable for the district court to assume that the amounts of the earlier thefts were roughly equivalent to the amounts of later ones.
This same evidence also shows why the court’s estimate of damages conforms to the Guidelines standard. The commentary to Section 2B1.1 instructs that district courts “need only make a reasonable estimate of the loss” and that “the court’s loss determination is entitled to appropriate deference” because “[t]he sentencing judge is in a unique position to assess the evidence and estimate the loss based upon that evidence.” U.S.S.G. § 2B1.1 cmt. 3(C) (emphasis added). Courts are to consider “factors such as ... the scope and duration of the offense” when estimating the loss amount. Id. cmt. 3(C)(v). The district court properly considered this factor, as shown by the statement it made when rejecting Mr. McArthur’s argument that the amount of loss traceable to him was limited to $1.6 million:
To believe the 1.6 [million loss] story would require me to find, which I cannot do, there is no evidence, that during the perhaps nine or 10 years where you ... can’t see what happened that Mr. McArthur took a much, much smaller amount tha[n] he took in the later years, and those later years are the years where controls were tighter, and it simply is not credible.
R. Vol. IV, at 161-62.
This reasoning, together with the evidence recounted above, convinces us that the district court’s estimate — particularly the lower end of its range — was not unreasonable under the Guidelines. To be sure, Mr. McArthur introduced evidence that shows some of the $5 million total missing from the Bank’s account was due to bad checks, bank fees, other mathematical computations, and theft by another employee, see id. at 111-12, but these facts of themselves do not render the district court’s estimate unreasonable.
In sum, Mr. McArthur concedes that range of loss attributable to him is between $1.6 million and $3.8 million. After a lengthy evidentiary hearing during which Mr. McArthur was represented by able defense counsel, the district court found he was responsible for at least $2.5 million in loss — an amount squarely within this conceded range — and enhanced his sentence accordingly. The record contains sufficient evidence to support this finding. We therefore affirm the district court’s decision to apply the enhancement.
C. The $3 Million Restitution Order Was Not Clearly Erroneous.
Mr. McArthur next argues that the district court erred by imposing a $3 million restitution order. He acknowledges that the Mandatory Victims Restitution Act, 18 U.S.C. § 3663A(c)(l)(A)(ii), requires restitution in this case, but argues that the amount of the award was too high because “the government did not establish by a preponderance that Mr. McArthur had caused a $3 million loss.” Appellant’s Br. 19.
As discussed above, however, $3 million was the low end of the district court’s estimated loss range, which we have held was not unreasonable. This amount is also within the loss range Mr. McArthur conceded was attributable to him. These facts, combined with the testimony and other evidence discussed above, persuade us the record supports a finding that Mr. McArthur caused a $3 million loss. The district court’s restitution order was therefore proper.
D. Acceptance of Responsibility
The district court decreased Mr. McArthur’s offense level by two levels un*837der § 3El.l(a) of the Sentencing Guidelines for acceptance of responsibility. He claims that he was entitled to the additional one-level decrease under § 3El.l(b). We disagree.
After Mr. McArthur filed his brief, this Court published United States v. Moreno-Trevino, 432 F.3d 1181 (10th Cir.2005), which held “that prosecutors have considerable discretion to file a motion” under § 3El.l(b). Id. at 1186. It also held that a court’s power to “review the government’s refusal to file a Section 3El.l(b) motion and grant a remedy” extends only to refusals that are “(1) animated by an unconstitutional motive, or (2) not rationally related to a legitimate government end.” Id. (internal quotation marks and citation omitted).
These holdings answer most of Mr. McArthur’s objections. He argues that the government failed to move for the § 3El.l(b) reduction based on a misperception that his acceptance was untimely, which he alleges was not a rational basis for doing so. This argument miseharacterizes § 3El.l(b). That section makes an additional one-level reduction available to defendants whose timely acceptance of responsibility “permit[s] the government to avoid preparing for trial and permitting the government and the court to allocate their resources efficiently.” U.S.S.G. § 3El.l(b). As the government notes, Mr. McArthur’s acceptance of responsibility “did not save the government anything in proving substantial loss and destruction of a financial institution” because he “converted the sentencing hearing into a small trial” about the amount of loss he caused. Appellee’s Br. 46-47. The prosecutor made this argument below when he referred to testimony from defense witnesses at the sentencing hearing disputing Mr. McArthur’s involvement beyond the $1.6 million documented by Mr. Myers, the accountant. See R. Vol. IV, at 167.
It is not irrational for the government to decline to move for a one-level acceptance of responsibility reduction when the defendant pleads guilty to fraud but contests the loss amount traceable to him in the hopes of obtaining a lower § 2B1.1 enhancement. See United States v. Blanco, 466 F.3d 916, 918 (10th Cir.2006) (“Ensuring efficient resource allocation is a legitimate government end and a stated purpose of § 3El.l(b). And a prosecutor’s decision not to make a § 3El.l(b) motion on behalf of a defendant who requests independent [drug] reweighing, with its concomitant resource expenditure, is rationally related to that end.”). We therefore affirm the district court’s decision not to award Mr. McArthur an additional one-level reduction under § 3El.l(b).
E. Breach of the Plea Agreement
Finally, Mr. McArthur argues that the government’s failure to move for a § 3El.l(b) reduction was a breach of his plea agreement. We review de novo a claim that the government has breached a plea agreement. United States v. Werner, 317 F.3d 1168,1169 (10th Cir.2003).
Our review of the record persuades us that no breach of the plea agreement has occurred. One page of the statement in advance of plea is missing from the record, the result an apparent docketing error in the district court. See R. Vol. I, Doc. 35, at 5-7 (containing pages five and seven of the statement in advance of plea but omitting page six). As such, we rely on the recitation in Mr. McArthur’s brief of the plea agreement’s contents, which he quotes as stating:
Here, the plea agreement stated that the government would recommend that the defendant’s offense level under the Sentencing Guidelines be decreased by *838two or three levels for acceptance of responsibility, as appropriate, if, in the opinion of the United States, the defendant clearly demonstrates acceptance of responsibility for his offenses, as set forth in Section 3E1.1 of the Sentencing Guidelines.
Appellant’s Br. 31-32 (quoting R. Yol. I, Doc. 35, at 6-7).2
Mr. McArthur received a two-level reduction under § 3El.l(a) for acceptance of responsibility. The plain terms of the plea agreement — which set forth the government’s obligation as a disjunctive proposition, i.e., to recommend a reduction of two or three levels as appropriate — have thus been met. And the agreement vests the government with discretion to determine whether Mr. McArthur demonstrated acceptance of responsibility “as set forth in Section 3E1.1 of the Sentencing Guidelines,” which, as previously discussed, includes the requirement of “permitting the government and the court to allocate their resources efficiently.” U.S.S.G. § 3El.l(b). Simply because the government exercised its contractual discretion to reach a result unwanted by Mr. McArthur does not mean that a breach occurred. Indeed, the government’s conduct was well within the bounds of permissible action under the plea agreement. We thus find no breach of the agreement that would entitle Mr. McArthur to relief.
III. CONCLUSION
The judgment of the United States District Court for the District of Utah is AFFIRMED.
After examining the briefs and appellate record, this panel has determined unanimously that oral argument would not materially assist in the determination of this appeal. See Fed. R.App. P. 34(a)(2); 10th Cir. R. 34.1(G). This case is therefore submitted without oral argument. This order and judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. It may be cited, however, for its persuasive value consistent with Fed. R.App. P. 32.1 and 10th Cir. R. 32.1.
. We apologize to the parties for our delay in acting on this appeal, which somehow disappeared from the Court’s case-tracking system, and thank counsel for calling the matter to our attention.
. We are puzzled by Mr. McArthur’s ability to quote a non-existent record page. We assume he is able to quote the missing page because he has a copy of the entire agreement, notwithstanding the government’s failure to docket the entire agreement at the district court.