JERRY E. SMITH, Circuit Judge:

Roy Hebron pleaded guilty of conspiracy to defraud the United States in connection with major disaster benefits in violation of 18 U.S.C. §§ 371 and 1040. He appeals his sentence, arguing that the government violated the plea agreement by advocating for a higher loss calculation than the one agreed to and that the district court erred in its loss calculation by including legitimate claims with fraudulent ones. We affirm.

I.

Hebron was mayor of Ball, Louisiana. After Hurricane Rita made landfall in September 2005, Hebron and Brenda Kimball, the town clerk, applied for funds from the Federal Emergency Management Agency ("FEMA"). Through its Public Assistance Program, FEMA provides help to local governments so they may quickly recover from major disasters, reimbursing towns for work such as debris removal, emergency protective measures, and the repair of disaster damage to publicly owned facilities. Thus, FEMA helps towns cover the costs associated with hurricane recovery, such as extra hours worked by town employees and extra equipment used in recovery efforts. After the hurricane, Ball requested about $134,000 from FEMA.

In the wake of Hurricane Gustav three years later, Hebron and Kimball again requested more than $309,000 from FEMA on behalf of Ball. But after reviewing the claim, the FBI launched an inquiry into possible fraud that implicated almost every employee of the small town, but specifically targeting the mayor, town clerk, chief of police, and several other members of the police department.

The investigation revealed that town officials had engaged in extensive fraud intended to bilk FEMA out of hundreds of thousands of dollars. As examples, Hebron claimed that the town had used sixteen 1½-ton trucks during the Gustav cleanup efforts, when in reality it used one-ton trucks, a difference in cost of about $11,730. Kimball and another female employee were listed in the project worksheets submitted to FEMA as operating trucks and trailers for hours, but they performed no manual labor at all during the clean-up efforts, a discrepancy of $13,397. One employee told the FBI he worked for a few hours on one weekend using a chainsaw and filling sandbags, but the documents sent to FEMA had listed him as using a chainsaw and operating a truck and trailer for thirty-two days. These are but a few examples of the many fraudulent claims; the presentence report ("PSR") noted that "discrepancies could be found in practically every employee/contractor" claim.

Other fraudulent claims by Hebron and Kimball were more complete fabrications. For instance, Hebron and Kimball billed FEMA almost $10,000 for dumpsters used following Hurricane Gustav, at the same time seeking and receiving reimbursement from Keep Louisiana Beautiful, Inc., a nonprofit organization, for the same dumpsters. As another example, Hebron requested reimbursement for about $21,000 in overtime hours worked by the town's employees, but FEMA's policy provides for overtime compensation only if the applicant normally pays its employees for overtime hours worked. Because Ball does not have a history of paying its employees for overtime hours, Hebron intended to defraud FEMA of all the requested overtime compensation. Upon further investigation, the FBI learned that Ball also billed more than $11,000 in overtime expenses after Hurricane Rita, though the investigation into the Rita reimbursements was less thorough, so the extent of the fraud following Rita is less well known.

Hebron's role in all of this was extensive and integral. He and Kimball prepared and submitted the official FEMA documents and the fraudulent internal Town of Ball documents that served as backup for all the town's employees, such as employee time sheets and town checks payable to individual employees. Hebron even went so far as calling a meeting for all town employees at which each employee was presented with bi-weekly time sheets to sign. The employees did not know who had calculated the work hours performed or how it was figured, but Hebron openly discussed "fudging" time and squeezing as much from FEMA as possible. On a separate occasion, when Barber and another employee presented Hebron with mileage reports from the police cruisers, Hebron insisted that the mileage be inflated.

After being indicted on three counts, Hebron pleaded guilty, pursuant to a written plea agreement, on only the first count: conspiracy to defraud the United States in connection with major disaster benefits (18 U.S.C. §§ 371 and 1040). In addition to agreeing to dismiss the other two counts, the government agreed as follows:

The government recommended a loss calculation between $70,000 and $120,000; Hebron argued that the appropriate number was $66,798.57; and the PSR calculated the loss as over $320,000. The government then endorsed the PSR's calculation.

Loss calculation was the main focus of the sentencing hearing. Hebron argued for, at most, $105,556, and the government essentially supported the PSR's calculation of $320,000, contending that $105,556 was "just the floor" of the appropriate amount, although both numbers would be reasonable. Hebron's primary objection to the PSR's calculation was that it included likely legitimate payments to the town with the fraudulent ones and thus was unreasonable.

The court overruled Hebron's objections and adopted the PSR's sentencing calculation, which included a twelve-point increase because the loss was over $200,000; the court departed downward in recognition of Hebron's long career in public service. The court sentenced Hebron to 48 months in prison, three years of supervised release, $25,000 in fines, and $105,556.10 in restitution to FEMA, owed jointly and severally with his codefendants.

II.

Hebron contends that the government breached the plea agreement when it advocated for the $320,000 loss amount in contravention of the plea agreement's terms of a loss of less than $200,000. This court reviews the alleged breach under the plain-error standard, because Hebron did not object to any breach in the district court. Puckett v. United States, 556 U.S. 129, 134-43, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009). Hebron argues that, at sentencing, his challenge to the loss amount and his assertion that the government had taken a position at sentencing inconsistent with the position in its sentencing memorandum suffice to preserve error on appeal. To the contrary, without a specific objection alerting the district court that the government has breached the plea agreement, the error is not preserved.1

To meet the plain-error standard, Hebron must show that (1) there is error; (2) the error was clear and obvious, not subject to reasonable dispute; and (3) the error affected his substantial rights. Puckett, 556 U.S. at 135, 129 S.Ct. 1423. Assuming those three prongs are satisfied, this court has the discretion to remedy the error, but only if it seriously affects the fairness, integrity, or public reputation of judicial proceedings. Id. In evaluating whether a plea agreement was breached, we apply general principles of contract law, construing the terms strictly against the government as drafter, to determine "whether the government's conduct is consistent with the defendant's reasonable understanding of the agreement." United States v. Elashyi, 554 F.3d 480, 501 (5th Cir.2008) (citations and internal quotation marks omitted).

In the plea agreement, the government agreed to a loss calculation of under $200,000. Although it abided by that agreement in its initial sentencing memorandum, it contended at the sentencing hearing that a calculation of $320,000 was not only reasonable but should be applied. Although it acknowledged that $105,000 would also be reasonable, it contended vigorously that $105,000 was "just the floor" and that a higher amount should be imputed as loss.

It is evident that the government breached the agreement. Hebron reasonably understood it to require the government not to oppose a loss calculation of less than $200,000 or at least not to argue for a higher one. The various justifications offered by the government do not change the conclusion that the error was clear and obvious.

First, the government contends that its statements at sentencing were the result of merely providing candid and full disclosure of the facts in response to questioning. See United States v. Reeves, 255 F.3d 208, 211 (5th Cir.2001). Though the government did appropriately answer the court's questions about how the PSR had calculated the $320,000 amount, it "crossed the line" from executing its duty to lay out the facts to advocating for a loss amount greater than the one to which it agreed.2

For example, when the government advocated that the court use the "intended loss amount," the court questioned, "And that intended amount is the three twenty plus thousand dollars that's mentioned in the PSR at — is it 46?" The government responded, "I think it's Paragraph Number 47, Your Honor, in the amended or revised version dated May 9th of 2011. $320,868.22." Later, the government similarly argued that Hebron should be "held accountable for the entire amount," namely $320,000. The court also appears to have interpreted the government's statements as urging a higher loss calculation. The government "could have chosen to not take a position on the enhancement, but instead chose to remark on the appropriateness of its application," and, as a result, it violated the plea agreement by arguing for a higher loss calculation than agreed to, "even if mildly."3

Citing Puckett, 556 U.S. at 140 n. 2, 129 S.Ct. 1423, the government also maintains that, because the court requested specific argument on the issue of loss calculation, the government was no longer bound to the plea agreement on that issue. The Court in Puckett had left open the possibility that a clear breach of the plea agreement was not error, because of intervening circumstances between the plea and the sentencing hearing. Specifically, the government had agreed to an acceptance-of-responsibility downward adjustment, but before sentencing, the defendant had engaged in more criminal activity, so the Court noted that "the Government might well have argued that it was excused from its obligation." Id.

Here, in contrast, the court's asking of a question with regard to loss does not hinder performance so as to excuse the contractual obligation in the same manner as suggested in Puckett. Thus, the government breached the plea agreement, the breach was in error, and the error is clear.

Nevertheless, the breach did not affect Hebron's substantial rights, because it likely did not influence the sentence. To meet this third prong of the plain-error analysis in the sentencing context, Hebron bears the burden of showing with a reasonable probability that, but for the error, he would have received a lesser sentence. United States v. Villegas, 404 F.3d 355, 364 (5th Cir.2005); see also Puckett, 556 U.S. at 141-42, 129 S.Ct. 1423. The district court had extensive briefing on the loss issue, had read the thorough and comprehensive PSR that recommended a loss calculation of over $320,000, and had the benefit of lengthy oral argument and expert witness testimony. It ultimately adopted an amended version of the PSR, including its loss calculation.

The sentencing-hearing transcript reveals that the court based its sentencing decision on the facts presented in the PSR (as appropriately explained by the government), the sentencing guidelines and commentary, and the fact that Hebron had not proffered an alternative method of calculation; there is no indication that the government's specific arguments in favor of the higher loss calculation affected the sentence. Hebron provides no evidence to the contrary. In sum, the breach of the plea agreement likely did not affect the sentence, so Hebron's substantial rights were not affected and, as a result, the court did not plainly err.

Finally, even if the error affected Hebron's substantial rights, this is not the rare case in which we should exercise our discretion to require resentencing on the ground that the error "seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings." Puckett, 556 U.S. at 135, 129 S.Ct. 1423 (citations and internal quotation marks omitted). The district court carefully considered all of Hebron's various objections to the PSR and even granted a downward departure for his extensive career in public service, despite the court's one-word description of this case as "sad" and the court's personal expression of "disappointment in Mr. Hebron." The government's breach of the plea agreement added very little, aside from clarification of facts, to what the court already knew from the detailed PSR. And the issue of loss calculation, as explained below, is an arduous one in this case.

"Meeting all four prongs [of the plain-error test] is difficult, as it should be." Id. (citation and internal quotation marks omitted). Hebron has not satisfied that difficult standard; even if the third prong had been satisfied, we would not exercise our discretion to vacate the sentence.

III.

Hebron argues that the district court erred in its calculation of loss by including likely legitimate payments from FEMA to the Town of Ball with the fraudulent ones, in contravention of United States Sentencing Guidelines § 2B1.1. Although generally the calculation of the amount of loss is a factual finding reviewed for clear error, United States v. Sanders, 343 F.3d 511, 520 (5th Cir.2003), Hebron challenges the method used to calculate loss, which, as an application of the guidelines, is reviewed de novo, United States v. Harris, 597 F.3d 242, 250-51 (5th Cir. 2010). Nonetheless, the guidelines emphasize the deference that must be shown to the sentencing judge, who is in a unique position to assess the applicable loss, so this court need only determine whether the district court made "a reasonable estimate of the loss." U.S.S.G. § 2B1.1 cmt. 3(C).

The guidelines dictate an eight-level increase if the amount of loss was between $70,000 and $120,000 and a twelve-level increase if the loss was between $200,000 and $400,000. U.S.S.G. § 2B1.1(b)(1). The applicable loss is generally the greater of actual loss — which includes only reasonably foreseeable harm resulting from the fraud — and intended loss — which includes the harm intended to result from the offense. U.S.S.G. § 2B1.1 cmt. 3(A). In a case involving government benefits such as this, the guidelines commentary provides that

Id. cmt. 3(F)(ii).

The district court adopted the PSR's loss calculation, which separated the various categories of reimbursements the town had requested from FEMA after Hurricanes Gustav and Rita. After Gustav, the town requested about $83,000 in labor reimbursements. Of that, about $21,000 was for overtime hours, which, as explained above, is all fraudulent because of both FEMA's and the town's reimbursement policies. In addition, the PSR noted that the time sheets for non-overtime hours for virtually every employee were falsified, and accurate time sheets either never existed or were destroyed. The probation officer, in preparing the PSR, thus was unable to determine how much of the requested labor reimbursements were legitimate and how much were fraudulent, so all $83,000 was included in the intended-loss calculation.

The same is true for equipment reimbursements. The town requested about $157,000 for equipment used during the clean-up, but as noted earlier, the FBI investigation revealed many falsifications, including false reporting of truck sizes ($11,730 of fraud), false reporting of who had used such equipment (a difference of about $13,400 in one instance), and false reporting of how many hours employees had used such equipment. Most of these were discovered as fraudulent by comparing employee statements with the project worksheets submitted to FEMA, but the PSR noted that these are "merely a sampling of obvious discrepancies." Thus, the PSR concluded: "Due to the extensive fraudulent reporting of equipment hours, there is no method to reasonably separate fraudulent claims from legitimate claims related to PW 83, Category A — equipment. Therefore, the entire amount will be considered fraudulent."

The PSR also included, as loss, all of the administrative expenses reported (about $5,000), in light of the fact that those hours were likely spent in preparing all the fraudulent documentation and included all the contracted work performed (about $9,700) because that work was plainly double-billed to a nonprofit organization. The PSR also found that the same sort of extensive fraud, which made it impossible to separate legitimate from fraudulent claims, is true with the policing hours and equipment billed to FEMA (about $54,500). In sum, the PSR calculated, as intended loss, all of the approximately $309,300 billed to FEMA for cleanup and protective efforts after Gustav.

With regard to Hurricane Rita, the PSR calculations were much more conservative. The investigation into the fraud after Hurricane Rita was less extensive, so of the $133,720 requested after Rita, the PSR included as loss only the fraudulently reported overtime hours (about $11,600), even though the same type of fraud that occurred after Gustav may have occurred after Rita. Thus, the PSR recommended a total intended loss of over $320,000.

For restitution purposes, however, the calculation was much lower. The PSR noted that the town likely benefited from the fraudulent payments from FEMA much more so than did Hebron himself (or any of his co-defendants). The PSR therefore included in the restitution calculation only "certain acts to which specific values can be associated with the defendant," totaling about $105,600. For the most part, this included only reimbursement payments that the probation officer knew to be fraudulent.

Both sides agree that the sentencing guidelines require that loss calculations in government-benefit cases include only fraudulent ones and not payments to which the town was legitimately entitled. The parties also agree, as did the district court, that at least some of the reimbursements requested were for legitimate labor performed and equipment used. Finally, all agree that there is no reasonable way to separate the legitimate FEMA reimbursements from the fraudulent ones; indeed, the district court relied on the PSR's calculations in part because Hebron was unable to provide an alternative method that could reliably isolate the fraudulent payments. Thus, the central question is whether it was unreasonable for the district court to have considered all of the requested reimbursements from FEMA after Gustav as intended loss because, on account of Hebron's fraudulent conduct, the fraudulent requests cannot be separated from the legitimate ones.

Hebron contends that the court used an unreasonable method because the burden is on the government to show some factual basis for concluding that all of the payments resulted from fraud. See United States v. Randall, 157 F.3d 328, 331 (5th Cir.1998). Because it cannot, Hebron argues, the amount calculated as restitution, which includes only reimbursements for which the government has direct evidence showing fraud, should be used (about $105,600). Further, the guidelines require that loss be calculated on "a reasonable estimate ... based on available information," U.S.S.G. § 2B1.1 cmt. 3(C); Hebron contends that instead of using only the "available information" that shows fraudulent conduct, the government and the district court have just thrown up their hands by including all requested payments.

The government responds on several fronts. First, it points out that the PSR noted only the most obvious discrepancies uncovered by the investigation and that the fraud was so pervasive and extensive that the $105,000 restitution calculation used by Hebron is almost certainly an underestimation. Second, by including only overtime payments for its Rita calculation, the government points out that the PSR likely underestimated the fraud for the Rita reimbursements, which was likely as extensive as for Gustav. Considering this, it is likely that the fraudulent payments after both hurricanes totaled more than $200,000, the threshold number for sentencing purposes. Third, and most compellingly, the government argues that, although it generally bears the burden of proving loss, in a case in which the defendant's fraud is so pervasive that it thwarts the government's ability to do so, reasonable estimates are permissible unless the defendant shows that they are inaccurate. Hebron, the government asserts, should not be able to hide behind his own extensive fraud to escape a longer sentence.

There is no binding Fifth Circuit precedent directly on point, but a review of cases in which district courts have made a "reasonable estimate" of loss provides some guidance. The defendant in United States v. John, 597 F.3d 263, 279 (5th Cir.2010), was convicted of stealing and disseminating the corporate bank account information of seventy-six companies; the PSR calculated intended loss by aggregating the credit limits on each account and adding the amount by which the credit limit was exceeded on one particular account. Although the actual loss was only $78,750, that calculation yielded an intended loss of $1,451,865. Id. at 278-79. This court upheld that calculation, despite the fact that only four of the seventy-six accounts were fraudulently charged (and only one to its maximum credit limit), because the district court could reasonably infer that the defendant and her confederates intended to steal from the other seventy-two accounts they had taken information from and disseminated. Id. at 279-81. Similarly, this court several times has upheld loss calculations that aggregate the credit limits of stolen credit cards, even though the government was not able to prove that the defendant would use all the credit cards that were stolen or would charge them to their limits.4

Unpublished cases from this circuit and cases from our sister circuits provide more guidance. In United States v. Fisk, 233 Fed.Appx. 371, 373 (5th Cir.2007), the loss was calculated as the total of all ten insurance claims that were at least partially fraudulent. The defendant objected, contending that the court erred by including the legitimate portions of the insurance claims with the fraudulent ones. Noting that insured parties are generally not entitled to any part of an insurance claim where the figures have been inflated, this court upheld the district court's decision to shift the burden "to Fisk to show that certain portions of each insurance claim [were] legitimate" once the government had met its burden by showing that at least some portion of each claim was fraudulent. Id. Because Fisk, like Hebron, submitted no evidence to make such a showing, the entire amount of all the insurance claims was counted as loss. Id.

The decision in United States v. Miell, 661 F.3d 995 (8th Cir.2011), cert. denied, ___ U.S. ___, 132 S.Ct. 1777, 182 L.Ed.2d 555 (2012), provides the most analogous case. A landlord was charged with mail fraud after fraudulently retaining the security deposits of hundreds of tenants by inflating the costs of repairs needed after they moved out and often demanding additional alleged repair costs. Id. at 997. The district court calculated the loss by multiplying the number of rental units by the average security deposit per unit, then subtracting the average amount of security deposit returned for those units that had any amount of their deposit returned. Id. at 1001. The defendant objected, noting that this calculation included the costs of legitimate repairs along with the fraudulent ones. The Eighth Circuit nonetheless upheld the calculation, reasoning:

We agree with Miell, which presents facts strikingly similar to this case. Hebron should not reap the benefits of a lower sentence because of his ability to defraud the government to such an extent that an accurate loss calculation is not possible. As the government reasons, Hebron should not be able to hide behind his extensive fraud to escape a longer sentence. Thus, endorsing the method articulated in Fisk, we conclude that although the government generally bears the burden of showing that the alleged intended loss was garnered by fraudulent means, where the government has shown that the fraud was so extensive and pervasive that separating legitimate benefits from fraudulent ones is not reasonably practicable, the burden shifts to the defendant to make a showing that particular amounts are legitimate. Otherwise, the district court may reasonably treat the entire claim for benefits as intended loss.

There may be alternative methods that could have yielded a more accurate calculation. For example, the probation officer could have requested from FEMA data about nearby towns of a similar size, then consider the average amount requested after Gustav as an estimate of the amount of legitimate reimbursements requested by the town, then subtracting that amount from the total request to reach the intended loss. Although other courts have taken a similar approach in circumstances like these, see United States v. Sufi, 455 Fed. Appx. 672 (6th Cir.), cert. denied, ___ U.S. ___, 132 S.Ct. 1772, 182 L.Ed.2d 552 (2012), the facts of this case do not disclose whether FEMA has such data, whether Hurricanes Gustav and Rita were large and powerful enough to affect different parts of the state in a uniform manner, or whether a sampling of similarly sized towns around Ball would have a small enough standard deviation such that the average reimbursement claim amount would be a reasonable estimate. This court need not determine whether the district court's estimate was the most reasonable, but rather only that it is a reasonable calculation.

Hebron provided no figures such as the one suggested above, nor any other evidence, to furnish the court with a reasonable estimate of the amount of benefits legitimately requested by the town. Meanwhile, the government has persuasively shown that Hebron's fraud, which included the fabrication of nearly every relevant town record, was so extensive and pervasive that separating the town's legitimate claims from the fraudulent ones is, as conceded by all parties, impossible. As a result, the court committed no error by including the entire amount requested from FEMA after Hurricane Gustav, as well as a small portion requested after Hurricane Rita, as intended loss.

The judgment of sentence is AFFIRMED.