RIPPLE, Circuit Judge.

Kevin Thomas O'Doherty was charged in a six-count indictment with various offenses related to his failure to file income tax returns or to pay taxes from 2001-2003. After entering into an agreement with the Government, Mr. O'Doherty pleaded guilty to one count of tax evasion, in violation of 26 U.S.C. § 7201. At sentencing, the district court calculated an offense level of 21, carrying a range of 37-46 months' imprisonment under the sentencing guidelines. The district court imposed a 24 months' sentence, more than a year below the advisory guidelines range. Mr. O'Doherty now raises several challenges to the guidelines calculation. We agree with the district court's sentencing calculations and therefore affirm the judgment of the district court.

I

BACKGROUND

A. Facts

Mr. O'Doherty was a commodities trader for thirty-nine years. At some point during this period, he paid for the services of a fraudulent tax consultant, and, under that individual's guidance, he did not file individual income tax returns for the better part of a decade.

In the mid-to-late 1990s, Mr. O'Doherty used the firm Refco as his clearing broker. Apparently, during this period, Mr. O'Doherty traded in his own name, and Refco reported his gross income from trades on 1099 forms filed with the Internal Revenue Service ("IRS").

During 2001, Mr. O'Doherty "changed tactics" from trading in his own name to "creat[ing] shell corporations" to conduct his trading activities. R.34 at 8. Specifically, he set up four accounts at two different financial institutions, each in the name of a separate entity. Those accounts received his trading profits, partnership distributions, consulting fees and payments from traders for seat leases during the charged period. He used the funds in the accounts to pay his personal expenses. He also used the entities to conceal what was essentially his personal ownership of assets. Through these entities, Mr. O'Doherty received gross income of $158,480, $617,809 and $337,848 in tax years 2001-2003, respectively.

In 2007, the Government instituted a civil action against Mr. O'Doherty; it alleged that Mr. O'Doherty had failed to file tax returns in 1994, 1995, 1997, 1998 and 2000, and that his total tax liability for those years was $917,801. That tax liability was calculated on the basis of Mr. O'Doherty's 1099s prepared by Refco. The civil proceeding was not resolved at the time of Mr. O'Doherty's criminal prosecution, but instead was stayed, apparently at Mr. O'Doherty's request.

B. District Court Proceedings

In this criminal action, commenced in 2009, the Government charged Mr. O'Doherty with three counts of tax evasion, in violation of 26 U.S.C. § 7201, and three counts of failing to file federal income tax returns, in violation of 26 U.S.C. § 7203. The charged conduct related only to tax years 2001, 2002 and 2003.

1. The Plea Agreement

Mr. O'Doherty entered into an agreement with the Government in which he pleaded guilty to one count of tax evasion for tax year 2001. The agreement included specific information relating to the tax losses from the charged conduct:

R.18 at 6 (citing U.S.S.G. §§ 2T1.1(a)(1), 2T4.1(H), 1B1.3). Paragraph 6 set forth the factual basis for the charges related to Mr. O'Doherty's failure to file returns from 2001 through 2003. That paragraph also includes specific language memorializing that the defendant admitted the facts underlying the charges and that these facts "constitute relevant conduct pursuant to Guideline § 1B1.3." Id. at 2.

The agreement also included a lengthy section relating to the parties' positions on the appropriate guidelines calculation:

Id. at 8-9. The agreement also set forth the parties' opposing positions on the proper application of the sophisticated means enhancement found in U.S.S.G. § 2T1.1(b)(2). Finally, the agreement noted that "[e]ach party is free to recommend whatever sentence it deems appropriate" to the court. Id. at 9.

2. The Plea Hearing

At the plea hearing, the Government advised the court that both parties understood that there might be further adjustment in the total tax loss and pointed out that the plea agreement specifically allowed for a change in that figure. The court advised Mr. O'Doherty that there could be no guarantee as to the sentence that he would receive and specifically noted that the court was not bound by the guidelines calculations but only by the statutory maximum of five years. Mr. O'Doherty told the district court that he understood that no promises had been made to him and that the only understanding that he had with the Government was the one set forth in the plea agreement.

3. The Positions of the Parties at Sentencing

During the preparation of the presentence investigation report ("PSR"), the Government submitted a memorandum to the probation office. That memorandum included the same calculation that the Government had used in the plea agreement, including an estimation that the appropriate base offense level was 20 (tax loss of more than $400,000 and less than $1 million dollars). It further took the position that the facts of the case supported an upward adjustment of two levels for the use of a sophisticated means to mask the unpaid taxes and a three-level downward adjustment for the acceptance of responsibility. The resulting total offense level was 19. With a criminal history category of I, the resulting advisory guidelines sentencing range was 30-37 months. The Government recommended a sentence within that range.

When it filed its presentence report, the Probation Office took a different view. It reached a much larger tax loss figure by adding tax losses from uncharged conduct occurring from 1994-2000 together to the charged conduct from 2001-2003. In estimating the loss attributable to the uncharged conduct during the earlier period, the PSR used the figure sought in the civil action covering those earlier years, $917,801. When this figure was combined with the tax losses admitted in the plea agreement, the resulting total tax loss calculation was more than $1 million but less than $2.5 million. This calculation resulted in a base offense level of 22, two levels higher than if the losses had remained at the level suggested by the Government and noted in the plea agreement.

Mr. O'Doherty responded to the PSR by filing a motion to continue the sentencing hearing. He noted that, after the plea agreement had been reached, he filed amended returns for tax years 2001-2003 that showed a tax liability of less than $400,000 during that charged period. He pointed out that the PSR failed to account for this reduced liability. He also contended that the PSR erred in including as relevant conduct the tax losses alleged in the civil suit relating to the earlier years from 1994-2000. In his view, inclusion of those years as relevant conduct was not contemplated by the plea agreement, and, in any event, the tax losses alleged in the civil complaint were too speculative to form the basis for sentencing in the criminal case. His sentencing memorandum reiterated these arguments and also discussed mitigating factors at some length. As a result, he argued for a lower guidelines calculation and a downward adjustment.

The Government also filed with the court a sentencing memorandum. On the subject of tax loss, the Government simply noted that, given the agreed-upon figures for 2001-2003, "the PSR's conclusion that the total tax loss for the prosecution period and for all relevant conduct is more than $1 million and less than $2.5 million meets the Guidelines' requirement of a reasonable estimate based on the available evidence." R.25 at 6.

4. Sentencing Hearing

At the sentencing hearing, the district court began with the issue of tax loss. The Government reiterated its position that it "did not object to [the] calculation" in the PSR. R.34 at 4. It also noted that state tax losses should be included in the calculation. With those numbers, the losses for the 2001-2003 period alone were in excess of $400,000; combined with the additional earlier years identified in the civil complaint and subsequent years through 2009, total losses were estimated reasonably at over $1 million.1 R.34 at 4, 11. The Government therefore agreed that, as a result of the additional tax loss amounts, the PSR was correct in its estimation that the appropriate base offense level was 22.

Mr. O'Doherty then argued for a base offense level of 18, two lower than that contemplated in the plea agreement and four lower than that recommended in the PSR. He restated his view that further corrected tax returns for 2001-2003 had lessened the tax liability for that period to under $400,000. Because he believed the Government was bound contractually to limit its recommendation regarding relevant conduct to those years referenced explicitly in the plea agreement, he contended that a loss of less than $400,000 represented the total loss that could be used to arrive at his base offense level.2

The district court ruled the failure to file returns during the entire 1994-2003 period was relevant conduct, although it would not consider conduct occurring after 2003. Further, the court elected to use the figures charged in the civil complaint as the estimate for tax liability for years 1994-2000, because "those are the final figures, at least the ones we have to work with, and they total $917,000." Id. at 14. Combined with the losses for the charged period of 2001-2003, the court noted that the total loss was "$1.2 million plus," and the base offense level was appropriately 22. Id.

The hearing's focus then turned to whether Mr. O'Doherty had employed sophisticated means. The Government submitted that the application note to the relevant Guideline specifically referenced the use of shell corporations as justifying application of the enhancement. The Government argued that the purpose of the various entity accounts was nothing "other than to channel Mr. O'Doherty's actual personal income through a business entity to conceal the fact that it was income to him." Id. at 15. Mr. O'Doherty contended, however, that the accounts had legitimate business purposes and were not solely to hide income; one was in the name of a brokerage firm that comprised some 25 affiliated small traders. The court ruled:

Id. at 16. The court applied the two-level enhancement under § 2T1.1(b)(2) and a three-level reduction for acceptance of responsibility to arrive at an offense level of 21. When combined with Mr. O'Doherty's criminal history category of I, the resultant sentencing range under the Guidelines was 37 to 46 months.

The court then heard argument on the § 3553(a) factors. Mr. O'Doherty argued for a below-guidelines sentence, focusing primarily on Mr. O'Doherty's family; his daughter was battling cancer at the time of sentencing, and Mr. O'Doherty was the primary caretaker to his granddaughter. He further noted that, outside of these tax offenses, he had led an honorable life and that, as a result of his conviction, he already had been stripped of his trader's license and was without a profession. He contended that a below-guidelines sentence was appropriate given his family circumstances, under Guideline 5H1.6.3 The Government maintained its request for a within-guidelines sentence. It contended that Mr. O'Doherty's life circumstances were similar to those faced by many defendants, that his criminal conduct spanned many years, which demonstrated disregard for the law, and that his offense was a serious one.

After reviewing the circumstances, including the family health issues, the court stated:

R.34 at 30-31. After again noting his cooperation and his family medical issues, the court concluded that "a sentence within the guidelines, which is 37 to 46 months, is considerably higher than probably need be." Id. at 31. Accordingly, the court sentenced Mr. O'Doherty to 24 months' imprisonment, followed by a three-year term of supervised release.

II

DISCUSSION

Mr. O'Doherty submits that he is entitled to resentencing for three reasons. First, he claims that the Government materially breached the plea agreement when it assented to the PSR's tax loss calculations, which included additional years of relevant conduct. Second, he claims that the total amount of tax loss found by the district court at sentencing was not proven by sufficient evidence. Finally, he claims that the district court erred in applying the sophisticated means enhancement of Guideline 2T1.1(b)(2). We shall address each contention in turn.

A. Interpretation of the Plea Agreement on Relevant Conduct

We first address the appropriate time period from which to calculate relevant conduct for sentencing. According to Mr. O'Doherty, the plea agreement bound the Government to limit its recommendation to losses accrued during the charged period only. In his view, although the Probation Office was free to recommend that conduct other than that covered by the plea agreement be included in the calculation, the Government was precluded, by virtue of its contractual undertaking in the plea agreement, not to assent to any such recommendation. Therefore, we must examine the nature of the promises made on the subject of relevant conduct in the agreement.

We review plea agreements using ordinary rules of contract interpretation, but we are mindful of "the special public-interest concerns that arise in the plea agreement context." United States v. Monroe, 580 F.3d 552, 556 (7th Cir.2009). Accordingly,

Id. (modification in original) (internal citations and quotation marks omitted). "We interpret the terms of the agreement according to the parties' reasonable expectations and construe any ambiguities against the drafter—the government—and in favor of the defendant." United States v. Woods, 581 F.3d 531, 534 (7th Cir.2009). "The government must fulfill any promise that it expressly or impliedly makes in exchange for a defendant's guilty plea." United States v. Ingram, 979 F.2d 1179, 1184 (7th Cir.1992). The remedy for breach of a plea agreement is specific performance and a remand for resentencing before a different judge, or a remand to permit the defendant to withdraw his plea. United States v. Diaz-Jimenez, 622 F.3d 692, 694 (7th Cir.2010). Mr. O'Doherty seeks resentencing.

Mr. O'Doherty emphasizes that the plea agreement's recitation of the facts is limited to only the charged period of 2001-2003. He notes that the agreement's section on relevant conduct states that "based on the facts now known to the government," the "anticipated offense level is 19." R.18 at 8. In his view, because the Government was aware of his full course of conduct at the time it entered into the agreement, its decision not to incorporate the earlier period into the written contract is tantamount to a promise not to raise it at sentencing. He acknowledges that the section continued with language that the calculations are "preliminary in nature, and are non-binding predictions upon which neither party is entitled to rely" and that the Government may "conclude that different or additional Guideline provisions apply." Id. In his view, however, these "boilerplate" provisions cannot vitiate the more specific language of the agreement. Appellant's Br. 24.

Our principal difficulty with Mr. O'Doherty's argument is that it misconstrues the language of the pertinent section of the agreement, and "a party's rights under a plea agreement are limited by what the parties in fact agreed to," United States v. Schilling, 142 F.3d 388, 395 (7th Cir.1998). As we already have noted, the section concerning relevant conduct provides that "[t]he defendant acknowledges that the government can prove" that the tax loss from the charged period is $425,766. R.18 at 6. It says nothing about any promise by the Government to limit its relevant conduct recommendation to those amounts with respect to the charged years, nor does it say anything whatsoever about any obligations with respect to the uncharged years. Moreover, the subsequent language—that the calculations are non-binding predictions, not entitled to reliance by any party—further clarifies the parties' understanding on this issue.

United States v. Schilling, 142 F.3d 388 (7th Cir.1998), is instructive. There, the defendant entered into a plea agreement in which he acknowledged the purchase and sale of 300,000 gallons of fuel for which he failed to pay excise taxes. The Government made no reciprocal promise to limit its recommendation and retained "`the right to fully apprise the Court of the nature of the criminal conduct.'" Id. at 393 (quoting the plea agreement). When the Government stepped forward at sentencing with evidence showing a much more significant figure for the fraud, the defendant claimed a breach. The district court found none, and we affirmed. Among the factors guiding our interpretation, we noted both the Government's reserved right and the one-sided nature of the acknowledgment of criminal conduct. See id. at 396-98. Those factors are mirrored in the agreement now before us.

Furthermore, beyond the literal language of the plea, Mr. O'Doherty's own conduct surrounding the plea supports the view that both parties understood and intended that the losses stated in the agreement remained uncertain. During the plea colloquy, for example, Mr. O'Doherty's attorney indicated to the court that there was a "fairly good chance" that the tax losses would be less than the figure— in excess of $400,000—admitted in the plea agreement and that the expected reduction "would then affect the guideline sentence." R.44 at 12. When the court expressed some confusion about whether the parties had agreed to a tax loss number, the Government attorney noted, "[B]oth parties acknowledge there may be further calculations, and the plea agreement allows for that, that if there are additional calculations that the tax amount may change." Id. The court then clarified, "So, if he argues that it is less than $400,000, that would not void the agreement is what you are telling me?" Id. The Government responded in the affirmative. Id. at 13. Mr. O'Doherty's attorney did not dispute this interpretation. In fact, Mr. O'Doherty did argue for a tax loss figure of less than $400,000—and continues to do so before this court. We see no principled basis for concluding that the agreement bound the Government to the initial tax loss figure but permitted Mr. O'Doherty to challenge it.

Mr. O'Doherty makes the related argument that, even if the Government were entitled to argue different figures for the years charged, it was not permitted to include new years altogether. Again, we see nothing in the language or structure of the agreement that supports this interpretation.

B. Proof of Tax Loss

Mr. O'Doherty next argues that the Government failed to meet its burden of proof with respect to the tax loss amounts upon which his sentence was based. He contends that the Government "submitted no proof to substantiate the claimed tax loss for" the additional years. Reply Br. 4. Further, he explains that there is a "legal difficulty with using 1099[ ]s to determine tax loss." Id.

The Government must prove tax loss figures at sentencing by a preponderance of the evidence. United States v. Schroeder, 536 F.3d 746, 752 (7th Cir. 2008). However, the Guidelines themselves acknowledge that identifying a perfect figure often will be impossible: "In some instances, such as when indirect methods of proof are used, the amount of the tax loss may be uncertain; the guidelines contemplate that the court will simply make a reasonable estimate based on the available facts." U.S.S.G. § 2T1.1, app. 1.

Furthermore, we long have held that

United States v. Artley, 489 F.3d 813, 821 (7th Cir.2007) (internal quotation marks and citations omitted) (affirming a sentence as based upon sufficient evidence, even though the statements establishing the drug quantity amounts in the PSR were hearsay); see also United States v. Coonce, 961 F.2d 1268, 1280 (7th Cir.1992) (setting forth the shifting burdens).4

Here, the PSR identified a pending civil case by its case number and correctly recounted the amount of tax sought by the Government for the earlier years. The PSR noted that the probation officer had conducted a telephonic interview with IRS Agent Marta Grijalva, who stated that the outstanding taxes sought in the civil case were calculated on the basis of available tax documents, including 1099s.

The information contained in the PSR is sufficiently reliable to support the Government's position at sentencing. The PSR sets forth the means by which it obtained the information, and, in turn, the means by which the IRS itself obtained the information. Mr. O'Doherty did not come forward with any evidence to suggest that the PSR's figures were incorrect. Indeed, he has maintained that he has no better evidence. Nevertheless, he believes that the Government is required to prove, using some means better than the 1099s relied upon by the IRS, his actual taxable income for these years. We already have rejected this view. See United States v. Chavin, 316 F.3d 666, 678 (7th Cir.2002) (noting that a defendant is not entitled to create a "perfect" return to calculate tax loss in criminal proceedings); see also id. at 676-79 (rejecting the defendant's argument that tax loss should take into account legitimate, unclaimed deductions, which in that case would have reduced the defendant's tax liability to roughly twenty-five percent of that determined to be the tax loss at sentencing).

Mr. O'Doherty failed to meet his burden to draw the facts of the PSR sufficiently into question. The district court therefore was entitled to rely on the PSR in making its calculations. In any event, the sentencing transcript makes clear that the district court did consider the fact that the tax losses in the PSR potentially had been overstated and factored that consideration, along with family health and related matters, into the ultimate sentence under 18 U.S.C. § 3553(a). See R.18 at 30-31.

C. Sophisticated Means

Finally, Mr. O'Doherty challenges the application of the two-level enhancement for use of a "sophisticated means" under the tax evasion guideline, U.S.S.G. § 2T1.1(b)(2). We review the district court's finding that the defendant used sophisticated means for clear error. United States v. Becker, 965 F.2d 383, 390 (7th Cir.1992). Application Note 4 to this guideline provides,

U.S.S.G. § 2T1.1, app. 4. Mr. O'Doherty contends that his use of a corporate structure was not "especially complex or especially intricate." Id. Further, he maintains that the corporations served legitimate purposes and were not constructed exclusively to hide tax liability.

Our cases interpreting this enhancement have held that it "does not require a brilliant scheme, just one that displays a greater level of planning or concealment than the usual tax evasion case." United States v. Fife, 471 F.3d 750, 754 (7th Cir. 2006) (concluding that the use of four corporations without physical offices or accounting journals to shield income justified the enhancement). We also have acknowledged that conduct less sophisticated than the exemplary list provided in the application note may still warrant application of the enhancement. See United States v. Kontny, 238 F.3d 815, 820-21 (7th Cir. 2001) (holding that the enhancement was warranted where the defendants avoided employment taxes by writing separate checks to conceal overtime wages to employees and accounting for those additional amounts as non-wage expenses); Becker, 965 F.2d at 390 (depositing receipts in son's bank account and in a "warehouse bank" with accounts designated only by number justified enhancement). Indeed, "the essence of the definition is merely deliberate steps taken to make the offense... difficult to detect." Kontny, 238 F.3d at 821 (modification in original) (internal quotation marks omitted).

Mr. O'Doherty failed to file tax returns over a significant period of time. Still, during the charged period, he used corporations to avoid the direct reporting of income in his name, and he used the funds in those corporations as personal funds. See R.18 at 4 (plea agreement's recitation of facts). Although he protests that corporations are ubiquitous "in most modern business transactions," Appellant's Br. 36, their use to impede the discovery of personal income, as they were used here, permits the imposition of the enhancement.

Conclusion

The Government did not breach the plea agreement when it concurred with the recommendations of the PSR regarding relevant conduct. Further, the scope of that conduct was explained in the PSR, and Mr. O'Doherty failed to present evidence that sufficiently challenged its reliability or accuracy. Accordingly, the district court was entitled to rely on the PSR in making its factual determinations. Finally, Mr. O'Doherty's chosen method to perpetrate his fraud was sufficiently sophisticated to justify application of the sophisticated means enhancement. The judgment of the district court is affirmed.

AFFIRMED