
    UNITED STATES of America, Appellant, Cross-Appellee, v. John CANOVA, Defendant-Appellee, Cross-Appellant.
    Docket Nos. 03-1291(L), 03-1300(XAP).
    United States Court of Appeals, Second Circuit.
    Argued: Jan. 9, 2004.
    Decided: June 21, 2005.
    
      Eric J. Glover, Assistant United States Attorney, District of Connecticut, Hartford, Connecticut (John H. Durham, Deputy United States Attorney; Maria A. Kahn and William J. Nardini, Assistant United States Attorneys, on the brief), for Appellant, Cross-Appellee.
    Paul Shechtman, Stillman & Friedman, P.C., New York, New York (Nathaniel Z. Marmur, on the brief), for Defendanb-Ap-pellee, Cross-Appellant.
    Before: SACK and RAGGI, Circuit Judges.
    
    
      
      . The Honorable Ellsworth Van Graafeiland, who was a member of this panel and voted with the majority, passed away following argument in this case. This appeal is being decided by the remaining two members of the panel, who are in agreement. See Local Rule § 0.14(b).
    
   RAGGI, Circuit Judge.

The United States appeals from so much of the April 7, 2003 final judgment of the United States District Court for the District of Connecticut (Alfred V. Covello, Judge) as sentenced John Canova to a one-year term of probation after a jury trial at which defendant was found guilty of various substantive and conspiratorial crimes relating to his involvement in a multi-million-dollar Medicare fraud. The government asserts that the district court erred (1) in refusing to apply loss and obstruction enhancements to the calculation of Canova’s Sentencing Guidelines, and (2) in granting a downward departure based on defendant’s history of public service and good works. Canova defends the district court’s sentencing rulings but cross-appeals from its denial of his motion for a new trial.

We reject Canova’s argument that the district court abused its discretion in denying him a new trial, and, accordingly, affirm the judgment of conviction as it pertains to Canova’s guilt. As for the government’s sentencing challenge, its request for de novo review of the district court’s departure decision pursuant to 18 U.S.C. § 3742(e) is now foreclosed by United States v. Booker, — U.S. -, -, 125 S.Ct. 738, 764-66, 160 L.Ed.2d 621 (2005), which specifically excises § 3742(e) from federal sentencing law and instructs that sentences be reviewed on appeal only for “reasonableness.” Because the reasonableness of a sentence, even under the discretionary regime recognized in Booker, depends in part on a district court’s consideration of the Sentencing Guidelines, see 18 U.S.C. § 3553(a)(4)-(5), a significant error in the calculation or construction of the Guidelines may preclude affirmance. See United States v. Rubenstein, 403 F.3d 93, 98-99 (2d Cir.2005). We conclude that there was such an error in the district court’s calculation of the loss amount relevant to the fraud guideline, but we find no error in the district court’s rejection of a Guidelines enhancement for perjury nor in its exercise of Guidelines departure authority based on defendant’s public service and good works. Accordingly, we remand the case with directions to vacate the sentence and to resentence consistent with this opinion and the Supreme Court’s decision in Booker, and not inconsistent with United States v. Crosby, 397 F.3d 103 (2d Cir.2005).

I. Background

A. The Crimes of Conviction

1. The Charges

John Canova, who at the relevant time served as Vice President for Operations of Raytel Cardiac Services, Inc. (“Raytel”), was charged in a six-count indictment with (1) conspiring to defraud the United States from October 1999 through October 2001 by making false statements to Medicare agents in violation of 18 U.S.C. § 1001, and to influence, obstruct, or impede a Medicare audit in violation of 18 U.S.C. § 1516, see 18 U.S.C. § 371; (2) falsely representing in a December 6, 1999 letter to Medicare that Raytel was in compliance with Medicare specifications for testing pacemakers when he knew that it was not, see id. § 1001; (3) making a similar false representation in a January 27, 2000 letter to a Medicare auditor, see id.; (4) making various false representations with respect to Raytel’s records and archive system in a March 28, 2000 letter to a Medicare auditor, see id.; (5) obstructing a Medicare audit on January 24, 2000, by directing Raytel’s Connecticut employees falsely to represent that Raytel was in full compliance with government testing specifications, see id. § 1516; and (6) obstructing a criminal investigation by making false statements to federal agents on June 23, 2000, with respect to Raytel’s pacemaker testing, see id. § 1518.

Count Six was dismissed prior to trial for reasons not relevant to this' appeal. On the remaining charges, a jury found Canova guilty on Counts One, Two, Three, and Five, and not guilty on Count Four. In light of that verdict, and the district court’s subsequent denial of a motion for a new trial, we view the evidence “‘in the light most favorable to the government, crediting any inferences that the jury might have drawn in its favor.’ ” United States v. Boyd, 222 F.3d 47, 49 (2d Cir.2000) (quoting United States v. Salameh, 152 F.3d 88, 107 n. 1 (2d Cir.1998) (per curiam)); accord United States v. Rubenstein, 403 F.3d at 96.

2. The Conspiracy to Defraud Medicare

a. Raytel’s Pacemaker Testing for Medicare

At times relevant to the indictment, Raytel performed transtelephonic pacemaker testing for Medicare patients at government expense. Transtelephonie monitoring allows a technician at a remote location to test the operation of a pacemaker by having a patient use a portable device to transmit telephonic signals that can then be converted into a conventional electrocardiogram (“ECG”) report for review by a supervising cardiologist.

For Medicare to cover the expense of its transtelephonie testing, Raytel was obliged to comply with Section 50-1 of the Medicare Coverage Issues Manual, which required that a pacemaker be monitored in three functioning modes for thirty seconds each, with the results recorded on strips of magnetic tape (the “30-30-30 test”). See Medicare Program; National Coverage Decisions, 54 Fed.Reg. 34,555-03, 34,580 (Aug. 21, 1989). At the first-step of the “30-30-30 test,” a technician records on a magnetic strip the pacemaker’s operation for thirty seconds in a free-running or “demand mode,” during which the pacemaker supplies an electric charge to the heart only when it senses that the organ is falling behind the programmed heart rate. At the second step, a technician records a strip of the pacemaker’s operation for thirty seconds in a “magnetic mode,” during which the patient uses a magnet to close a switch inside the pacemaker, causing the device to fire an electric charge to the heart at regular intervals regardless of the patient’s pulse. This exercise typically reveals whether the pacemaker’s battery needs to be replaced and whether the heart is properly responding to the charge firing. At the third step, a technician records a strip of the pacemaker’s operation for a final thirty seconds in the “demand-after-magnet mode,” during which the magnet is removed and the pacemaker is allowed to return to free-running functioning. This segment of the test permits a technician to verify that a pacemaker’s internal switch has reopened and that the patient has suffered no ill effects from the constant firing of the pacemaker during the magnetic-mode phase of the test.

Because a cardiologist would typically need to review only representative segments of the first two phases of the test, a technician would generally attach only strip excerpts to the report submitted to the doctor, providing the full test results upon specific request. Before 1995, when Raytel switched to computerized testing, its technicians were able to prepare strip excerpts from the first two test modes as the third was concluding. Because the computer only displayed information as it was being recorded, however, it took longer for technicians employing this technology to identify and prepare representative strips. This delay in processing assumed significance in the aggregate because of the number of tests each Raytel technician was expected to perform — rising in 1999 from thirty-two to thirty-five to forty tests per day. This, in turn, led some Raytel technicians to depart from Medicare specifications and to record only an abbreviated strip — or no strip at all — of the last test phase. At trial, the government offered evidence indicating that, in the period December 1999 to March 2000, technicians at Raytel’s Connecticut facility complied with Medicare’s pacemaker testing specifications only 22 to 34.7 percent of the time.

b. Canova’s Involvement in the Fraud Scheme

At trial, Canova did not seriously dispute Raytel’s non-compliance with Medicare testing requirements. Rather, he challenged the government’s ability to prove his knowing participation in any scheme to defraud the government in connection with these tests or to obstruct a Medicare audit.

To carry its burden on the issue of Canova’s guilty knowledge, the government relied on both circumstantial and direct evidence. As background, it sought to demonstrate that it was Canova’s heightened performance quotas that led Raytel technicians to abbreviate the 30-30-30 test. Ronald Vincent, a former manager of Raytel’s Connecticut facility who pleaded guilty to obstruction pursuant to a plea agreement, testified:

John [Canova] would call ... and want to know why, what are we going to do to get to that target, depending on, you know, if we were fairly close, you know, it wouldn’t be that bad, but if we were far behind on target, John would be pretty animated as to why we were not on target, and want to find out why we weren’t on target, and what we were going to do to get close to being on target.

Trial Tr. at 604.

Various employees of the Connecticut facility, including Vincent, his predecessor Alexander Puziak, and technician Dawn Amaro, testified that, under pressure to meet the higher quotas, technicians began to cut short the demand-after-magnet phase of the 30-30-30 test. Amaro explained that, instead of recording a full 30-second strip for this phase, some technicians would run “10 or 15” seconds of strip, thereby converting the required 30-30-30 test into a “30-30-10” test. Id. at 278.

Sometime before leaving Raytel’s employ in October 1998, Puziak brought this fact to Canova’s attention, reporting that “there were some individuals not in compliance” with the 30-30-30 test requirements. Id. at 376. When Canova replied “[t]hat everyone had to be in compliance, that nothing could suffer,” Puziak told him that such a demand was “unreasonable ... in the allotted time.” Id.

By the spring of 1999, Connecticut managers and technicians were so frustrated with Canova’s performance quotas that non-compliance with the last phase of the 30-30-30 test had become routine. Vincent bluntly reported this situation to Ca-nova: “Look, it’s not an option of not doing the demand after magnet in the computer anymore. We’re not doing it, period. There’s no demand after magnet being done, period, in the computer, no one’s doing it .... ” Id. at 605. Raytel manager Glenn Pelletier, also testifying pursuant to a cooperation agreement, stated that in March 2000, he too told Canova that technicians were not performing the entire 30-30-30 test “all the time.” Id. at 733.

Sometime in 1999, a notice was posted at the Connecticut facility instructing technicians that they were not required to run any strip for the demand-after-magnet phase of pacemaker testing; they could simply listen to the transmitted signal to satisfy themselves that the pacemaker had returned to its free-running functions. Steven Boecklin, another Connecticut manager, testified that this action had its origins in a 1999 conversation in which Cano-va suggested that the Medicare manual’s requirement of “[a] minimum 30 seconds of readable ECG [strip]” might be construed not to require a technician to create a contemporaneous strip of the demand-after-magnet phase of the test because such a strip, if needed, could be generated later from the archived recording of the telephone call. Id. at 535. Boecklin stated that when he attempted to confirm this interpretation with Medicare, the persons with whom he spoke could not answer his questions. Nevertheless, he and Vincent decided that there was, in fact, a “loophole” in the Medicare requirements that did not require a thirty-second tape of the demand-after-magnet test.

c. Canova’s Efforts to Obstruct the Medicare Audit

The Health Care Financing Administration (“HCFA”), part of the Department of Health and Human Services, administers and supervises the Medicare program by contracting with private “carriers,” who, among other things, receive, disburse, and account for Medicare funds paid to the providers of covered services. See 42 U.S.C. § 1395u. During the times relevant to this case, Medicare’s Connecticut carrier, United HealthCare Insurance Company (“United HealthCare”), received an anonymous complaint suggesting that Raytel was not in compliance with Medicare’s specifications for transtelephonic pacemaker monitoring. After reviewing medical records, United HealthCare informed Raytel by letters dated October 11, 1999, October 18, 1999, and December 2, 1999, that it refused to pay or was seeking reimbursement for having paid Medicare claims for monitoring that failed to produce thirty-second test strips for each of the three required test modes. The December 2, 1999 letter explicitly warned Raytel “that misrepresenting your services to Medicare is a fraudulent situation and that the Inspector General has the authority to exclude from coverage your services should you decide to continue to bill your services incorrectly to Medicare.” Letter from United HealthCare to Raytel of Dec. 2,1999, at 4.

In a December 6, 1999 letter that was the basis for the first § 1001 substantive charge, Canova appealed Medicare’s reimbursement demands, falsely insisting “that [Raytel] ha[s] complied with all relevant regulations.” Letter from Canova to United HealthCare of Dec. 6, 1999. Indeed, Canova specifically stated that Raytel was complying with Medicare’s requirements for the production of 30-second strips at each phase of the testing process: “The guidelines require that a monitoring service obtain a 30-second strip in free-running mode, 30 seconds in magnet mode and 30 seconds after magnet. Raytel obtains these strips utilizing its PC based testing system.” Id.

Canova’s appeal prompted a Medicare audit of Raytel’s Connecticut facility. The day before the auditors’ January 24, 2000 on-site inspection, Canova sent an e-mail to Raytel’s Connecticut managers that was the basis for the substantive § 1516 obstruction charge. Noting that the focus of the audit was Medicare’s “requirement that Raytel take 90 seconds of ECG,” Ca-nova instructed the managers to tell the auditors that Raytel “do[es] follow the [required] procedures” for the production of these strips, when, in fact, he knew that was not the case. E-Mail from Canova to Meroe of Jan. 23, 2000.

At the conclusion of its on-site tour, the audit team asked Raytel to produce monitoring records from June through December 1999 for fifteen pacemaker patients. By the end of the day, Raytel could supply testing records only for September and October 1999, showing six seconds of data. Nevertheless, in a January 27, 2000 letter to the head of the audit team that was the basis for the second substantive § 1001 charge, Canova falsely asserted that Ray-tel’s “standard operating procedure [was] to obtain the full 90 seconds of ECG required by [Medicare] as outlined in Publication 06, Section 50-1, Part B, Definition of Transtelephonic Monitoring.” Letter from Canova to Toor of Jan. 27, 2000, at 2. Canova further represented that Raytel would promptly retrieve and forward to the auditors “a complete printout of the entire 90-second recording” for the tests of the fifteen patients “you asked to see.” Id. at 1.

By March 2000, it was apparent that Raytel could not supply the requested records. The audit team nevertheless decided to treat its review of Raytel’s operation as “educational” and to require the company to reimburse Medicare only for those fees referenced in United HealthCare’s December 2, 1999 letter or paid on behalf of the fifteen patients whose records could not be produced during the audit. Otherwise, Raytel was afforded thirty days to correct deficiencies in its archive system and to “certify[ ] that Raytel is in compliance with Medicare’s regulations and [that] the data in [its] records meet[ ] all the requirements for pacemaker testing as listed in Publication 06, Section 50-1 of the MCM.” Letter from Toor to Canova of Mar. 5, 2000.

On March 7, 2000, Canova ordered Vincent to prepare a chart identifying the fifteen patients whose records had been sought by the auditors as well as the months when Raytel had tested their pacemakers. Vincent transmitted the information to Canova by telefax, only to have the chart returned to him the same day, also by telefax, with certain dates blacked out. Canova instructed Vincent to retrieve copies of Raytel’s summary reports for the remaining dates and to delete from those reports certain signatures to make it appear that they had been printed directly from archive records. Pelletier, whom Vincent recruited to help with this task, testified that Vincent told him that Canova wanted the records “cleaned up, because he represented to Medicare that [Raytel’s computer system] could produce these, and it can’t.” Trial Tr. at 753. Both Vincent and Pelletier testified that they transmitted the altered reports to Canova in New York.

Pelletier further testified that, in March 2000, at Canova’s request, he attempted to retrieve Raytel’s full computer records for certain pacemaker patients. Of thirty retrieved reports, only one demonstrated compliance with Medicare’s 30-30-30 test specifications. When, in a March 20, 2000 telephone conversation, Pelletier so advised Canova, Canova directed that the records be sent to him.

Testifying contrary to Puziak, Vincent, Pelletier, and Boecklin, Canova stated that it was not until March 22, 2000, when he reviewed the documents forwarded by Pel-letier, that he learned that Connecticut technicians had not been complying with Medicare’s 30-30-30 test requirements. See id. at 996. Canova instructed his New York and Connecticut supervisors to issue memoranda to Raytel’s technicians emphasizing the need to obtain a total 90 seconds of strip to satisfy Medicare’s testing specifications.

A few days later, on March 28, 2000, Canova wrote to the chief Medicare auditor. Without any mention that Raytel had now located some of the test records formerly requested, much less that those tests demonstrated the company’s noncompliance with the 30-30-30 test, Canova reported simply that the company had established a “new archive system ... populated with tests starting with December 6th, 1999,” and that he was certifying Ray-tel’s compliance with Medicare’s regulations for tests conducted after that date. Letter from Canova to Toor of Mar. 28, 2000.

B. The Rule S3 Motion for a New Trial

1. The Timing of the Motion

Two days after verdict, on September 27, 2002, Canova moved, with the government’s consent, for an extension of the time to file post-trial motions to October 18 of that year. The court granted the motion on October 4. On October 17, Cano-va sought and the court granted another unopposed extension to October 28, 2002.

2. The Grounds for Seeking a New Trial

On October 28, 2002, Canova moved for a new trial pursuant to Fed.R.Crim.P. 33, on the ground that the government’s evidence, particularly as to his guilty knowledge, was flawed, contradictory, and in some respects false.

Canova argued that Vincent’s testimony about Canova’s returning the March 7, 2000 telefax transmission with certain test dates blacked out was belied by trial evidence, specifically, the fact that the cover sheet for the telefax had not been found in Vincent’s Connecticut office, and the condition of the telefax found in Canova’s New York files suggested that the dates had been blacked out before Canova received the document. Further, Canova reported that post-trial investigation into the operation of his telefax machine and telephone numbers demonstrated the falsity of Vincent’s account. Canova submitted that the telefax legend at the bottom of the document found in his file was properly understood to indicate its receipt, not re-transmission. He submitted that the one-hour difference between the legends at the top and bottom of the retrieved document could be explained by the discovery of a comparable time discrepancy in the internal clocks of Canova’s and Vincent’s tele-fax machines.

Canova further argued that the prosecution had unfairly insinuated that he had lied on cross-examination in explaining that the deletion of certain information from a pacemaker test report found in his files was done to permit the document to be used for marketing purposes. He offered a post-trial affidavit from Raytel’s Marketing Manager, indicating that such redactions were consistent with her department’s practices.

Canova also argued that the March 23, 2000 Donovan Memorandum did not support the government’s suggestion that Raytel’s New York technicians were not complying with 30-30-30 test requirements. He offered a post-trial affidavit from Michael Donovan stating that his memorandum was intended to remedy a different problem: the tendency of technicians to run “both the demand and the demand after strips in the demand screens” of their computers. Donovan Aff. ¶4 (Oct. 17, 2002). Donovan explained that in January 1999, he had instructed technicians that they needed to show the demand-after-magnet test in the demand-after magnet screen. Id. ¶ 5. His March 23, 2000 memo was intended to communicate the need to record the entire demand-after-magnet test in the demand-after-magnet screen, and to highlight the impropriety of recording part of the test on that screen and part on the demand screen. Id. ¶¶ 5-6.

3. The District Court’s Denial of a New Trial

Although the government opposed Cano-va’s Rule 33 motion as both untimely and lacking in merit, the district court agreed only with the latter argument. In an unpublished memorandum opinion, the court concluded that a jury could reasonably have found from the trial evidence that Canova, “in an effort to increase the volume of tests and revenue, [had] importuned technicians at Raytel to skip the third [Medicare testing] requirement and/or not take the minimum 30 seconds of ECG strips in each of the three portions of the test.” United States v. Canova, No. 3:01 CR 264(AVC), at 3 (D.Conn. Mar. 18, 2003). Further, “the jury may have reasonably found that in order to conceal Raytel’s non-compliance with the monitoring requirements, the defendant conspired to obstruct a federal audit,” and “knowingly made false statements to Medicare representatives.” Id.

Insofar as Canova specifically challenged the government’s proof of his guilty knowledge, the court summarized the testimony of Puziak, Vincent, and Pelletier, and concluded therefrom that the jury could reasonably have found that, “as early as 1998,” defendant knew that Raytel was not complying with Medicare’s testing specifications, id. at 8, and that his knowledge of this “problem” continued into December 1999 and January 2000, when he made the false statements of which he was found guilty, id. at 9.

To the extent Canova presented new evidence to challenge the prosecution’s case, the court decided that no new trial was warranted because the defendant had “failed to prove ... that he was justifiably ignorant of said evidence at the time of the trial despite due diligence.” Id. at 11. The court rejected the suggestion that the prosecutors had presented “improper argument or evidence” at trial, so as to excuse Canova’s failure to secure the aforementioned evidence for trial. In any event, the court concluded that, even if Canova’s new arguments “might add new support to his claim of innocence with a second jury, he ha[d] not demonstrated a miscarriage of justice or exceptional circumstances” sufficient to warrant a new trial. Id. at 12.

C. Canova’s Sentencing

The Probation Department, in its pre-sentence report (“PSR”) to the court, recommended that Canova’s total offense level under the Sentencing Guidelines be calculated by grouping the four counts of conviction pursuant to U.S.S.G. § 3D1.2(b) and using the fraud guideline then applicable to the § 1001 substantive and conspiratorial crimes, U.S.S.G. § 2F1.1 (1998). See U.S.S.G. § 3D1.3(a) (stating that for offenses grouped pursuant to § 3D1.2(b), the offense level for the group should be determining by reference to the highest offense level of the counts in the group). Following this path, the PSR calculated Canova’s base offense level at six, see id. § 2F1.1(a), with enhancements of thirteen levels for a $5-million loss to Medicare, see id. § 2F1.1(b)(1)(N); two levels for more than minimal planning, see id. § 2F1.1(b)(2)(A); two levels for leadership role, see id. § 3B1.1(c); and two levels for obstruction of justice based on his trial testimony, see id. § 3C1.1. With a total offense level of 25, and a criminal history of I, the PSR reported Canova’s Sentencing Guidelines range at 57 to 71 months of incarceration. The PSR also noted, however, three grounds for a possible downward departure: (1) the $5-million loss determination might be viewed to overstate the seriousness of the offense, see id. § 2F1.1, cmt. n. 11; (2) Canova’s work as a volunteer firefighter might be considered extraordinary community service, cf. id. § 5H1.11; and (3) these two factors in combination, if not individually, might take Canova’s case outside the heartland of the Guidelines, see id. § 5K2.0.

Canova filed written objections to the PSR’s proposed loss and obstruction enhancements and moved for a downward departure based on a history of public service and good works. The government did not respond to defendant’s Guidelines objections either in writing or when afforded an opportunity to be heard orally by the court, nor did it object to a good-works departure.

In considering Canova’s objections, the district court concluded that the evidence was insufficient “to support a loss calculation of five million dollars.” Sentencing Tr. at 24. It observed that to find such a loss, it would have to conclude that Ray-tel’s “abbreviated tests were worthless. And there simply was not evidence that the tests were of no value.” Id. at 25. To the contrary, defense evidence indicated that “no loss, or no value was lost, by the abbreviation” of the required tests. Id. Thus refusing to apply any loss enhancement to the calculation of Canova’s fraud guideline, the district court decided to adopt “an alternative method of calculating the disposition here.” Id. It relied on U.S.S.G. § 2J1.2 rather than § 2F1.1 to determine the applicable Guidelines range. See U.S. Sentencing Guidelines Manual, app. A (identifying § 2J1.2 as appropriate guideline for violations of 18 U.S.C. § 1516; identifying § 2F1.1 as appropriate guideline for violations of 18 U.S.C. § 1001); see also U.S.S.G. § 3D1.3(a).

Starting with the base offense level of twelve prescribed by § 2J1.2, the district court applied a two-level enhancement for Canova’s leadership role, see U.S.S.G. § 3Bl.l(c), but rejected any further enhancements. Specifically, the court declined to apply a two-level obstruction enhancement for Canova’s trial testimony, see id. § 3C1.1, observing that such an enhancement would require it to “find that the defendant not only perjured himself, but he did so with the specific intent to obstruct justice.” Sentencing Tr. at 26. Upon review of the case’s “massive record,” the court concluded that it was “unable” to find “that there was such a specific intent.” Id. Thus, with a total offense level of 14 and a criminal history of I, Canova faced a Guidelines sentencing range of 15 to 21 months of incarceration.

The court decided not to sentence Cano-va within this range, but to grant a six-level downward departure in consideration of “service to his country and his community,” which included six years’ service in the United States Marine Corps, “exemplary and many times courageous service” as a volunteer firefighter, and Good Samaritan aid to “three total strangers who were in extreme medical distress.” Id. at 26-27. The court further supported its departure decision by reference to trial evidence suggesting that Medicare representatives could not themselves “tell from the language of [Medicare’s] policy that the demand after magnet phase of this so-called 30-30-30 test was required.” Id. at 27.

Accordingly, on each of the four counts of conviction, the district court sentenced Canova to one year of probation, a $1,000 fine, and a $100 special assessment, the sentences to run concurrently as to the probation term and fine, consecutively as to the special assessment for a total of $400.

11. Discussion

We address Canova’s cross-appeal from the district court’s denial of a new trial before the government’s appeal of Cano-va’s sentence because a favorable ruling on the cross-appeal would render the government’s sentencing challenge moot.

A. Canova’s Motion for a New Trial

Canova asserts that the district court abused its discretion in denying his motion for a new trial pursuant to Fed. R.Crim.P. 33. The government submits that we can reject this argument on either of two grounds: (1) the district court lacked jurisdiction to entertain Canova’s Rule 33 motion because it was not timely filed, or (2) the district court’s denial of the motion was well within its discretion. While Canova’s motion may, indeed, have been" untimely, recent Supreme Court precedent casts doubt on whether such a defect is properly characterized as “jurisdictional.” See Kontrick v. Ryan, 540 U.S. 443, 454, 124 S.Ct. 906, 157 L.Ed.2d 867 (2004). If the defect is not jurisdictional, the timeliness challenge is necessarily forfeited because the government initially consented to the filing extension that it now claims the district court was not empowered to grant. See id. at 456, 124 S.Ct. 906 (noting that “a critical difference between a rule governing subject-matter jurisdiction and an inflexible claim-processing rule” is that the latter can “be forfeited if the party asserting the rule waits too long to raise the point”). The parties did not have the benefit of Kontrick when they briefed the question of jurisdiction; nevertheless, we do not request further submissions on the issue because the government’s jurisdictional challenge, at best, raises a statutory not a constitutional concern, see Fama v. Commissioner of Corr. Servs., 235 F.3d 804, 816 n. 11 (2d Cir. 2000) (noting that “the Supreme Court has barred the assumption of ‘hypothetical jurisdiction’ only where the potential lack of jurisdiction is a constitutional question”), and its alternative argument that the district court did not abuse its discretion clearly supports affirmance.

1. The Timeliness of Canova’s Rule 33 Filing

a. The Filing Limitations of Rule 33

Rule 33 states that “[ujpon the defendant’s motion,” the district court “may vacate any judgment and grant a new trial if the interest of justice so requires.” Fed. R.Crim.P. 33(a). The time limits for filing a Rule 33 motion are as follows: FecLR.Crim.P. 38(b). These time limits were expressly “framed to resist ad hoc relaxation” and, thus, may fairly be characterized as “rigid.” Carlisle v. United States, 517 U.S. 416, 434-36, 116 S.Ct. 1460, 134 L.Ed.2d 613 (1996) (Ginsburg, J., together with Souter and Breyer, JJ., concurring) (discussing identical language in Fed.R.Crim.P. 29 (prescribing time limits for filing a motion for a judgment of acquittal)). Indeed, the sternness of Rule 33’s time limitations is emphasized by Rule 45(b). Subpart (1) of that rule recognizes that district courts generally enjoy broad discretion to extend filing times under the federal criminal rules either “(A) before the originally prescribed or previously extended time expires; or (B) after the time expires if the party failed to act because of excusable neglect,” Fed.R.Crim.P. 45(b)(1), but subpart (2) identifies a specific exception to this principle: “The court may not extend the time to take any action under Rules 29, 33, 34, and 35, except as stated in those rules ” (emphasis added). See also Carlisle v. United States, 517 U.S. at 425-26, 116 S.Ct. 1460 (rejecting argument that a district court retains inherent authority to grant extensions outside the time limits identified in the rules referenced in Rule 45(b)(2)).

(1) Newly Discovered Evidence. Any motion for a new trial grounded on newly discovered evidence must be filed within 3 years after the verdict or finding of guilty.
(2) Other grounds. Any motion for a new trial grounded on any reason other than newly discovered evidence must be filed within 7 days after the verdict or finding of guilty, or within such further time as the court sets during the 7-day period.

Rule 33 states that a district court may extend the time for filing new trial motions, but only if the court takes such action “during the 7-day period” following the verdict or finding of guilty. Fed. R.Crim.P. 33(b)(2). Moreover, the plain language of the rule does not contemplate open-ended extensions; the “further time” within which a defendant must file a Rule 33 motion must be “set [ ] during the seven day period.” Id. (emphasis added). Reading Rule 33 to “mean[ ] what it says: A court can only extend the time in which to grant a motion for a new trial if a court fixes such time within 7 days of the verdict or finding of guilty.” United States v. Hall, 214 F.3d at 178 (construing identical language in Rule 29); United States v. Hocking, 841 F.2d 735, 736-37 (7th Cir. 1988) (explaining that district court lacked authority to extend time to file Rule 33 motion after seven-day period had elapsed).

In this case, although the district court’s October 4, 2002 order extending Canova’s Rule 33 filing date to October 18, 2002, fell within the prescribed seven-day period, see Fed.R.Crim.P. 45(a) (specifying rules for calculating time), the court’s subsequent October 17, 2002 order granting Canova a further extension to October 28, 2002, fell well outside that narrow window. Accordingly, it appears that the district court was prohibited from entering the October 17 order or entertaining the October 28 motion. In an effort to avoid this result, Canova asserts that his October 28, 2002 filing does not depend on the district court’s untimely October 17, 2002 extension order. Rather, he insists that his filing was timely under the district court’s October 4, 2002 order. Canova notes that the district court itself characterized its October 4, 2002 order as one extending Canova’s filing time until “October 18, 2002 ‘plus any reasonable additional time that [Canova] needed to file the motions.’ ” Canova Reply Br. at 2 (quoting United States v. Canova, No. 3:01 CR 264(AVC), at 7 (D.Conn. Mar. 18, 2003)). We accord substantial deference to a district court’s construction of its own orders, cf. United States v. Spallone, 399 F.3d 415, 423 (2d Cir.2005), but the construction cannot be based on an error of law, see generally Zervos v. Verizon New York, Inc., 252 F.3d 163, 169 (2d Cir.2001). The construction that Canova attributes to the district court would be so impermissibly based because an open-ended extension bounded only by “reasonableness” fails to comport with the rule’s mandate that any extended filing time be “set[ ] during the 7-day period” following verdict.

In reaching this conclusion, we note that the language cited by Canova — “plus any reasonable additional time that [Canova] needed to file” — does not actually appear in the district court’s October 4, 2002 order. That order simply states that Cano-va’s September 27, 2002 motion is “GRANTED.” United States v. Canova, No. 3:01 CR 264(AVC) (D.Conn. Oct. 4, 2002). Nor did Canova employ the quoted language in his motion, such that the district court’s succinct order might be construed to adopt the motion’s prayer for relief. What Canova requested was an extension of the time “to file post-trial motions” to a specific date, “October 18, 2002,” with a boilerplate request for “such other and further relief as the Court may deem just and proper.” Motion for Extension of Time to File Post-Trial Motions, at 2 (Sept. 27, 2002). The reasonable conclusion to draw from this motion and the court’s one-word order is that the court “granted” Canova’s request to extend his filing time to October 18, 2002, but did not identify any other “just and proper relief’ to be granted on October 4, 2002.

Canova submits that a broader construction of the court’s October 4th order is supported by the context in which the ruling was made. He points specifically to a telephone conversation between his counsel and the trial judge’s law clerk occurring on September 27, 2002, two days after verdict. In that conversation, counsel advised the clerk that he intended to seek a three-week extension of the prescribed time to file motions. The clerk responded favorably and, representing that he was speaking for the court, advised counsel that “any reasonable extension beyond the three weeks would [also] be granted.” Grudberg Aff. at 1-2 (Nov. 27, 2002). Because the district court accepted counsel’s account of this conversation as correct, we do likewise. Nevertheless, it makes no difference to the outcome. Because Rule 33 requires a court to “set” any further time for the filing of a Rule 33 motion within seven days of verdict, a court could not expand its extension authority by granting a defendant timely Rule 33 relief to some indefinite additional time that the court may subsequently deem “reasonable.” Such an open-ended extension order would be erroneous as a matter of law.

In sum, because the only extension date actually “set” by the district court within seven days of verdict was October 18, 2002, and because Canova failed to adhere to that deadline, the district court was not authorized under Rule 33 to entertain his untimely October 28, 2002 motion. In view of the perils involved in timely pursuing extensions to move for a new trial pursuant to Rule 33 or a judgment of acquittal pursuant to Rule 29, trial counsel would be well advised, on rendition of a verdict, to make an oral motion for a new trial or judgment of acquittal (asking the court to extend time for briefing, where necessary) rather than simply to request additional time to make the motion.

b. The Jurisdictional Implications of Rule SS’s Filing Limitations

Because the government initially consented to Canova filing his Rule 33 motion on October 28, 2002, its timeliness challenge to the motion, even if meritorious, is necessarily forfeited unless the error is jurisdictional. See Kontrick v. Ryan, 540 U.S. at 458-59, 124 S.Ct. 906. This court has previously characterized the time limits of Rule 33 as “jurisdictional,” see United States v. McCarthy, 271 F.3d 387, 399 (2d Cir.2001); United States v. Lussier, 219 F.3d 217, 220 (2d Cir.2000), as have our sister circuits, see, e.g., United States v. Glenn, 389 F.3d 283, 287 (1st Cir.2004); United States v. Eberhart, 388 F.3d 1043, 1049 (7th Cir.2004); United States v. Correa, 362 F.3d 1306, 1309 (11th Cir.2004); United States v. Erwin, 277 F.3d 727, 732 (5th Cir.2001); United States v. Emuegbunam, 268 F.3d 377, 397 (6th Cir.2001); United States v. Villalpando, 259 F.3d 934, 937-38 (8th Cir.2001); United States v. Hall, 214 F.3d at 177-79 (D.C.Cir.2000); United States v. Quintanilla, 193 F.3d 1139, 1148 (10th Cir.1999); United States v. Gaydos, 108 F.3d 505, 512 (3d Cir.1997); United States v. Smith, 62 F.3d 641, 648 (4th Cir.1995); United States v. Cook, 705 F.2d 350, 351 (9th Cir.1983). This is hardly surprising given the Supreme Court’s characterization of Rule 45(b)’s strictures on extensions of time as “mandatory and jurisdictional.” See United States v. Robinson, 361 U.S. 220, 228-29, 80 S.Ct. 282, 4 L.Ed.2d 259 (1960).

More recently, however, the Supreme Court has reminded us that “ ‘jurisdiction’ ... ‘is a word of many, too many, meanings.’ ” Kontrick v. Ryan, 540 U.S. at 454, 124 S.Ct. 906 (quoting Steel Co. v. Citizens for Better Env’t, 523 U.S. 83, 90, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998)). As a result, courts, including the Supreme Court, “have been less than meticulous” in using the term, frequently employing “ ‘jurisdictional’ to describe emphatic time prescriptions in rules of court,” when the word should, in fact, be reserved “for prescriptions delineating the classes of cases (subject-matter jurisdiction) and the persons (personal jurisdiction) falling within a court’s adjudicatory authority.” Id. at 454-55, 124 S.Ct. 906. In making this point, Kontrick specifically contrasted the Supreme Court’s past use of the term “jurisdictional” in United States v. Robinson, 361 U.S. at 229, 80 S.Ct. 282, to refer to the time limitations of Fed.R.Crim.P. 45(b), with its careful avoidance of that term in Carlisle v. United States, 517 U.S. at 419-23, 116 S.Ct. 1460, when analyzing the time limitations of Rule 29, see also id. at 434-36, 116 S.Ct. 1460 (Ginsburg, J., together with Souter and Breyer, JJ., concurring) (expressing view that Rules 29 and 45 are simply “tight” time prescriptions, not limitations on a court’s subject matter jurisdiction).

In light of Kontrick’s discussion of the ambiguity in the word “jurisdictional,” it might be appropriate for us to explore the meaning of our past characterization of Rule 33’s filing limitations as “jurisdictional.” But see United States v. Eberhart, 388 F.3d at 1049 (continuing to treat Rule 33 as jurisdictional because Kontrick did not specifically overrule United States v. Robinson, 361 U.S. at 229, 80 S.Ct. 282, or United States v. Smith, 331 U.S. 469, 474 n. 2, 67 S.Ct. 1330, 91 L.Ed. 1610 (1947)). We are loath to do so, however, in this case in which the parties filed their briefs without the benefit of Kontrick. While we could, of course, request supplemental briefing, there seems little point in putting the parties to that extra burden because, even if, in the end, we were to reject the government’s jurisdictional challenge and to consider its timeliness challenge forfeited, we would still undoubtedly affirm the district court’s denial of a new trial because the record amply demonstrates that this ruling was well within the court’s discretion. Accordingly, because the jurisdictional challenge in this case is statutory rather than constitutional, we may assume hypothetical jurisdiction, see Fama v. Commissioner of Corr. Servs., 235 F.3d at 817, and proceed to explain our reasons for reaching that conclusion, leaving to another day’s resolution whether Rule 33’s time limits are appropriately characterized as jurisdictional in light of Kontrick.

2. The District Court’s Rejection of the Motion on the Merits

Even if Canova’s Rule 33 motion had been timely filed, that would not entitle him to relief on appeal because the district court did not abuse its discretion in denying him a new trial. As Canova acknowledges, a trial court exercises “broad discretion” in ruling on a new trial motion, and we review its decision deferentially, reversing only for abuse of discretion. United States v. Ferguson, 246 F.3d 129, 133 (2d Cir.2001). In considering whether to grant a new trial, a district court may itself weigh the evidence and the credibility of witnesses, but in doing so, it must be careful not to usurp the role of the jury. See United States v. Autuori, 212 F.3d 105, 120 (2d Cir.2000); accord United States v. Ferguson, 246 F.3d at 133. The “ultimate test” is “whether letting a guilty verdict stand would be a manifest injustice .... There must be a real concern that an innocent person may have been convicted.” United States v. Ferguson, 246 F.3d at 133 (citation and quotation marks omitted); see also United States v. Aponte-Vega, 230 F.3d 522, 525 (2d Cir.2000) (per curiam).

In concluding that this case does not present such a concern, the district court pointed to a number of prosecution witnesses who had offered direct evidence of Canova’s guilty knowledge of the Raytel testing fraud and of his active role in deceiving Medicare auditors about this fraud. Canova argues that these witnesses were not credible because their accounts were riddled with inconsistencies, and they had motives to testify falsely. These arguments, however, were forcefully presented to the jury through the vigorous cross-examinations and arguments of Ca-nova’s able trial counsel. Nevertheless, the jury, which had the opportunity to see the witnesses testify, to weigh their testimony against the other evidence in the case, and to hear the arguments of the prosecution, found Canova guilty beyond a reasonable doubt on four of the five charges tried. Only “exceptional circumstances” warrant a district court’s intruding upon “the jury function of credibility assessment,” United States v. Sanchez, 969 F.2d 1409, 1414 (2d Cir.1992); accord United States v. Ferguson, 246 F.3d at 133; United States v. Autuori, 212 F.3d at 120, and the experienced trial judge found none in this case. To the contrary, he explicitly found that the jury could reasonably have concluded from the totality of the evidence that Canova had importuned Raytel employees not to comply with Medicare testing requirements and had then made false statements to conceal this conduct. Under these circumstances, the district court’s decision not to grant Cano-va a new trial fell well within its broad discretion.

The fact that Canova proffered some new evidence in support of his Rule 33 motion warrants no different conclusion. When a defendant proffers new evidence to support a Rule 33 motion, a court may appropriately consider whether (1) counsel could have “discovered the evidence with due diligence before or during trial; (2) the evidence demonstrates that a witness in fact committed perjury; (3) the new evidence is material; and (4) the new evidence is not cumulative.” United States v. Middlemiss, 217 F.3d 112, 122 (2d Cir. 2000). As the district court observed, Ca-nova’s new evidence, which essentially derived from Raytel employees and records, was certainly available to him at the time of trial. Canova’s assertion that he had no reason to procure this evidence for trial because he had not anticipated certain government tactics and arguments is unconvincing. The evidence in question all pertained to matters that Canova knew would be in issue at trial, even if he did not know the government’s exact position on these matters. In any event, the evidence, even when viewed most favorably to Canova, did not demonstrate any witness’s actual perjury. At best, it would have afforded defense counsel additional grounds on which to impeach prosecution witnesses whose credibility had already been vigorously challenged or to bolster Canova’s own suspect credibility. The district court did not abuse its discretion in concluding that such evidence was insufficient to raise “a real concern that an innocent person may have been convicted.” United States v. Ferguson, 246 F.3d at 133 (citation and quotation marks omitted); see generally United States v. Monteleone, 257 F.3d 210, 219 (2d Cir.2001) (noting that “inconsistencies in testimony” do not, by themselves, demonstrate that the witness actually committed perjury for purposes of reviewing a new trial motion); United States v. Gambino, 59 F.3d 353, 366 (2d Cir.1995) (“Nondisclosure of cumulative evidence tending only to further impeach a witness’ general credibility is not grounds for granting a Rule 33 motion.”).

In sum, assuming jurisdiction to hear Canova’s new trial motion, we conclude that the denial of that motion on its merits was not an abuse of the district court’s discretion. Accordingly, we reject defendant’s cross-appeal and affirm so much of the judgment of conviction as establishes his guilt on the four specified crimes.

B. Canova’s Sentence

1. Postr-Booker Review

The government appeals Canova’s probationary sentence on the grounds that the district court miscalculated his Sentencing Guidelines range and, in any event, erred in granting him a downward departure based on extraordinary public service and good works. To the extent it urges this court to examine the departure decision de novo pursuant to 18 U.S.C. § 3742(e), as amended in 2003 by the PROTECT Act, see Pub.L. No. 108-21, 117 Stat. 650 (Apr. 30, 2003); United States v. Simmons, 343 F.3d 72, 78 (2d Cir.2003), such review is now foreclosed by the Supreme Court’s decision in United States v. Booker, — U.S. —, 125 S.Ct. 738, 160 L.Ed.2d 621, which, inter alia, excised § 3742(e) from federal sentencing law to permit the federal Sentencing Guidelines to be treated as advisory rather than mandatory, thereby surviving a Sixth Amendment challenge, see id. at 764-65. Booker instructs that sentences should be reviewed on appeal only for “unreasonableness.” Id. at 765-66.

In applying this more deferential standard of review, we focus primarily on the sentencing court’s compliance with its statutory obligation to consider the factors detailed in 18 U.S.C. § 3553(a). Id. at 766 (noting that § 3553(a) factors “will guide appellate courts, as they have in the past, in determining whether a sentence is unreasonable”). Prior to Booker, sentencing courts understandably gave predominant, indeed controlling, weight to two factors identified in § 3553(a): the sentencing range established by the federal Sentencing Guidelines, see id. § 3553(a)(4), and the pertinent policy statements of the Sentencing Commission, see id. § 3553(a)(5). To assess whether this formerly common error resulted in an unreasonable sentence in a particular case, this court has remanded unpreserved Sixth Amendment challenges to pre-Booker sentences to the district court for it to determine if a defendant’s sentence would have been materially different if the court had understood that the Guidelines were advisory rather than mandatory. See United States v. Crosby, 397 F.3d at 117-18.

This case differs from most post -Booker appeals in that the defendant raises no Sixth Amendment challenge to his probationary sentence. Rather, the government complains that the district court miscalculated the applicable Guidelines as well as misapprehended its departure authority within the Guidelines system. The argument is not rendered irrelevant by Booker. As Crosby recognized, even under an advisory Guidelines system, district courts “will normally have to determine the applicable Guidelines range ... in the same manner as before Booker [],” id. at 111— 12, in order to decide whether “(i) to impose the sentence that would have been imposed under the Guidelines, i.e., a sentence within the applicable Guidelines range or within permissible departure authority, or (ii) to impose a non-Guidelines sentence,” id. at 113. In United States v. Rubenstein, we recently ruled that a Guidelines error that “appreciably] influence[s]” this decision could render the final sentence unreasonable. 403 F.3d at 98.

Thus, we review the government’s sentencing challenges to determine whether any error presents this concern so as to warrant remand for resentencing.

2. The Enhancement Challenges

a. The Fraud Loss

The government contends that the district court erred in concluding that no loss enhancement to the base offense level for fraud, see U.S.S.G. § 2Fl.l(a), was supported by the evidence. It asserts that the record compelled a thirteen-level enhancement because defendant’s crimes caused or were intended to cause a loss to Medicare of $5 million. See id. § 2Fl.l(b)(l)(N). We review the factual determinations underlying a district court’s loss calculation at sentencing for clear error and its application of the Sentencing Guidelines de novo. See United States v. Garcia, Nos. 03-1407, 03-1429, 2005 WL 1444146, 413 F.3d 201, 221-24 (2d Cir. June 21, 2005) (explaining that clear error standard of review remains applicable for appellate challenges to judicial fact-finding at sentencing after United States v. Booker)-, United States v. Seli-outsky, 409 F.3d 114, 119 (2nd Cir.2005) (recognizing that, after excision of § 3742(e), court continues to review issues of fact for clear error); see also United States v. Crosby, 397 F.3d at 112 (observing that, “with the mandatory use of the Guidelines excised,” a court’s identification of the applicable sentencing range to be considered pursuant to 18 U.S.C. § 3553(a)(4)-(5) proceeds “in the same manner as before Booker [ ]”).

Because fraud is a crime of infinite variety, see generally United States v. Altman, 48 F.3d 96, 102 (2d Cir.1995), it presents particular challenges for sentencing courts striving to achieve proportionality in sentencing while reducing unwarranted disparity, see generally U.S. Sentencing Guidelines ch. 1, pt. A.3 (identifying reduced disparity and proportionality based on the severity of the offense as two key goals of the Sentencing Reform Act of 1984, 18 U.S.C. § 3551 et seq.); United States v. Booker, 125 S.Ct. at 767 (explaining that post-Booker sentencing contemplates consideration of Guidelines to serve goals of “avoiding unwarranted sentencing disparities” and “proportionality”). The Sentencing Commission has identified “loss” as a critical factor in assessing the relative seriousness of a fraud offense. It defines loss as the “value of the money, property, or services unlawfully taken” from the victim, U.S.S.G. § 2F1.1, cmt. n. 8, and provides for a series of step increases from the base offense level of six depending on the dollar loss at issue in the particular fraud offense, see id. § 2Fl.l(b)(l).

The Commission has long recognized that the calculation of exact loss amounts in individual cases is no easy task. Accordingly, it instructs that, in applying the Sentencing Guidelines, “loss need not be determined with precision”; a sentencing court “need only make a reasonable estimate of the loss, given the available information.” Id. § 2F1.1, cmt. n. 9; see United States v. Carboni, 204 F.3d 39, 46 (2d Cir.2000); cf. United States v. Crosby, 397 F.3d at 112 (noting, in deciding whether to impose a non-Guidelines sentence, judges might “avoid the need to resolve all of the factual issues necessary to make precise determinations,” in appropriate cases, of monetary loss where either of two sentencing ranges is applicable). The district court acknowledged this principle, but concluded that the government had failed to adduce reliable evidence that it had sustained any loss from the testing fraud. Indeed, it noted that the defendant’s evidence suggested that Medicare had suffered no loss of clinical value. We identify two flaws in this analysis.

(1) A Victim Who Pays for Goods or Services on the Fraudulent Representation that They Conform to Certain Specifications Has Sustained a “Loss”

To the extent defendant adduced evidence that the tests performed by Raytel were as clinically sound as the tests required by Medicare, this fact does not mean that the government sustained no loss from the charged fraud. Canova’s fraudulent representations did not, after all, pertain to the clinical value of the tests performed, see U.S.S.G. § 2F1.1, cmt. n. 3(a); they pertained to the particular test specifications being performed, see id., cmt. n. 3(e). When a party fraudulently procures payment for goods or services by representing that they were produced or provided according to certain specifications, it is not the task of a sentencing court to second-guess the victim’s judgment as to the necessity of those specifications. Whether the testing time on a pacemaker, the number of rivets on an airplane wing, or the coats of paint on a refurbished building is a matter of necessity or whim, the fact remains that the victim has been induced to pay for something that it wanted and was promised but did not get, thereby incurring some measure of pecuniary “loss.” See United States v. Bhutani, 266 F.3d 661, 670 (7th Cir.2001) (ruling that loss calculation did not depend on whether defendant’s fraudulent adulteration of a drug in fact had an adverse medical effect; “there was a loss because consumers did not get what they bargained for”); cf. United States v. Maurello, 76 F.3d 1304, 1314 (3d Cir.1996) (noting that a victim who contracts to have a building constructed “according to certain specifications” and receives “the services for which he bargained” sustains no loss “despite the fact that he has received them from a person who was not legally authorized to offer them”; Jacob & Youngs, Inc. v. Kent, 230 N.Y. 239, 244, 129 N.E. 889, 891 (1921) (Cardozo, J.) (explaining that doctrine of substantial performance is available only to “the transgressor whose default is unintentional and trivial”; by contrast, “[t]he willful transgressor must accept the penalty of his transgression. For him there is no occasion to mitigate the rigor of implied conditions.”) (citations omitted)).

United States v. Chatterji, 46 F.3d 1336 (4th Cir.1995), discussed at length by the parties, is not to the contrary. In that case, the Fourth Circuit concluded that a defendant’s fraudulent representations to the Food and Drug Administration (“FDA”) to secure approval for a particular drug did not cause any loss to consumers because the marketed “products were exactly what they purported to be.” Id. at 1341. Under the circumstances, the court viewed the fraud as purely “regulatory”; nevertheless, it expressed “little doubt that economic loss would exist” if “a drug with fraudulently-obtained FDA approval ... is something less than it is represented to be.” Id. at 1342; see also U.S.S.G. § 2B1.1, cmt. n. 3(f)(v)(III) (now providing special rule for loss calculation in cases involving regulatory approval obtained by fraud). In this case, the tests for which the government paid Raytel millions of dollars were not “exactly what they purported to be,” ie., 30-30-30 tests, but “something less” with respect to the specified production of thirty seconds of magnetic tape in the final test phase. Similarly distinguishable is United States v. Schneider, a case finding no loss to a victim where the defendant procured a contract by fraud but thereafter performed “to the perfect satisfaction of the contracting agency.” 930 F.2d 555, 558 (7th Cir.1991). In this case, Raytel did not perform to the “perfect satisfaction” of the government. Instead, the very essence of Canova’s fraud scheme was to conceal from the government the fact that Raytel was not performing pacemaker tests according to Medicare specifications in order to induce payments that would otherwise not have been made.

This does not mean that a victim’s loss in a substitute goods or services case necessarily equals the full contract price paid. The Guidelines suggest that, in such cases, loss is properly measured by looking to the “reasonably foreseeable costs of making substitute transactions and handling or disposing of the product delivered or retrofitting the product so that it can be used for its intended purpose,” plus the “reasonably foreseeable cost of rectifying the actual' or potential disruption to [the victim’s] operations caused by the product substitution.” U.S.S.G. § 2F1.1, cmt. n. 8(c). In some circumstances, product adjustments may so easily be accomplished that the fraudulent-substitution causes the victim only a small loss. In other circumstances, where the goods or services must be recommissioned, the loss may be considerable. But in no case do the Guidelines contemplate a court rewriting the parties’ contract to excise specifications paid for but not received and, thereby, concluding that the victim sustained no loss.

The government does not appear to have urged the district court to engage in any calculation of loss along the lines outlined in Note 8(c). We need not here consider whether such a calculation could be made on the present record because, for reasons discussed in the next section, we conclude that the government’s right to recoup monies paid Raytel for testing not conforming to specifications provides a satisfactory alternative for calculating “intended loss.” Before turning to that discussion, however, we reiterate the key point of this part of our analysis: a party who contracts to have goods produced or services performed according to certain specifications, and who pays for those goods or services in reliance on a fraudulent representation that they conform to the specifications, has sustained a measure of pecuniary loss for purposes of calculating the fraud guideline, and a defendant cannot avoid a loss enhancement by offering evidence that no one other than the victim places any value on the demanded specification.

(2) The Defendant’s Fraudulent Scheme to Prevent Medicare from Recovering Payments Made to Raytel Pursuant to the Testing Fraud Itself Caused a Calculable “Intended Loss”

The Sentencing Commission has clearly stated that “if an intended loss that the defendant was attempting to inflict can be determined, this figure will be used if it is greater than the actual loss.” Id. § 2F1.1, cmt. n. 8. As this court explained in United States v. Carboni “[intended loss is tantamount to the probable loss from a particular misstatement because one is presumed to intend the natural and probable consequences of one’s acts.” 204 F.3d at 47 (quoting United States v. Jacobs, 117 F.3d 82, 95 (2d Cir.1997)) (quotation marks omitted). Canova submits that “intended loss” has no bearing on the calculation of his Guidelines range because it pertains only to unconsummated frauds, and his charged fraud was complete. We are skeptical as to whether fraud lends itself to the bright line drawing urged by Canova, but we need not resolve that question in this case because defendant’s conspiratorial crime, in fact, involved two closely related fraud schemes.

Canova’s completed conduct relates only to the first fraud: Raytel’s procurement of millions of dollars in Medicare funds through false representations that it was testing pacemakers in accordance with government specifications. This was understandably the focus of the district court’s attention when it considered whether the government had sustained a loss from Raytel’s abbreviated testing procedures. But Canova also engaged in a second fraud, which was not fully consummated as a result of government detection. Pursuant to this fraud, Canova made further false representations to Medicare agents to obstruct an audit of Raytel, thereby preventing the government from recovering monies paid to Raytel pursuant to the testing fraud. Indeed, each of Ca-nova’s substantive § 1001 convictions involved false statements made in furtherance of this second fraud.

The parties apparently agree that the government, through its carrier United Healthcare, was legally entitled to recoup from Raytel its full payment for any pacemaker tests not performed according to Medicare specifications. Nor does there appear to be any question that Canova was aware of this right. United HealthCare’s December 2, 1999 letter demanded that Raytel reimburse Medicare its payment for two pacemaker tests that did not conform to specifications. The auditors’ March 5, 2000 letter also ordered Raytel to reimburse Medicare the monies paid for fifteen tests that Raytel could not document complied with specifications. Cano-va’s trial testimony made plain that he understood what was at stake: “I processed in Connecticut about 15, 20,000 tests a month. That’s a large bullet to take as a financial hit.” Trial Tr. at 987.

The intended loss calculation from a fraud scheme aimed at preventing this re-coupment is, therefore, relatively straightforward. The Medicare payments to Raytel for pacemaker testing during the two-year period covered by the audit (approximately $10 million) can be multiplied by the percentage of tests found not to comply with Medicare specifications (65.3 to 78 percent). Opting for a more conservative approach, the government urged the district court to conclude that at least 50 percent of Raytel’s tests did not conform to Medicare specifications, resulting in a loss of $5 million. This loss amount finds support not only in the cited trial evidence, but in Raytel’s own acceptance of a $5-million restitution order as part of the plea agreement in its criminal case. While Ca-nova may not be bound by Raytel’s acknowledgment of this restitution obligation, such an admission by a perpetrator of the charged fraud scheme precludes a court from concluding that no reliable evidence supports a $5-million loss calculation.

In sum, although a district court enjoys considerable discretion in calculating the loss applicable to a particular fraud, the record in this case did not permit it to conclude that the government sustained no loss from Canova’s fraudulent schemes to substitute an abbreviated pacemaker test for the longer one required by Medicare specifications and to conceal that fraudulent substitution in order to prevent the government from exercising its right to recoupment. The record supports an intended loss of recoupment in an amount of $5 million, and such a loss should have been factored into the Guidelines considered by the district court in imposing sentence.

Because there is a significant difference between a Guidelines range calculated to include this loss and the Guidelines range relied upon by the district court, the error might well have affected the ultimate sentence, even though the district court applied a downward departure. See generally United States v. Elefant, 999 F.2d 674, 678 (2d Cir.1993) (recognizing that “[t]he degree of downward departure appropriate from one starting point will not necessarily be the same as is appropriate from a lower [or higher] starting point”). Indeed, such an “appreciable influence” could obtain “even under the discretionary sentencing regime that will govern [a] resentencing,” because the applicable Guidelines range may serve as “a benchmark or a point of reference or departure” as the court exercises its expanded discretion. United States v. Rubenstein, 403 F.3d at 98. We do not here decide that every incorrectly calculated Guidelines sentence will necessarily require a remand for resentencing. See id. at 101 (Cardamone, J., concurring) (cautioning against such a conclusion). We conclude simply that “the influence” of a $5-million error in the calculation of a fraud guideline has sufficient potential to “appreciabl[y] influence” the ultimate sentence even under the more discretionary post-Booker sentencing regime to warrant a remand with instructions to vacate Cano-va’s sentence and to resentence him. Id. at 101; cf. United States v. Godding, 405 F.3d 125, 127 (2d Cir.2005) (per curiam) (ordering Crosby remand and noting concern “that the brevity of the term of imprisonment imposed ... does not reflect the magnitude of the theft of nearly $366,000 over a five-year period,” explaining that 18 U.S.C. § 3553(a)(2)(A) requires sentencing court to consider the need for sentence “to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense” (quotation marks omitted)).

b. The Perjury Enhancement

The government argues that the district court further erred in failing to enhance Canova’s offense level for obstruction of justice pursuant to U.S.S.G. § 3C1.1 in light of his trial perjury. In reviewing a challenge to a district court’s application of § 3 C 1.1, we examine its findings of fact only for clear error, and whether those facts constitute obstruction of justice is a question of law that we review de novo. See United States v. Garcia, 413 F.3d 201, 221-24, Nos. 03-1407, 03-1429; see also United States v. Crosby, 397 F.3d at 112.

Section 3C1.1 provides for a two-level enhancement if a defendant willfully obstructs or attempts to obstruct justice in the course of prosecution. See U.S.S.G. § 3C1.1. The relevant commentary identifies perjury as conduct that can trigger this enhancement. See id., cmt. n. 4(b). The government submits that the district court misunderstood — and, therefore, likely misapplied — the relevant case law because it stated that a § 3C1.1 enhancement required it “to find that the defendant not only perjured himself, but [that] he did so with the specific intent to obstruct justice,” Sentencing Tr. at 26, when obstructive intent is already an element of perjury. The government further contends that the trial record compelled a finding that Canova intended to obstruct justice, and that the district court’s findings to the contrary were not sufficiently specific to permit review. We reject these arguments as uniformly without merit.

To begin, we reject the government’s contention that the district court misunderstood the elements of perjury. As the Supreme Court recognized in United States v. Dunnigan, the criminal law establishes three elements for perjury: (1) “false testimony” given “under oath or af-finnation”; (2) “concerning a material matter”; (3) given “with the willful intent to provide false testimony, rather than as a result of confusion, mistake, or faulty memory.” 507 U.S. 87, 94, 113 S.Ct. 1111, 122 L.Ed.2d 445 (1993) (citing 18 U.S.C. § 1621); see also Leonard B. Sand, et al., 2 Modem Federal Jury Instructions (Criminal), Instr. 48-4 (2004). Acknowledging that some of its own precedents had not interpreted perjury to constitute obstruction of justice “unless the perjury is part of some greater design to interfere with judicial proceedings,” United States v. Dunnigan, 507 U.S. at 93, 113 S.Ct. 1111, the Supreme Court ruled that, when a defendant objects to a § 3C1.1 enhancement based on trial testimony, “a district court must review the evidence and make independent findings necessary to establish a willful impediment to or obstruction of justice, or an attempt to do the same, under the perjury definition we have set out,” id. at 95, 113 S.Ct. 1111 (emphasis added).

Following Dunnigan, this court, in United States v. Zagari, stated that “to base a § 3C1.1 enhancement upon the giving of perjured testimony, a sentencing court must find that the defendant 1) willfully 2) and materially 3) committed perjury, which is (a) the intentional (b) giving of false testimony (c) as to a material matter.” 111 F.3d 307, 329 (2d Cir.1997); accord United States v. Ben-Shimon, 249 F.3d 98, 102 (2d Cir.2001) (per curiam ). Indeed, Zagari emphasized that the willfulness contemplated by § 3C1.1 was distinct from the intent required to prove perjury. See 111 F.3d at 329 n. 20. The former refers to a defendant’s “specific purpose of obstructing justice,” whereas the latter refers to his “purposeful giving of the false testimony.” Id. In light of this distinction and Zagari’s identification of perjury as one of three elements necessary to a § 3C1.1 enhancement, we cannot conclude that the district court erred as a matter of law in observing that application of a § 3C1.1 enhancement required it to find more than perjury. It was further required to find that the perjury had been committed with the specific intent to obstruct justice.

The district court having correctly identified the applicable law, its conclusion that the requisite obstructive intent was not established by a preponderance of the evidence is a finding of fact to which we accord considerable deference. Indeed, because a witness’s obstructive intent, like his credibility, is sometimes revealed by the demeanor of his testimony as well as its content, we are particularly hesitant to second-guess a trial judge’s finding that a witness’s testimony, though perjurious, was not specifically intended to obstruct justice. See generally Mathie v. Fries, 121 F.3d 808, 812 (2d Cir.1997) (noting particularly strong deference due a district court’s findings of fact based on credibility assessments of witnesses it has heard testify). While the government points us to certain statements by Canova that are not easily attributed to confusion or mistake, or to some purpose other than obstruction, we cannot conclude that the record as a whole leaves us with “the definite and firm conviction” that the trial court erred in failing to find obstructive intent established by a preponderance of the evidence. United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948); accord Mathie v. Fries, 121 F.3d at 812.

Finally, to the extent the government suggests that the district court’s findings on the issue of obstructive intent were inadequate, this court has already ruled that a district court is not required to support a decision not to apply an obstruction enhancement with specific findings of fact. See United States v. Vegas, 27 F.3d 773, 782 (2d Cir.1994).

For all these reasons, we find no error in the district court’s decision not to apply an obstruction enhancement to the calculation of Canova’s Sentencing Guidelines range.

3. The Departure from the Guidelines Range

The government argues that the district court overstepped its departure authority under the Guidelines when it granted Canova a downward departure based on public service and good works. Defendant submits that the government’s failure to object to this departure ground in the district court waives the argument on appeal. We agree and specifically reject the government’s attempt to excuse its omission by claiming lack of adequate no-tice to the challenged departure before sentencing. Nevertheless, because we remand this case for resentencing and because 18 U.S.C. § 3553(a)(5) “contemplates consideration of policy statements issued by the Sentencing Commission, including departure authority,” United States v. Crosby, 397 F.3d at 112, it is appropriate for us briefly to explain why we reject the government’s departure challenge on the merits.

Sentencing Guideline 5H1.11 states that “[m]ilitary, civic, charitable, or public service; employment-related contributions; and similar prior good works are not ordinarily relevant in determining whether a sentence should be outside the applicable guideline range.” As the government concedes, the guideline generally discourages departures on the stated grounds; it does not bar them absolutely. In such circumstances, even under a mandatory Guidelines system, a court was authorized to grant a downward departure “if the [discouraged] factor is present to an exceptional degree or in some other way makes the case different from the ordinary case where the factor is present.” Koon v. United States, 518 U.S. 81, 96, 116 S.Ct. 2035, 135 L.Ed.2d 392 (1996); accord United States v. Sprei, 145 F.3d 528, 534 (2d Cir.1998).

The record plainly demonstrates the “exceptional degree” of Canova’s public service and good works. As a college student, he volunteered for the Marine Corps, in which he honorably served his country for six years, mostly in the active reserves. For seven years, he also served his Long Island community as a volunteer firefighter, sustaining injuries in the line of duty three times. On one such occasion, he risked his life by entering a burning building to rescue a three-year old hiding under a bed, but his efforts were to no avail; the child subsequently died in the hospital. While performing as a volunteer firefighter, Canova also participated in the successful delivery of three babies and administered cardio-pulmonary resuscitation (“CPR”) to persons in distress. This military and volunteer service all occurred more than twenty years before sentencing; nevertheless, more recent incidents demonstrated that Canova’s commitment to helping persons in distress was an instinctive part of his character. Notably, on three occasions, Canova acted as a Good Samaritan (1) administering CPR to an elderly man who experienced sudden cardiac arrest at a theme park, (2) administering CPR to a priest who suffered a heart attack on an airport rental car bus, and (3) assisting a woman who fainted on a public street until paramedics arrived. In each instance, other persons on the scene were so stunned by the distressful occurrence as to be rendered helpless. Only Canova rushed forward to address the emergencies.

Under these circumstances, we reject the argument that the district court, which had the opportunity to take Canova’s measure throughout his trial and numerous court appearances, abused its discretion in granting a downward departure for extraordinary public service and good works. Accordingly, consideration of this factor on remand would not, by itself, render a re-sentence unreasonable. Cf. United States v. Rubenstein, 403 F.3d at 100-01.

III. Conclusion

To summarize, we conclude:

(1) that Canova’s October 28, 2002 motion for a new trial was properly denied because, assuming the district court’s jurisdiction to entertain defendant’s untimely filing, its rejection of the motion on the merits was not an abuse of discretion; and

(2) that Canova’s sentence must be remanded with instructions to vacate and resentence because an error in the calculation of defendant’s Guidelines range is sufficiently significant to raise a question as to the reasonableness of the sentence imposed.

Accordingly, the judgment of the district court is Affirmed with respect to guilt, but the case is Remanded to the district court with instructions to vacate defendant’s sentence and to resentence consistent with this opinion and United States v. Booker, — U.S.-, 125 S.Ct. 738, 160 L.Ed.2d 621, and not inconsistent with United States v. Crosby, 397 F.3d 103. 
      
      . Section 50-1 states, in pertinent part:
      In order for transtelephonie monitoring services to be covered, the services must consist of the following elements:
      1. A minimum 30-second readable strip of the pacemaker in the free-running mode;
      2. Unless contraindicated, a minimum 30-second readable strip of the pacemaker in the magnetic mode; and
      3. A minimum 30 seconds of readable ECG strip.
      Medicare Program; National Coverage Decisions, 54 Fed.Reg. at 34,580.
     
      
      .Although telephone calls from Raytel technicians to pacemaker patients lasted, on average, seven minutes, some calls could last as long as half an hour if the patient was unfamiliar with the test process, hard of hearing, or infirm.
     
      
      . Vincent testified that he did not reach such an understanding with Boecklin.
     
      
      . We note that in July 2001, the HCFA was renamed the Centers for Medicare and Medicaid Services and is referenced as such in the current Medicare regulations. ■ See Centers for Medicare & Medicaid Services; Statement of Organization, Functions and Delegation of Authority; Reorganization Order, 66 Fed.Reg. 35,437-03 (July 5, 2001).
     
      
      . There was no evidence that the altered documents were ever submitted to Medicare. In fact, the documents were seized from Vincent’s office on June 23, 2000, during the execution of a search warrant at Raytel’s Connecticut facility.
     
      
      . Not insignificantly, when Canova was interviewed by federal agents on June 23, 2000, he continued to disavow Raytel’s non-compliance with Medicare testing specifications. He told the agents that Pelletier had advised him of "a possibility that the third strip of the test was not being conducted in the Connecticut office,” but that he (Canova) had conducted a personal review and determined "that there were no instances, none at all, that the third strip was not being done.” Id. at 823.
     
      
      . The government offered in evidence the March 23, 2000 memorandum issued by Michael Donovan, Raytel's New York Supervisor, which states in relevant part:
      
        It has been brought to my attention that when we test patients we need to show 30-second strips for each portion of the test. Therefore, with that in mind we must complete 30-second strips for the demand, magnet and demand after magnet tests. In the past I informed the floor that we must show a demand after magnet test per Medicare/Medicaid guidelines, this remains in effect but now we must show 30 seconds of strip for each test to be compliant with these guidelines. So altogether, you must show 90 seconds of test strips for each test you complete. You still only chop two test strips unless otherwise directed.
      
      
        If you do not get a good demand strip and get a good demand after magnet test strip, you can no longer finish the demand after magnet test in the demand portion. You are going to have to go back to the demand portion of the test and ask the patient to run another 30-second test. If that comes in clear, then you can chop that portion of the test. Do not chop in the demand after magnet portion of the test. We must show chops from the demand and magnet portions of the test only, unless otherwise by S.I. ’s or per supervisor.
      
      GX 87 (Donovan Mem. (Mar. 23, 2000) (emphasis in original)).
     
      
      . At trial, the prosecutor had confronted Ca-nova with a test report found in his files on which the patient’s and doctor's names had been obliterated with correction fluid. When asked if he had altered this report because the patient had the same zip code as one of the persons whose records were being sought by the Medicare audit team, Canova replied that the deletions were made to allow the record to be used for marketing purposes, not to deceive Medicare.
     
      
      . Effective November 1, 2001, § 2F1.1 was deleted by consolidation with § 2B1.1. See U.S.S.G. § 2F1.1 historical n. (2001) (citing app. C, amend. 617); see also United States v. Korman, 343 F.3d 628, 629 n. 1 (2d Cir. 2003). Because the 2001 version of the Guidelines in effect at the time of Canova's sentencing contemplated a more severe sentence for fraud than the 1998 version in effect at the time he committed the charged crimes, compare, e.g. U.S.S.G § 2B1.1(b)(1)(J) (2001) (providing eighteen-level enhancement to base offense level of six for a fraud involving a $5-million loss), with id. § 2F1.1(b)(1)(N) (1998) (providing for thirteen-level enhancement to same base offense level for same loss), the district court relied on the 1998 version in calculating sentence. See United States v. Fitzgerald, 232 F.3d 315, 318 (2d Cir.2000) (per curiam); United States v. Broderson, 67 F.3d 452, 456 (2d Cir.1995). The parties do not argue, and thus we have no occasion to consider, whether Booker's transformation of the Guidelines from a mandatory to an advisory system warrants any different conclusion with respect to the applicable Guidelines version. Accordingly, unless otherwise noted, this opinion references the 1998 version of the Guidelines. See United States v. Fitzgerald, 232 F.3d at 319 (noting that court should apply a version of the Guidelines in its entirety).
     
      
      . To support this conclusion, Canova offered the opinions of several cardiologists. He further noted that the Veterans Administration did not record ECG strip in the post-magnet phase of pacemaker testing, nor was such recording part of the protocol recommended in the 2002 Guideline Update for Implantation of Cardiac Pacemakers and Antiarrhyth-mia Devices, the "bible” for doctors managing patients with pacemakers.
     
      
      . Canova paid the fine and special assessment on April 4, 2003, the day he appeared for sentence.
     
      
      . Although our decision to affirm this case on the ground that the district court did not abuse its discretion renders our discussion of tlie time limitations of Rule 33 and their jurisdictional import dicta, we nevertheless think such discussion serves as a useful caution as to the sternness of this rule's filing requirements.
     
      
      . Effective December 1, 2002, there was a "general restyling of the Criminal Rules to make them more easily understood and to make style and terminology consistent throughout the rules.” Fed.R.Crim.P. 33, Note to 2002 Amendments. Because these changes were "stylistic only,” id,, this opinion quotes the current version of the rules for ease of reference.
     
      
      . In considering the strict time requirements of the rules specified in Rule 45(b)(2), it is worth noting that a defendant who fails to file within the prescribed times is not left without avenues to challenge a criminal conviction. He may still pursue direct appeal and a post-conviction motion pursuant to 28 U.S.C. § 2255. See Carlisle v. United States, 517 U.S. at 436, 116 S.Ct. 1460 (Ginsburg, J„ together with Souter and Breyer, JJ., concurring).
     
      
      .One of the 2002 stylistic changes to Rules 29 and 33 was the substitution of the word “sets” for "may fix” in parallel clauses referring to the specification of the extended filing period during the prescribed seven days after verdict.
     
      
      . We note that Canova does not argue that his attorney detrimentally relied on any representations made by a law clerk so as to excuse his untimely October 28, 2002 filing under the "unique circumstances” doctrine articulated by the Supreme Court in Thompson v. INS, 
        375 U.S. 384, 84 S.Ct. 397, 11 L.Ed.2d 404 (1964). Thus, we need not here consider the continued vitality of that doctrine, which has been questioned by some of our sister circuits. See United States v. Marquez, 291 F.3d 23, 28 (D.C.Cir.2002); United States v. Hocking, 841 F.2d at 737. We do, however, note that Ca-nova's case is distinguishable from Thompson in important respects. Notably, in Thompson, the Supreme Court excused an untimely notice of appeal because the appellant had postponed filing in reliance on the district court's specific assurance that he had properly presented a motion to that court that would toll the appellate filing deadline. See Thompson v. INS, 84 S.Ct. at 398; cf. Mendes Junior Int’l Co. v. Banco do Brasil, S.A., 215 F.3d 306, 315 (2d Cir.2000) (recognizing that deadlines for filing federal appeals might be relaxed in "unique circumstances” where "a party has performed an act which, if properly done, would postpone the deadline for filing ... and has received specific assurance by a judicial officer that this act has-been properly done,” but finding "no predicates for its application here” (quotation marks and alterations omitted)). By contrast, in this case, the conversation between Canova’s counsel and a law clerk did not deter defendant from filing a timely Rule 33 motion that very day and having a specific extension granted. Nothing in Thompson suggests that, in these circumstances, equity requires a court to honor possible misinformation about a party's right to be heard on an untimely successive extension application.
     
      
      . At issue in Kontrick were time limits imposed by the federal bankruptcy rules on a creditor's objections to a debtor’s discharge.
     
      
      . In Smith, the Supreme Court, without expressly using the word "jurisdiction,” ruled that a district court was not empowered to reconsider its denial of a timely Rule 33 motion for a new trial after the conviction had been affirmed on appeal. Noting that at common law, a court’s power over its judgments expired with the term of court, Smith concluded that the Federal Rules of Criminal Procedure, "in abolishing the term rule,” did not extend a district court’s power to act "indefinitely,” but rather "confine[d] it within constant time periods.” Id. at 474 n. 2, 67 S.Ct. 1330.
     
      
      . Crosby cautioned that § 3553(a) does not require that a district court "definitively resolve” all Guidelines disputes preliminary to imposing a non-Guidelines sentence, id. at 112 (citing specifically certain complex loss calculations and Guidelines departure issues), and we do not suggest otherwise.
     
      
      . At the same time, the Commission expressly authorizes courts to depart from the Sentencing Guidelines when monetary loss either overstates or understates the seriousness of the particular fraudulent conduct. See U.S.S.G. § 2F1.1, cmt. n. 11. In concluding that the district court erred in its calculation of the loss attributable to Canova’s fraudulent conduct, we express no view as to whether any such departure might be appropriate in this case.
     
      
      . Schneider distinguished between two types of fraud: (1) "where the offender — a true con artist ... — does not intend to perform his undertaking ...; he means to pocket the entire contract price without rendering any service in return”; and (2) where a “fraud is committed in order to obtain a contract that the defendant might otherwise not obtain, but he means to perform the contract (and is able to do so) and to pocket, as the profit from the fraud, only the difference between the contract price and his costs.” 930 F.2d at 558. In the former case, the court concluded that "the contract price is a reasonable estimate of ... the expected loss.” Id. In the latter case, however, if the contract is performed "to the perfect. satisfaction of the contracting agency,” Schneider concluded that there was no loss. Id.
      
      This case does not fit within either of these categories. Instead, it presents a third type of fraud, involving no deceit in the initial contract procurement, but fraud in its performance, as a party trying to protect its profit margin stops complying with certain contract specifications while at the same time falsely representing strict compliance in order to secure payments from the victim of his deceit. Such a fraud does cause pecuniary loss because the victim paid for but did not receive all the terms of its bargain.
     
      
      . Where a victim has sustained a loss, the precise amount of which is not readily quantifiable, the profit realized by the defendant may also provide an alternative loss estimate. See U.S.S.G. § 2F1.1, cmt. n. 9 ("The offender’s gain from committing fraud is an alternative estimate that ordinarily will underestimate loss.”).
     
      
      . "Recoupment” is defined in the regulations as "[t]he recovery by Medicare of any outstanding Medicare debt by reducing present or future Medicare payments and applying the amount withheld to the indebtedness.” 42 C.F.R. § 405.370. The statutory and regulatory scheme governing the administration of Medicare authorizes carrier-initiated audits of providers, like the United Healthcare audit of Raytel, to protect against fraud and overpayment, see 42 U.S.C. § 1395u; 42 C.F.R. § 421.200 (providing non-exclusive list of carrier functions, including provider audits); see generally Pani v. Empire Blue Cross Blue Shield, 152 F.3d 67, 73 (2d Cir.1998) (explaining that carriers "are indispensable components of the governmental program and are in a unique position to combat the drain on public resources caused by fraudulent claims”), and the recoupment of any payments made to a provider for services not covered by Medicare or not in compliance with Medicare's specifications, see 42 U.S.C. § 1395gg; 42 C.F.R. §§ 405.371(a)(2), 405.373; see generally United States v. Lakey Clinic Hosp., Inc., 399 F.3d 1 (1st Cir.2005) (discussing availability of judicial and administrative proceedings to recover overpayment to provider who, inter alia, violated Medicare reimbursement policies); County Ambulance Serv., Inc. v. Thompson, 218 F.Supp.2d 309, 311 (E.D.N.Y.2002) (reviewing statutory and regulatory framework).
     
      
      . Because of the significant overlap between the actual loss caused by the testing fraud and the intended loss from the recoupment fraud, a district court could reasonably rely on the one more easily calculated in determining the appropriate loss enhancement for this case.
     
      
      . The dual materiality requirement addressed the particular concern raised in Za-gari as to whether intentionally false testimony material to the state proceeding in which it had been given also had to be material to the federal proceeding that it purportedly obstructed. See 111 F.3d at 329.
     
      
      . At the same time, a district court’s finding of a specific intent to obstruct justice may derive from its assessment of the three elements of perjury. For this reason, Dunnigan urges district' courts "to address each element of the alleged perjury in a separate and clear finding." 507 U.S. at 95, 113 S.Ct. 1111. In the end, however, application of the § 3C1.1 enhancement depends on whether the court is convinced by its review of those predicates that the defendant's intent was, in fact, to obstruct justice. See id. (holding that enhancement may be applied if court "makes a finding of an obstruction of, or impediment to, justice that encompasses all of the factual predicates for a finding of perjury”).
     
      
      . We nevertheless reiterate our observation in Crosby that, after Booker, a district judge can fairly consider policy statements concerning departures and fairly decide to impose a non-Guidelines sentence without "definitively resolv[ing]” close questions regarding the "precise meaning or application of a [departure] policy statement.” United States v. Crosby, 397 F.3d at 112.
     
      
      . To the extent the district court determined that Canova’s public service and good works warranted a six-level departure, it may, of course, reconsider that decision on remand in light of the higher Guidelines range dictated by proper application of a loss enhancement. See United States v. Elefant, 999 F.2d at 678. Moreover, in light of Booker, the district court may decide on remand, after considering the applicable Guidelines and policy statements, as well as the other factors outlined in 18 U.S.C. § 3553(a), not to sentence Canova within the Guidelines scheme, but to impose a non-Guidelines sentence.
     