SUMMARY ORDER
On August 26, 2003, Gary Agnew was indicted on 15 counts of mail fraud, 18 U.S.C. § 1341, and one count of federal employees compensation fraud, 18 U.S.C. § 1920. [AA at 13-18] A trial on this indictment was held in the United States District Court for the District of Connecticut (Hall, J.), beginning on March 22, 2004 and ending on March 30, 2004. [AA at 7-8] The jury returned a verdict of guilty on all 16 counts, and on December 6, 2004, Agnew was sentenced to 21 months imprisonment and ordered to pay $84,403 in restitution. [AA at 714] In April 2005, this Court remanded the sentence to the district court pursuant to United States v. Crosby, 397 F.3d 103,118-20 (2d Cir.2005). [AA at 653] On June 13, 2005, the district court concluded that there was no basis to modify its original sentence. [AA at 703] Agnew filed a timely notice of appeal. [AA at 726] We assume the parties’ familiarity with the facts, proceedings below, and specification of issues on appeal.
“A criminal defendant who challenges the sufficiency of the evidence shoulders a heavy burden, but not an impossible one.” United States v. Jones, 393 F.3d 107, 111 (2d Cir.2004). ‘We review such challenges de novo, and will affirm if, viewing all the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Id. (internal quotations marks and citations omitted) (emphasis added). In reviewing such a challenge, the court “must view the evidence, whether direct or circumstantial, in the light most favorable to the government, crediting every inference that could have been drawn in its favor.” United States v. Tubol, 191 F.3d 88, 97 (2d Cir.1999) (internal quotation marks omitted). Agnew’s claim that the evidence was insufficient to establish materiality contradicts the evidence presented at trial, which the jury was entitled to credit. Since it is possible that some rational jury could credit the testimony of the physicians and the representative of the Department of Labor, Agnew’s sufficiency claim must fail.
In reviewing Agnew’s challenges to the sentencing enhancements, we must “accept the findings of fact of the district court unless they are clearly erroneous and ... give due deference to the district court’s application of the guidelines to the facts.” 18 U.S.C. § 3742(e) (1994). The district court’s factual findings with respect to sentencing need be supported only by a preponderance of the evidence. See, e.g., United States v. Cassiliano, 137 F.3d 742, 747 (2d Cir.1998). This district court did not clearly err here. Agnew’s claims on the obstruction of justice enhancement contradict testimony presented at trial, which the court had discretion to credit. “[W]hen a trial judge’s finding is based on his decision to credit the testimony of one of two or more witnesses, each of whom has told a coherent and facially plausible story that is not contradicted by extrinsic evidence, that finding, if not internally inconsistent, can virtually never be clear error.” Anderson v. Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985). Agnew’s arguments *379that the loss calculation was erroneous were not preserved at trial. Although Agnew relies on United States v. Sofsky to suggest that we should apply a less rigorous application of the plain error rule, we stated in Sofsky that strict compliance with “the rigorous standards of Rule 52(b)” was relaxed “[b]oth because the alleged error relates only to sentencing and because Sofsky lacked prior notice.” 287 F.3d 122, 125-26 (2d Cir.2002) (emphasis added). We further elaborated in United States v. Gordon that where the petitioner had full notice, plain error analysis under Rule 52(b) would be applied with “full rigor.” 291 F.3d 181, 191 (2d Cir.2002). The district court made a reasonable estimate and reasonably reduced the gross amount by benefits to which Agnew was entitled,1 so the loss calculation does not constitute clear error. We additionally reject Agnew’s claim that the Department of Labor had a duty to mitigate its damages once a criminal investigation was underway against Agnew.
Finally, Agnew contends that the district court’s Apprendi error in its jury instructions regarding Count 16 violated his Sixth Amendment rights. Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). Because Agnew did not assert an objection to the jury instructions in the district court, his claim is renewable only for plain error. See Fed.R.Crim.P. 52(b); United States v. Thomas, 274 F.3d 655, 666 (2d Cir.2001) (en banc). Agnew’s reliance on United States v. Hurn, 368 F.3d 1359 (11th Cir. 2004), is misplaced. In Hum, the defendant challenged the jury instruction, which included the $1,000 threshold, as insufficient to require the jury to find that a causal link existed between her false statements and her receipt of benefits. Id. at 1362. The court rejected the argument, explaining that instructions using the language of the statute, “falsely obtained,” sufficiently required a finding of the causation element challenged by the defendant. Id. (“A reasonable juror would be likely to conclude that a benefit is obtained ‘falsely’ if it is obtained as a result of a fraudulent or misleading statement or omission.”). Agnew’s argument that the omitted element prevented the jury from finding the $1,000 threshold beyond a reasonable doubt fails the test of Neder v. United States, 527 U.S. 1, 17, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999). Overwhelming evidence supports a finding against the defendant on the question of amount of benefits received. The jury’s convictions on Counts 1-15 necessarily found amounts in excess of $1,000, individually or in aggregate. The Apprendi error was thus harmless.
We have considered Agnew’s remaining claims and find them to be without merit. Based on the foregoing, the judgment of the district court is AFFIRMED.