
517 F.3d 1163 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
James F. GARRO, Defendant-Appellant.
No. 06-50513.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted September 25, 2007.
Filed February 28, 2008.
*1164 Frank J. Ragen, Julie A. Blair, and Michael Pancer, San Diego, CA, for the appellant James Garro.
*1165 Karen P. Hewitt, United States Attorney, Bruce R. Castetter and Mark R. Rehe, Assistant United States Attorneys, San Diego, CA, for appellee the United States.
Before: J. CLIFFORD WALLACE, SANDRA S. IKUTA, and N. RANDY SMITH, Circuit Judges.
WALLACE, Senior Circuit Judge:
Garro appeals from his 135-month prison sentence after a jury conviction of eight counts of wire fraud, see 18 U.S.C. § 1343, eleven counts of money laundering, see 18 U.S.C. §§ 1956(a)(1)(A)(i), (a)(1)(B)(i), and one count of tax evasion, see 26 U.S.C. § 7201. He argues that the district court erroneously applied the Sentencing Guidelines and imposed an unreasonable sentence under 18 U.S.C. § 3553(a). We have jurisdiction pursuant to 18 U.S.C. § 3742 and we affirm Garro's sentence.[1]

I.
In September and October of 1999, Garro, holding himself out to be a self-employed financial consultant for foreign countries wanting to stimulate their economies, raised $37.5 million dollars from five investors: (1) TLC America ($20 million); (2) Child's Hope ($10 million); (3) Kelldeer & Carrington ($3.5 million); (4) Veronica Disabello ($2 million); and (5) Curtis Martin ($2 million). The money was for the purpose of entering what Garro called a "Leveraged Investment Program," which would buy and resell "medium term bank notes" in foreign markets. Each investor entered into a written contract with Garro's business entity, Sienna Financial, Ltd., and was promised at least double his or her investment in fifteen days.
On October 28, 1999, Garro sent investors a letter indicating that one phase of the program was complete and that each investor could expect a wire transfer of profits no later than November 1, 1999. Garro prepared this letter with the help of Louis Cimaglia. During the course of the scheme, Garro used Cimaglia as a "long-distance secretary" from Cimaglia's home in Maryland. Cimaglia was a point of contact with investors and would create documents, send and receive faxes, and field investor telephone calls for Garro. For his role in Garro's scheme, Cimaglia pled guilty to one count of conspiracy to commit wire fraud.
November 1 came and went without payment of any profits. After this date passed, investors began contacting Garro with concerns. On November 10, 1999, Garro sent a letter apologizing and explaining that the profits were even greater than anticipated but were so high that they "had come under strict scrutiny" and been delayed. The letter promised that 200% profits would be in investors' bank accounts no later than November 17, 1999.
November 17 passed with no disbursement of profits. On December 3, 1999, Garro had Cimaglia send another letter indicating that the money was ready for disbursement but that Garro had to travel personally to banks to effect the wire transfers. Contrary to that and subsequent assurances, no investor received promised profits. In the end, no investor received any profits.
In fact, the investor money was never invested at all. Investors deposited the *1166 money into an escrow account and later released it into Garro's control. Garro then moved the money from the escrow to a couple of Bank of America accounts held by a corporation that he incorporated and owned, Navajo Capital. Once the money was in Garro's Navajo Capital corporate accounts, he used it to buy and remodel three homes, manipulating the transactions to mask his involvement in the purchases.
For example, Garro purchased a Santa Fe, New Mexico, residence through Santa Fe Abstract, Ltd. To do this, he moved $30 million from one of Navajo Capital's Bank of America accounts to one of its Union Bank accounts, then moved $25 million from the Union Bank account to a U.S. Bank account held by Citation Financial Management to obscure his transactions further. That money was then moved to another account at U.S. Bank. Then, $17.49 million was transferred from the second Citation Financial Management account to a Texas Bank One account held by Merlin Financial, an entity Garro owned, and then to yet another Texas Bank One account held by Merlin Financial. Merlin Financial then wired $2,344,635 to Santa Fe Abstract. Garro, through another of Navajo Capital's Bank of America accounts, had also directly wired $260,000 to Santa Fe Abstract. The Santa Fe home was then paid for in cash by Camelot International, LLC, another entity created by Garro. Garro signed the purchase agreement in the name "Elissa M. Dee," his employee. He also wrote a letter, signed Elissa Dee, directing the seller that the buyer's name remain confidential.
Garro used similarly complex transactions involving multiple bank accounts, corporate shells, cash, and others' names to purchase homes in La Jolla and Encinitas, California. Most of the rest of the investor money stayed in accounts held by Garro and his corporate entities. No money was ever put into the investment programs he described to investors.
After failing to receive profits, the investors each eventually demanded their money back. TLC America, after investing $20 million on September 13, 1999, became worried when no profits appeared. On October 12, 1999, Garro returned $4 million of its principal. On November 5, 1999, after TLC America's president, Ernest Cossey, told Garro that he was very concerned about the investment, Garro sent TLC America another $2 million along with a letter assuring Cossey that the program was still working and profits were forthcoming. This failed to reassure Cossey, who wrote Garro on November 12, 1999, stating that TLC America did not wish to remain in the program and asking Garro to return the rest of its principal. Garro asked Cossey to be patient, telling him that the money was coming, and returned another $4 million of TLC America's principal on December 16, 1999. TLC America continued to contact Garro asking for its money back without success. Finally, on September 29, 2000, Garro agreed to convey his La Jolla home to TLC America to repay the remainder of TLC America's principal.
Child's Hope also became concerned after investing $10 million on September 24, 1999, and failing to see profits within the promised fifteen days. Child's Hope's director began to "dog [Garro] every day to get[Child's Hope's] funds back." On November 18, 1999, a Child's Hope lawyer sent Garro a letter demanding that he return the money in full and threatening legal action. Garro initially refused to comply but on November 24, 1999, he returned $3.5 million to Child's Hope. Child's Hope signed a release acknowledging that it had received the $3.5 million on December 8, 1999, but at that point "didn't feel *1167 like there was any validity to the program itself" and wanted to get out of the scheme. After months of pestering, Garro wired Child's Hope the remaining $6.5 million of its principal on January 20, 2000.
Kelldeer & Carrington never received back the $3.5 million that they had invested, despite negotiations and agreements with Garro. Disabello eventually received all but $550,000 of her principal. Martin received all $2 million of his principal in November 1999.
The Federal Bureau of Investigation (FBI) began investigating Garro in 2000. He was arrested in October 2002 for wire fraud. On March 15, 2005, a twenty-count indictment charged Garro with wire fraud, money laundering, and tax evasion. On April 4, 2005, after a seven-day trial, a jury returned guilty verdicts on all twenty counts. Following a two-day sentencing hearing, on August 25, 2006, Garro was sentenced to 135 months in prison, three years of supervised release, and over six-million dollars in restitution.

II.
We review the district court's interpretation of the Sentencing Guidelines de novo, the district court's application of the Guidelines to the facts for abuse of discretion, and the district court's factual findings for clear error. United States v. Cantrell, 433 F.3d 1269, 1279 (9th Cir.2006). Although the Guidelines are only advisory, a material error in calculating the sentencing range is grounds for resentencing. Id. at 1280.

A.
Garro first argues that the district court erroneously calculated the amount of loss for sentencing purposes. Under the applicable set of Sentencing Guidelines, Garro's crime carried a base level of six. See USSG § 2F1.1(a) (1998). The district court found that the amount of loss in Garro's fraudulent scheme exceeded $20 million, resulting in a sixteen-level increase. See USSG § 2F1.1(b)(1)(Q) (1998). Garro contends that the district court erred in calculating the amount of loss for sentencing purposes by failing to offset the money that he received by the money that he returned to investors. A calculation of the amount of loss is a factual finding reviewed for clear error. See United States v. Lawrence, 189 F.3d 838, 844 (9th Cir.1999). The "loss need not be determined with precision," but "need only [be] a reasonable estimate . . . given the available information." United States v. Bussell, 504 F.3d 956, 960 (9th Cir.2007) (quoting USSG § 2F1.1, cmt. n. 8 (1994)).
Although Garro did, in some form or another, return a substantial portion of the money he had taken, the district court found that most of the money that Garro returned could not be credited to him because it was returned after his scheme was detected, and an amount of loss for sentencing purposes is only offset by money returned "prior to the discovery of the offense." United States v. Bright, 353 F.3d 1114, 1118 (9th Cir.2004); United States v. Stoddard, 150 F.3d 1140, 1146 (9th Cir.1998).
The district court found that Garro's offense was "discovered" by TLC America on November 12, 1999, and by Child's Hope on December 8, 1999, the dates on which TLC America and Child's Hope contacted Garro requesting their money back. The court found that TLC America's November 12, 1999 letter to Garro, stating unequivocally that TLC America "did not wish to remain" in the program and asking for the return of its full deposit, sufficed to show that TLC America was "on notice of irregularities" by that date, especially because two weeks had gone by since Garro told TLC America that it would receive its profits no later than November 1, 1999. *1168 The court also found that Child's Hope's steps to retrieve money, particularly the release that it signed on December 8, 1999, showed that it, too, was "on notice" of deceptive conduct on Garro's part.
Not counting the money returned to TLC America after November 12, 1999 and to Child's Hope after December 8, 1999, the amount of loss occasioned by Garro's scheme totaled $20 million. Add to that Veronica Disabello's $550,000 and Kelldeer & Carrington's $3.5 million, which Garro admits was never repaid, and the amount exceeds $20 million without regard to any other losses.
Garro disputes these findings, arguing that the investors' requests to receive their money back was not a discovery of the offense because the investors had not discovered the criminal nature of Garro's actions. This argument is unavailing; we do not require that victims discover the actual crime to determine that a fraud has been "discovered." In Bright, for example, we held that a defendant's fraud had been "discovered" when investors wrote to him demanding their money back. 353 F.3d at 1118.
Here, the district court did not clearly err in determining that Garro's fraud had been "discovered" for sentencing purposes on dates when his investors, after waiting and never receiving a cent of promised profits after delays and empty reassurances, began demanding their money back. Investors need not make any specific criminal accusations or say any magic words for a court to conclude that the offense has been discovered.
Garro's claim that the investors merely got cold feet in a high-stakes investment scheme is belied by the fact that, by the time they requested their money back, the investors had been promised a 100% return on their investments within fifteen days and had been told that they would see the money no later than November 1, 1999. Indeed, on November 10, 1999, Garro promised investors that the profits had already been made and that they had only to wait for disbursement. When the dates by which Garro promised payment came and went without disbursement of a single penny, investors not only had reason to be disappointed that their financial bets did not work out, they also had reason to believe that the entire program was a sham. While fraud may not be "discovered" merely when investors voice concerns, what happened in this case went considerably further. The failure of Garro to deliver on his unqualified promises coupled with investors' demands for their money back shows the district court's findings were not clearly erroneous. The district court properly applied the "economic reality approach" by refusing to credit repayments Garro made as part of "an effort to reduce accountability" after the investors discovered Garro's fraud. Stoddard, 150 F.3d at 1146.

B.
Garro also argues that the district court employed the wrong standard of proof in arriving at its loss calculation: the district court used a "preponderance of evidence" rather than a "clear and convincing" standard of proof. As Garro failed to object in the district court, we review for plain error. See United States v. Jordan, 256 F.3d 922, 925 (9th Cir.2001).
Although a preponderance of evidence standard is ordinarily applied to establish facts used in sentencing, when the combined effect of contested enhancements would have "an extremely disproportionate effect on the sentence imposed," we apply a balancing test to determine whether the higher "clear and convincing" standard of proof should apply. See United States v. Staten, 466 F.3d 708, 718 (9th Cir.2006); United States v. Riley, 335 F.3d *1169 919, 926-27 (9th Cir.2003); Jordan, 256 F.3d at 928-29. In identifying the appropriate standard of proof, we have distinguished between enhancements based upon charged conduct for which the defendant has been convicted, and enhancements based upon uncharged conduct. See, e.g., Riley, 335 F.3d at 926-27. In Riley, we declined to apply the clear and convincing standard of proof because the enhancement at issue was "based entirely on the extent of the conspiracy to which [the defendant] pled guilty." Id. at 926. Here, the government's indictment charging Garro with a wire fraud scheme specifically alleged that he raised $37.5 million dollars. A jury found Garro guilty of the conduct alleged in the indictment. Thus, the district court's enhancement to Garro's sentence for loss exceeding $20 million was based on conduct for which Garro was charged and convicted. As the sentencing enhancement for amount of loss was not based on uncharged or acquitted conduct, it was not plain error for the district court to use a preponderance of evidence standard of proof.
Garro's argument fails for another reason. Even if the district court's application of a preponderance standard of review were an error, it would not be "plain." Jordan, 256 F.3d at 926. The court's use of the preponderance standard of proof did not, in light of the evidence at trial and the court's findings at sentencing, "seriously affect[ ] the fairness, integrity, or public reputation of the judicial proceedings." Id. (internal quotation marks omitted).

C.
Garro next contends that the district court erroneously included $13 million dollars of money that he returned to investors when it calculated that he had laundered $78 million. Even if that were true, which we do not decide, the error would be harmless: the twelve-level enhancement imposed by the district court applies to sums between $60 and $100 million dollars. Thus, even excluding the $13 million, the total amount of money Garro laundered still falls within the range to which a twelve-level enhancement applies. Therefore, the alleged error is harmless and thus not a ground for resentencing. See, e.g., United States v. Crawford, 185 F.3d 1024, 1029 (9th Cir.1999) (sentencing errors reviewed for harmlessness).

D.
Garro also argues that the district court erred in enhancing his sentence for using "sophisticated means." The district court found that Garro had "used and incorporated numerous shell corporations, many of which he incorporated during this scheme," that he had intentionally "left behind numerous confusing and misleading documents" regarding the investors' funds, that he had forged signatures on real estate transactions, and had made "other associates sign for him for other real estate purchases, to avoid having his name appear on the transaction or assets." Garro's objection notwithstanding, his conduct was precisely what the Sentencing Guidelines describe as indicating "sophisticated means": "conduct such as hiding assets or transactions, or both, through the use of . . . corporate shells." USSG § 2F1.1, cmt. n. 15 (1998).
Garro also argues that it was improper for the district court to impose an enhancement for both more than minimal planning and the use of sophisticated means. We have not addressed that specific issue, but the Eleventh Circuit has rejected the same argument. See United States v. Humber, 255 F.3d 1308, 1314 (11th Cir.2001) ("We conclude that USSG § 2F1.1(b)(2)(A) and USSG § 2F1.1(b)(5)(C) are to be applied cumulatively, and not in the alternative"). We agree with the Eleventh Circuit's approach *1170 because it accords with the language and structure of the Guidelines, as well as our precedent on related issues.
First, the Guidelines suggest, at least generally, that the two enhancements can be applied together. The application notes to the Guidelines explain that "[t]he offense level adjustments from more than one specific offense characteristic within an offense guideline are cumulative (added together) unless the guideline specifies that only the greater (or greatest) is to be used." USSG § 1B1.1, cmt. n. 4 (1998). Indeed, in the Guidelines, elements that are intended to be alternative rather than cumulative are clearly defined as such. See, e.g., USSG § 2F1.1(b)(2) (1998) ("If the offense involved (A) more than minimal planning, or (B) a scheme to defraud more than one victim, increase by 2 levels"). There is no such definition of the enhancements for more than minimal planning and sophisticated means. Each is in a separate section, and the application notes do not provide that the enhancements are mutually exclusive. See id. § 2F1.1(b)(2), (6), cmt. nn. 2, 15. The Guidelines on their face, then, permit the enhancements to be applied cumulatively.
Moreover, our interpretation is supported by the fact that application note 15 provides, "[i]f the conduct that forms the basis for an enhancement [for sophisticated means] is the only conduct that forms the basis for an adjustment under § 3C1.1 (Obstruction of Justice), do not apply an adjustment under § 3C1.1." Just as the Guidelines provisions explicitly indicate when one enhancement excludes imposition of another, the application notes also indicate when imposition of one enhancement impacts or excludes imposition of another. Neither the Guidelines nor their commentary provide that enhancements for more than minimal planning and sophisticated means are mutually exclusive, and we will not create such a rule.
Garro points out that § 2F1.1 cmt. n. 15 provides that "[t]he enhancement for sophisticated means . . . requires conduct that is significantly more complex or intricate than the conduct that may form the basis for an enhancement for more than minimal planning." From this he argues that the enhancement for more than minimal planning is therefore encompassed in the enhancement for sophisticated means, and that the two enhancements cannot be applied cumulatively. We will not embrace this interpretation because the comment note does not state that the two enhancements are mutually exclusive, unlike the express statements precluding the concurrent application of other enhancements.

E.
Garro argues that the district court erred in imposing a two-level enhancement based on his involvement of another person, Cimaglia, in his scheme. The district court's finding that Garro was a leader or organizer is reviewed for clear error. See United States v. Lopez-Sandoval, 146 F.3d 712, 716 (9th Cir.1998).
The two-level aggravating role enhancement applies "[i]f the defendant was an organizer, leader, manager, or supervisor in any criminal activity." USSG § 3B1.1(c) (1998). Contrary to Garro's argument, the law does not require that the supervised person be substantially involved in the criminal scheme. See United States v. Melvin, 91 F.3d 1218, 1225-26 (9th Cir.1996).
Cimaglia testified at trial that he prepared materials for Garro and interacted with investors under Garro's direction; additionally, there were tape recordings and writings presented as evidence at trial that showed Garro directing Cimaglia in execution of Garro's scheme. Based on this evidence, the district court did not *1171 clearly err in finding that Garro supervised Cimaglia.

F.
Garro disputes the district court's two-level sentence enhancement for obstruction of justice. A factual finding that a defendant obstructed justice is reviewed for clear error. United States v. Jimenez, 300 F.3d 1166, 1170 (9th Cir.2002). The Guidelines state that perjury is obstruction of justice for enhancement purposes. USSG § 3C1.1, cmt. n. 4(b) (1998). For a court to find that a defendant obstructed justice through perjury, it must find that (1) the defendant gave false testimony, (2) on a material matter, (3) with willful intent. United States v. Jimenez-Ortega, 472 F.3d 1102, 1103 (9th Cir.2007).
The district court found that Garro willfully offered several false, material statements at trial. Many of these statements expressly contradicted documents that he had prepared and sworn affidavits he had made. Additionally, in an attempt to place the blame on Cimaglia, Garro played a tape at trial contending that it related to the investment scheme at issue; the district court, however, found that it was obvious that the tape related to an entirely different investment scheme.
Garro does not dispute these findings, but argues that he had a "grandiose/delusional/demented mental status" and that he lacked the necessary mental state to act "willfully." He relies on the findings of a psychologist who evaluated him after one meeting and concluded that he had "unrealistic ideas about reality" and showed signs of dementia. The psychologist never concluded or suggested, though, that Garro was so impaired that he could not act willfully or that he actually believed his trial testimony to be true. Most important, the psychologist never suggested that Garro suffered from dementia at the time he testified. The district court found that, possible dementia notwithstanding, Garro was not credible and that his false testimony was willful. The district court's decision in light of the entire record and its observation of Garro is plausible and thus not clearly erroneous. See Cantrell, 433 F.3d at 1283-84.

III.
We review a district court's sentence for reasonableness in light of the sentencing factors set forth in 18 U.S.C. § 3553(a) and we reverse a sentence free of procedural error only if the district court abused its discretion. See Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 594, 597, 169 L.Ed.2d 445 (2007). A district court is required only to state the reasons for the sentence imposed in enough detail to satisfy an appellate court that it has "considered the parties' arguments and has a reasoned basis for exercising [its] own legal decisionmaking authority." Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 2468-69, 168 L.Ed.2d 203 (2007).
Garro argues that his sentence, which was fifty-three months below the correctly-calculated Guidelines range, was unreasonable and that the district court failed to account properly for the factors enumerated in 18 U.S.C. § 3553(a). However, the district court gave careful consideration to the section 3553 factors and supported its conclusions with reasoned analysis. In particular, it carefully considered the nature and circumstances of Garro's offense and the need to protect the public and deter crime. It listened to and considered Garro's arguments concerning his history and personal characteristics, including his psychological state and age, and awarded Garro a nearly three-level downward departure based on those factors. Though Garro argues that his sentence creates unwarranted sentencing disparities between *1172 him and others involved in his and other financial crimes, the district court reasoned that Garro was not similarly situated to those with whom he compared himself because they had either pled guilty or had committed different crimes. The district court did everything required by the Supreme Court and its chosen sentence was neither unreasonable nor reflective of an abuse of the ample discretion we afford to the district court under Gall. 128 S.Ct. at 597-602.
SENTENCE AFFIRMED.
NOTES
[1]  We affirmed Garro's conviction, which he challenged along with his sentence, in a separate disposition.
