Opinion by Judge GOODWIN; Partial Concurrence and Partial Dissent by Judge RYMER.
ORDER
The request for publication is GRANTED. The memorandum disposition filed August 8, 1997 is redesignated as an authored opinion by Judge Goodwin.
OPINION
GOODWIN, Circuit Judge:
Alex V. Stein appeals his sentence for violation of-18 U.S.C. § 1341, mail fraud, 18 U.S.C. § 1343, wire fraud, and 15 U.S.C. § 77q(a), securities fraud. He argues that the district court departed upward on improper grounds, failed to comply with Federal Rule of Civil Procedure 32, and incorrectly enhanced Stein’s sentence for obstruction of 'justice. He also argues that the district court sentenced him in a vindictive manner violating North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). We affirm in part, reverse two of the upward departures, vacate Stein’s sentence, and remand for resentencing.
Facts and Procedural History
Stein operated a fraudulent scheme claiming to offer investment in “risk free, fully hedged arbitrage” to the public. He promoted an elaborate investment scheme involving “loans” on large blocks of publicly traded stocks which would return enormous profits to his investors. In fact, Stein’s investments were neither “risk free” nor “fully hedged,” and he was losing money on his trades. In addition, he converted his investors’ money for personal use.
When Stein’s investors began demanding accountability, proof of gains, or their money back, he began creating and forging documents to assuage their concerns. He created forged brokerage account statements, forged bank statements, forged checks, and completely false account statements. When pressure began to mount, Stein told state and federal regulators, his investors, and his own attorneys, that all funds were securely invested in a “confidential” telecommunications contract worth $22 million. All contracts and related documents were completely false and all signatures were forgeries. Stein promised payment on June 1, 1988, but with the exception of a few insignificant amounts, Stein did not pay his investors.
On October 27, 1992, the government indicted Stein on fifty-two counts of mail fraud, securities fraud, wire fraud and money laundering. Stein was tried on three money laundering counts, thirty-three counts of fraud, and one count of conspiracy. The jury returned guilty verdicts on all but two the fraud counts. At sentencing the judge used the guideline for money laundering and calculated an offense level of twenty-five. Included in the twenty-five was a two-level increase for obstruction of justice as the dis[779]*779triet court found that Stein wilfully submitted a forged document during the trial. Stein had objected to this enhancement by offering the testimony of a handwriting expert and a private polygraph examination. The judge sentenced Stein to sixty months on the conspiracy count, sixty months on the fraud counts, and seventy-one months on the money laundering counts. He ordered the sentences to run concurrently. Stein appealed and we reversed his convictions for money laundering and remanded to the district court for resentencing. United States v. Stein, 37 F.3d 1407, 1411 (9th Cir.1994).
At his resentencing, Stein objected to the enhancement for obstruction of justice by offering a second private polygraph examination. He also objected to the government’s calculation of the amount of loss. The district court sentenced Stein to sixty months on the conspiracy count and eleven months on the fraud counts. He ordered the sentences to run consecutively. Stein filed a timely appeal.
Discussion
I. The Upward Departures
Stein contends that the district court departed upward on three impermissible grounds. First, he argues that the district court departed upward in an unlawful attempt to equalize the guidelines for fraud and money laundering. The record, however, does not reveal that any such desire motivated the district court’s sentencing.
Second, he argues that the district court erred in holding that a loss of $6.3 million “substantially exceeds” $5 million. Stein is correct. Though we review departure decisions for an abuse of discretion, “a ‘district court by definition abuses its discretion when it makes an error of law.’ ” United States v. Sablan, 114 F.3d 913, 916 (9th Cir.1997) (quoting Koon v. United States, — U.S. -, -, 116 S.Ct. 2035, 2047, 135 L.Ed.2d 392 (1996)). The government argues that because we have held that a four-level increase for a $20 million loss is reasonable, see United States v. Vargas, 67 F.3d 823, 826 (9th Cir.1995), a one-level increase for a loss of $6.3 million is reasonable as well. However, before the degree of departure is analyzed, application note 10 to the fraud guideline sets forth a threshold question of whether the loss at issue “substantially exceeds” $5 million. See U.S.S.G. § 2F1.1 emt. n. 10. We did not address this question in Vargas because “there [was] no question that $20 million ‘substantially exceeds’ $5 million.” Vargas, 67 F.3d at 826.
Losses from $2 million to $5 million — “a $3 million difference that results in the same sentence level increase” — warrant a ten-level sentence increase. United States v. Boula, 932 F.2d 651, 657 (7th Cir.1991). Following the rough exponential pattern established by the Commission, careful extrapolation would yield a subsequent loss level, warranting an eleven-level increase, of $5,000,001 to $10 million. Though we have held that district courts are not strictly bound by the exponential pattern in determining the appropriate degree of departure, see Vargas, 67 F.3d at 825-26, this pattern and the size of the steps must inform the district court’s inquiry into whether the amount of loss “substantially exceeds” $5 million. Given the size of the steps at the upper end of the loss table, the district court failed to identify how a $6.3 million loss “substantially exceeds” a $5 million loss, falls outside the Guidelines’ heartland, and warrants any upward departure. We therefore reverse the upward departure for a loss that “substantially exceeds” $5 million.
Third, Stein argues that the district court could not depart upward based solely on the number of victims. Stein misunderstands the district court’s ground for departure, which was in fact based on the combination of “more than minimal planning” and a “scheme to defraud more than one victim.” Nonetheless, the departure was not authorized by the Guidelines.
Application note 1 to the fraud guideline provides that if “several of the ... factors [enumerated in U.S.S.G.
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Opinion by Judge GOODWIN; Partial Concurrence and Partial Dissent by Judge RYMER.
ORDER
The request for publication is GRANTED. The memorandum disposition filed August 8, 1997 is redesignated as an authored opinion by Judge Goodwin.
OPINION
GOODWIN, Circuit Judge:
Alex V. Stein appeals his sentence for violation of-18 U.S.C. § 1341, mail fraud, 18 U.S.C. § 1343, wire fraud, and 15 U.S.C. § 77q(a), securities fraud. He argues that the district court departed upward on improper grounds, failed to comply with Federal Rule of Civil Procedure 32, and incorrectly enhanced Stein’s sentence for obstruction of 'justice. He also argues that the district court sentenced him in a vindictive manner violating North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). We affirm in part, reverse two of the upward departures, vacate Stein’s sentence, and remand for resentencing.
Facts and Procedural History
Stein operated a fraudulent scheme claiming to offer investment in “risk free, fully hedged arbitrage” to the public. He promoted an elaborate investment scheme involving “loans” on large blocks of publicly traded stocks which would return enormous profits to his investors. In fact, Stein’s investments were neither “risk free” nor “fully hedged,” and he was losing money on his trades. In addition, he converted his investors’ money for personal use.
When Stein’s investors began demanding accountability, proof of gains, or their money back, he began creating and forging documents to assuage their concerns. He created forged brokerage account statements, forged bank statements, forged checks, and completely false account statements. When pressure began to mount, Stein told state and federal regulators, his investors, and his own attorneys, that all funds were securely invested in a “confidential” telecommunications contract worth $22 million. All contracts and related documents were completely false and all signatures were forgeries. Stein promised payment on June 1, 1988, but with the exception of a few insignificant amounts, Stein did not pay his investors.
On October 27, 1992, the government indicted Stein on fifty-two counts of mail fraud, securities fraud, wire fraud and money laundering. Stein was tried on three money laundering counts, thirty-three counts of fraud, and one count of conspiracy. The jury returned guilty verdicts on all but two the fraud counts. At sentencing the judge used the guideline for money laundering and calculated an offense level of twenty-five. Included in the twenty-five was a two-level increase for obstruction of justice as the dis[779]*779triet court found that Stein wilfully submitted a forged document during the trial. Stein had objected to this enhancement by offering the testimony of a handwriting expert and a private polygraph examination. The judge sentenced Stein to sixty months on the conspiracy count, sixty months on the fraud counts, and seventy-one months on the money laundering counts. He ordered the sentences to run concurrently. Stein appealed and we reversed his convictions for money laundering and remanded to the district court for resentencing. United States v. Stein, 37 F.3d 1407, 1411 (9th Cir.1994).
At his resentencing, Stein objected to the enhancement for obstruction of justice by offering a second private polygraph examination. He also objected to the government’s calculation of the amount of loss. The district court sentenced Stein to sixty months on the conspiracy count and eleven months on the fraud counts. He ordered the sentences to run consecutively. Stein filed a timely appeal.
Discussion
I. The Upward Departures
Stein contends that the district court departed upward on three impermissible grounds. First, he argues that the district court departed upward in an unlawful attempt to equalize the guidelines for fraud and money laundering. The record, however, does not reveal that any such desire motivated the district court’s sentencing.
Second, he argues that the district court erred in holding that a loss of $6.3 million “substantially exceeds” $5 million. Stein is correct. Though we review departure decisions for an abuse of discretion, “a ‘district court by definition abuses its discretion when it makes an error of law.’ ” United States v. Sablan, 114 F.3d 913, 916 (9th Cir.1997) (quoting Koon v. United States, — U.S. -, -, 116 S.Ct. 2035, 2047, 135 L.Ed.2d 392 (1996)). The government argues that because we have held that a four-level increase for a $20 million loss is reasonable, see United States v. Vargas, 67 F.3d 823, 826 (9th Cir.1995), a one-level increase for a loss of $6.3 million is reasonable as well. However, before the degree of departure is analyzed, application note 10 to the fraud guideline sets forth a threshold question of whether the loss at issue “substantially exceeds” $5 million. See U.S.S.G. § 2F1.1 emt. n. 10. We did not address this question in Vargas because “there [was] no question that $20 million ‘substantially exceeds’ $5 million.” Vargas, 67 F.3d at 826.
Losses from $2 million to $5 million — “a $3 million difference that results in the same sentence level increase” — warrant a ten-level sentence increase. United States v. Boula, 932 F.2d 651, 657 (7th Cir.1991). Following the rough exponential pattern established by the Commission, careful extrapolation would yield a subsequent loss level, warranting an eleven-level increase, of $5,000,001 to $10 million. Though we have held that district courts are not strictly bound by the exponential pattern in determining the appropriate degree of departure, see Vargas, 67 F.3d at 825-26, this pattern and the size of the steps must inform the district court’s inquiry into whether the amount of loss “substantially exceeds” $5 million. Given the size of the steps at the upper end of the loss table, the district court failed to identify how a $6.3 million loss “substantially exceeds” a $5 million loss, falls outside the Guidelines’ heartland, and warrants any upward departure. We therefore reverse the upward departure for a loss that “substantially exceeds” $5 million.
Third, Stein argues that the district court could not depart upward based solely on the number of victims. Stein misunderstands the district court’s ground for departure, which was in fact based on the combination of “more than minimal planning” and a “scheme to defraud more than one victim.” Nonetheless, the departure was not authorized by the Guidelines.
Application note 1 to the fraud guideline provides that if “several of the ... factors [enumerated in U.S.S.G. § 2F1.1(b)(2)] applied, upward departure might be warranted.” U.S.S.G. § 2F1.1 cmt. n. I.1 Of the four [780]*780§ 2Fl.l(b)(2) factors, the district court found both “more than minimal planning” and a “scheme to defraud more than one victim.” Not every case involving “more than minimal planning” and a “scheme to defraud more than one victim” warrants upward departure. If the Guidelines intended that result, the factors would not be listed as alternative but rather as cumulative. See U.S.S.G. § 2F1.1, cmt. n. 1 (“The adjustments in § 2F1.1(b)(2) are alternative rather than cumulative.”); United States v. Davidson, 984 F.2d 651, 653 (5th Cir.1993) (“[T]he Guidelines’ Application Notes state that the enhancements available in § 2F1.1(b)(2) are alternative rather than cumulative, so that a court may not stack multiple (b)(2) factors.” (internal quotations omitted)); United States v. Copple, 24 F.3d 535, 547 n. 18 (3d Cir.1994). We believe the Third and Fifth circuits read the restrictive comment correctly.
Further, these two factors will often coexist, and enhancements or departures on these grounds essentially reach the same concerns. See U.S.S.G. § 2F1.1, cmt. background (“A complex scheme or repeated incidents of fraud is indicative of an intention and potential to do considerable harm.”). Because in most cases where one of these factors applies the other will apply as well, it is the rare case that the existence of both factors together will take the case outside the heartland of the Guidelines and justify a departure. It is more likely, as the Commission intended to punish the same harm with the two alternative factors, that applying both in a particular case would result in impermissible double counting.
Boula approved of an upward departure grounded in note 1 when there was both “more than minimal planning” and a “scheme to defraud more than one victim.” Boula and his co-defendant had defrauded 3000 victims, and they participated in “more than minimal planning” over eight years. See Boula, 932 F.2d at 656. Based on Boula’s conduct, the court stated that the “defendants’ scheme so exceeded the Guidelines base provisions in section 2F1.1(b)(2)” that upward departure was appropriate. Id.
The only basis the district court articulated as to how Stein’s conduct fell outside the heartland of the guidelines was that there were more than thirty victims, nothing near the 3000 relied upon in Boula. This number alone does not take this case outside the heartland of the Guidelines. The Commission took adequate account of the number of victims in this type of case through the loss table in § 2F1.1(b)(1) and through the one time enhancement available in § 2F1.1(b)(2), see Copple, 24 F.3d at 548-49; see also United States v. Mandel, 991 F.2d 55, 58 (2d Cir.1993), and thus the district court could not depart upward.2
II. Rule 32
Stein argues that the district court violated Rule 32 of the Federal Rules of Criminal Procedure by failing to conduct an evidentiary hearing to determine the amount of loss and by failing to resolve controverted matters at the sentencing hearing. Specifically, he contends that the district court did not properly account for an IRS audit summary sheet or for the possible recovery by a bankruptcy trastee of proceeds from his In Focus stock. Reviewing de novo whether the district court complied with Rule 32, see United States v. Karterman, 60 F.3d 576, 583 (9th Cir.1995), we find no error. We also find that the district court did not abuse its discretion in not holding an evidentiary hearing on the amount of loss. See United States v. Samo, 73 F.3d 1470, 1502 (9th Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 2555, 135 L.Ed.2d 1073 (1996).
Rule 32 requires that the district court make findings on unresolved objections and “afford counsel for the defendant ... an opportunity to comment ... on matters relating to the appropriate sentence,” Fed. R.Crim.P. 32(c)(1), but Rule 32 does not create a “general right to an evidentiary hearing at sentencing.” United States v. Real-Hernandez, 90 F.3d 356, 361 (9th Cir.1996). Where the district court allows the defen[781]*781dant to “rebut the recommendations and allegations of the presentence report either orally- or through the submission of written affidavits or briefs,” Rule 32 does not require an evidentiary hearing. Samo, 73 F.3d at 1502-03. In this case, the district court allowed Stein’s counsel to object to the presentence report both in writing .and at the sentencing hearing. Stein was allowed to introduce the IRS audit summary, and the district court considered Stein’s objections based on the IRS audit summary and the possible restitution to his victims. Thus, the district court did not abuse its discretion in not conducting an evidentiary hearing.
Stein introduced the IRS audit summary and argued about the possible recovery of proceeds from the In Focus stock to contest the presentenee report’s amount of loss finding. The district court judge agreed with the government that the summary did not reflect the loss Stein caused his victims and that the possible restitution did not affect the calculation of the victims’ loss. Thus, he found that Stein caused losses of $6.3 million. Rule 32 requires no more. See Karterman, 60 F.3d at 583 (holding that Rule 32 is satisfied where the district court considered the defendant’s objections, “but resolved the disputed facts against him.”).
III. Obstruction of Justice
In his first appeal, Stein argued “that the government failed to prove by a preponderance of the evidence that he ‘willfully’ attempted to obstruct justice.” See United States v. Stein, 37 F.3d 1407, 1411 (9th Cir. 1994). We rejected his claim. At resentencing the district court judge reimposed the obstruction of justice enhancement “for the same reasonfs]” as he did at the first sentencing. Stein again argues that this was error because his second polygraph examination demonstrated that he did not “willfully” attempt to obstruct justice. See U.S.S.G. § 3C1.1. We review the district court’s factual findings in support of a sentencing enhancement for clear error, see Stein, 37 F.3d at 1411, and we find no error.
In Stein’s first appeal, we affirmed the obstruction of justice enhancement noting that “the district court’s factual finding that Stein willfully submitted a forged document was not clearly erroneous.” Id. The new polygraph examination does not change this result. Though addressing the issue that we felt most lacking in the first polygraph, whether Stein offered the document knowing it had been forged by someone, the second polygraph report is also too conclusory to be probative. Further, the record remains “replete with examples of Stein using forged documents as a means of evading detection,” and Stein’s “handwriting expert merely offered the ‘cautious’ opinion that it was ‘unlikely’ that Stein himself forged the document.” Id. With all this evidence before it, the district court did not commit clear error in imposing an enhancement for obstruction of justice.
AFFIRMED in part, REVERSED in part, REMANDED FOR RESENTENCING.