Defendants-appellants Michael Palazzolo and Richard Olivieri (“Appellants”) appeal from sentences imposed on them by the United States District Court for the Southern District of New York (Allen G. Schwartz, District Judge) following their guilty pleas to a racketeering conspiracy charge. After conducting a sentencing hearing pursuant to United States v. Fatico, 579 F.2d 707 (2d Cir.1978), the district court took into account as relevant conduct for sentencing three additional racketeering acts for which Appellants were not indicted. Appellants challenge various aspects of this decision, including the standard of proof, the sufficiency of the evidence, the treatment of the acts as separate counts of conviction, and the version of the Sentencing Guidelines used. The government cross-appeals from the district court’s downward adjustment for acceptance of responsibility and from its fail*287ure to impose an upward adjustment for obstruction of justice.
We affirm.
BACKGROUND
Palazzolo and Olivieri were engaged in a deadly entrepreneurial scheme to kidnap successful narcotics traffickers and hold them for ransom. Palazzolo and Olivieri’s ten-member gang divided responsibilities for the criminal conduct along racial lines: the “black crew,” African-American men from the Bronx, identified potential victims and monitored their whereabouts; the “white crew,” white men from Rockland County and New Jersey, including Palazzolo and Olivieri, abducted the targets by impersonating police officers and held them for ransom. From late 1990 to mid 1991, the gang committed several kidnappings and murders within New York City.
On April 1, 1993, a fifty-nine count indictment was filed against Appellants and eight co-defendants, which charged them with participating in, and conspiring to participate in, the affairs of a racketeering enterprise in violation of 18 U.S.C. § 1962, as well as the commission of substantive offenses including extortion, 18 U.S.C. § 1951, kidnapping, 18 U.S.C. § 1201, and use of a firearm in connection with a crime of violence, 18 U.S.C. § 924(c).
On June 1, 1993, one week before their trial was to begin, Palazzolo and Olivieri pleaded guilty to the racketeering conspiracy charge pursuant to written plea agreements. The remaining counts were subsequently dismissed. During their plea allocutions, Palaz-zolo and Olivieri admitted to participating in two attempted kidnappings whose intended victims were Jorge Davila and an unidentified man. In each plea agreement, the government reserved the right to “present evidence at sentencing that [Appellants were] also involved in the kidnapping of Alvin Cas-sidy Goings, a/k/a ‘Butch,’ the attempted kidnapping of Richard Simmons, a/k/a ‘Fritz,’ and the kidnapping of Roberto Mercedes” and to “argue that [Appellants’] participation in these offenses should be considered as relevant conduct” under § 1B1.3 of the Sen-tenting Guidelines.
I. The Fatico Hearing
On various dates from April 18 to June 14, 1994, the district court conducted an extensive Fatico hearing to determine the scope of Appellants’ criminal behavior for sentencing purposes. During the hearing, the government presented testimony from Derrick Augustine, Keith Green, and James Brown, three members of the “black crew,” who had pleaded guilty and were cooperating with the government. Several disinterested witnesses testified as well. Palazzolo testified on his own behalf and presented a number of alibi witnesses.
A. The Mercedes Kidnapping
With respect to the kidnapping of Roberto Mercedes, Augustine, Green, and Brown all testified that Palazzolo and Olivieri had participated with them in the surveillance of Mercedes. Augustine and Brown testified that they had watched Appellants, posing as police officers, kidnap Mercedes from a Manhattan barbershop. They placed the time of the kidnapping between 2:00 and 3:00 p.m. on January 26, 1991. In addition, Brown recounted a meeting with members of the “white crew” after the abduction at which Appellants, fearful that Mercedes might identify them, discussed killing Mercedes. This testimony was corroborated by phone records showing calls charged to Palazzolo’s calling card on the day of the Mercedes kidnapping from Manhattan and the Spring Valley Marketplace, which wás near Palazzo-lo’s home, to, among other locations, the leader of the black crew’s apartment and Mercedes’s store.
Palazzolo denied having taken part in the Mercedes kidnapping and presented an elaborate alibi. Palazzolo testified that, on the morning of January 26 he exercised at a gym near his home in New City, New York, returned home for a shower, and then went shopping at a deli. He stated that he then went to Bruno’s Hair Salon, where his girlfriend Gina Caponigro worked, and visited with her for about an hour. Caponigro testified to this visit as well. Testimony from two *288of Caponigro’s co-workers and affidavits from two other co-workers also confirmed that Palazzolo had visited the salon. One coworker placed Palazzolo at the salon for at least a half-hour beginning between 1:30 and 2:00 p.m.; another stated that he was there “for an hour between the period of 12:30 p.m. and 2:30 p.m.”; and a third recalled “with certainty that [Palazzolo] was there between 2:30 and 3:00 p.m.” According to the testimony of John Kelly, a retired New York City police officer, the drive from the hair salon to the location of the kidnapping took approximately forty-six minutes.
Palazzolo testified that after the visit he went home and watched television until Ms. Caponigro joined him. According to Capo-nigro, she arrived at Palazzolo’s apartment at around 4:30 or 5:00 p.m. and found him watching television. She testified that approximately an hour later, Paula Pelegrino, a friend of the couple, brought her four-year-old daughter Victoria to Palazzolo’s apartment. Pelegrino confirmed that she dropped her daughter off at Palazzolo’s but placed the time closer to 4:30 or 4:45 p.m.
Palazzolo and Caponigro testified that after Pelegrino dropped Victoria off, the three ate dinner, watched television, and packed the car for a ski trip planned for the following day. They then went to see the film “Home Alone” at the Spring Valley Marketplace at 9:30 p.m., a story corroborated by Victoria’s testimony that she saw the movie with them “late at might.” After the film, according to Palazzolo and Caponigro, they returned home and went to bed. The next day, the three went to a ski area near Albany •
Palazzolo also testified that he gave his calling card number to Olivieri, who in turn provided it to other members of the conspiracy. He stated that the others had used his card without his permission so often that he had to request that the phone company change the number.
Olivieri’s effort to discredit the government’s version of the events was less systematic. Rene Perez, who was present in the barber shop when Mercedes was abducted, testified that his descriptions of the two kidnappers — five foot eleven inches, between 160 and 175 pounds — did not match Olivieri, who is six feet two inches and 235 pounds. Also, government witness Augustine admitted under cross-examination that he had previously testified that Olivieri had protested that killing Mercedes would be pointless.
B. The Goings Kidnapping and Simmons Attempt
Augustine, Green, and Brown also testified as to the elaborate plot to kidnap Alvin Goings, which involved several days of surveillance culminating in Goings’s abduction on a highway access road. Augustine and Brown stated that after the group stopped Goings’s car, they observed “Richie” [Olivieri] direct traffic and “Mikey” [Palazzolo] remove Goings from his car, handcuff him, and put him in the bogus police vehicle. The three testified further that $400,000 in ransom money was paid for Goings and that the white and black crews had argued over the equitable division of the money and who would keep Goings’s Rolex watch. The government also introduced evidence that two months after the Goings ransom, Palazzolo Had purchased a new Ford Explorer truck with $19,250 in cash. The witnesses were unable to pin down the precise date of the abduction, Augustine estimating it to be “right after Christmas” and Green indicating “between the second week and third week of January of ’91.”
Palazzolo denied participation in the Goings abduction. ' He testified that he had been enticed into joining the conspiracy in mid-January 1991, presumably after the Goings incident. He also submitted records of his employment in December 1990 and January 1991 and the results of a polygraph test in which he denied involvement that showed “no significant physiological responses on his recorded answers that would indicate deception.”
Olivieri relied on testimony elicited on cross-examination of the government’s witnesses. Green admitted that he had entered into a cooperation agreement with the government and hoped for a downward departure due to his substantial assistance in the case. Olivieri’s counsel also elicited that *289Green had first identified a photograph of Olivieri nearly three years after the kidnappings but only a short period after the two had been housed on the same floor of the Metropolitan Correctional Center (“MCC”). Augustine and Brown made similar admissions regarding their cooperation with the government and their identification of Olivi-eri. Brown also stated that, while incarcerated with Olivieri at the MCC, Olivieri asked him whether they were charged in the same case and he responded that he did not know Olivieri. Similarly, Augustine conceded that when he “first came in” from the conspiracy he denied knowing Olivieri or any other members of the white crew.
With respect to Appellants’ involvement in the attempted kidnapping of Richard Simmons, Palazzolo himself testified on direct examination that he and Olivieri had tried unsuccessfully to abduct Simmons. Augustine and Brown also testified that they had met with the Appellants on the night before the Appellants left with other members of the white crew to “arrest” Simmons.
II. The District Court’s Findings and Rulings
On September 16, 1994, the district court announced its factual findings. It found that the government had proven Appellants’ participation in the Mercedes, Goings, and Simmons incidents by “clear and convincing evidence,” and noted further that “the alibi offered by Mr. Palazzolo is simply not credible.” Finding that Palazzolo had “testified falsely” and that his testimony “was clearly not the result of confusion, mistake or faulty memory,” the court concluded that an enhancement for obstruction of justice was appropriate under United States v. Dunnigan, 507 U.S. 87, 93-95, 113 S.Ct. 1111, 1116, 122 L.Ed.2d 445 (1993). Despite Palazzolo’s false testimony, the district court granted Palazzo-lo’s request for a three-level adjustment for acceptance of responsibility in light of his plea agreement, confession to the Simmons attempt, and expression of remorse on the stand.
Appellants appeared for sentencing on September 23, 1994. Before imposing the sentences, the district court stated that it had reconsidered the proof against Palazzolo and Olivieri and that it no longer felt that the government had shown Appellants’ participation in the three incidents by clear and convincing evidence. Accordingly, the court amended its findings to reflect its belief that the government had only met the “preponderance of the evidence” standard. The court then altered its earlier imposition of the obstruction of justice enhancement, stating that “I do not find under these circumstances the firmness of conviction that I would want to have in order to apply the enhancement under section 3C1.1.”
The district court determined the offense level as to both Palazzolo and Olivieri after adjustments to be 33. Briefly stated, the adjusted base offense level was arrived at by applying U.S.S.G. § 2B3.2 (extortion) to the Goings and Mercedes kidnappings and U.S.S.G. § 2A4.1 (kidnapping) to the Simmons attempt as well as to the racketeering conspiracy to kidnap two other individuals, Jorge Davila and an unidentified man, which was the subject of the guilty plea. Under U.S.S.G. § 2B3.2, the base offense level of 18 (subsection (a)) was enhanced by 2 for implied threat (subsection (b)(1)), by 3 for the amount demanded (subsection (b)(2)), by 5 for use of a weapon (subsection (b)(3)), and by 4 for abduction (subsection (b)(5)) for a total offense level of 32. Under U.S.S.G. § 2A4.1 the base offense level of 24 was enhanced by 6 for the ransom demand (subsection (b)(1)) and by 2 for weapon use (subsection (b)(3)) for a total of 32. After the combined offense level was determined pursuant to U.S.S.G. § 3D1.4, the offense level for each Appellant was 36. The district court then applied a three-level downward adjustment for acceptance of responsibility to arrive at the final adjusted level of 33.
The resulting sentencing ranges for Palaz-zolo and Olivieri, whose criminal history categories were one and two, respectively, were 135 to 168 months and 151 to 188 months, respectively. The district court sentenced Palazzolo to 135 months imprisonment and Olivieri to 151 months imprisonment, each to be followed by three years of supervised release. These appeals and the cross-appeal followed.
*290DISCUSSION
Appellants’ two principal arguments on appeal are that the district court should have applied a higher standard than preponderance of the evidence in order to sentence them for the three alleged incidents’ of relevant conduct, and that, even if the preponderance standard was appropriate, the evidence at the Fatico hearing, was not sufficient to support the district court’s findings that Appellants participated in the Mercedes or Goings kidnappings.
Olivieri raises several additional points: 1) the district court erred in treating the three incidents as separate counts of conviction; 2) the court engaged in impermissible double counting when it imposed multiple enhancements; 3) the court used the wrong version of the Sentencing Guidelines when it imposed a five-level enhancement for brandishing a firearm; 4) the informants’ testimony at the Fatico hearing was legally incredible; 5) the district court erroneously imposed four “grouping points” on Olivieri; and 6) the court erred in applying the 1993 Sentencing Guidelines. In its cross-appeal, the government faults .the district court for declining to impose an enhancement for obstruction and allowing a three-point decrease for acceptance of responsibility. We address each contentiofl in turn.
I. The Proper Standard of Proof
Appellants acknowledge that the Sécond Circuit has held repeatedly that “disputed facts relevant to sentencing, even under the Guidelines, need be established only by a preponderance of the evidence.” United States v. Concepcion, 983 F.2d 369, 388 (2d Cir.1992), cert. denied, 510 U.S. 856, 114 S.Ct. 163, 126 L.Ed.2d 124 (1993); United States v. Rodriguez-Gonzalez, 899 F.2d 177, 182 (2d Cir.), cert. denied, 498 U.S. 844, 111 S.Ct. 127, 112 L.Ed.2d 95 (1990); United States v. Guerra, 888 F.2d 247, 251 (2d Cir.1989) (preponderance standard applies to findings of relevant conduct), cert. denied, 494 U.S. 1090, 110 S.Ct. 1833, 108 L.Ed.2d 961 (1990). They contend, however, that a higher standard should apply to their ease: first, because the district court’s findings of relevant conduct had such “dramatic implications” for Appellants’ sentences, and second, because Application Note 5 to Sentencing Guideline § lB1.2(d) requires proof beyond a reasonable doubt. We reject both contentions.
In arguing that the dramatic effect of the relevant conduct on their sentences implicates a higher standard of proof, Appellants rely heavily on United States v. Kikumura, 918 F.2d 1084 (3rd Cir.1990). In Kikumura, the district court departed from a guideline range of 27 to 33 months imprisonment and imposed a thirty-year sentence based upon uncharged conduct proven at the sentencing hearing. Id. at 1089. The Third Circuit vacated and remanded, holding that where “the sentencing hearing can fairly be characterized as ‘a tail which wags the dog of the substantive offense,’ ” the determinative facts at sentencing “must be established at least by clear and convincing evidence.” Id. at 1100-07 (quoting McMillan v. Pennsylvania, 477 U.S. 79, 88, 106 S.Ct. 2411, 2417, 91 L.Ed.2d 67 (1986)).
Kikumura does not require the use of the clear and convincing standard in this ease. First, we have never adopted the holding of Kikumura. Moreover, even if we were to agree with the Third Circuit’s approach, the facts of Kikumura are markedly different from those in this case. Kikumura involved a “twelve-fold, 330-month departure from the median of an applicable guideline range,” id. at 1102, which was “apparently the largest departure from an applicable guideline range, in absolute or percentage terms, since the sentencing guidelines became effective,” id. at 1089. Here, in contrast, the district court’s findings at sentencing of uncharged conduct increased Palazzolo’s offense level from 25 to 33 and the corresponding range from between 57 and 71 months to between 135 and 168 months. The findings increased Olivieri’s offense level, at a higher criminal history category, from 25 to 33 and the corresponding range from between 63 and 78 months to between 151 and 188 months.
We have upheld under the preponderance standard increases based on relevant conduct that are similar to or greater than those in this case. In United States v. Gigante, for example, the two defendants had a base of*291fense level of 18, which corresponded to a sentencing range of 27 to 33 months. 94 F.3d 53, 55 (2d Cir.1996), modifying United States v. Gigante, 39 F.3d 42 (2d Cir.1994). After numerous adjustments and departures based in part on acquitted conduct, defendants were sentenced to 188 and 200 months imprisonment, respectively. Id. at 55. We held that, although “the weight of the evidence, at some point along a continuum of sentence severity, should be considered with regard to both upward adjustments and upward departures,” the preponderance of the evidence standard was appropriately applied. Id. at 56. If the relevant conduct in Gigante did not sufficiently “wag the dog” to trigger a higher standard, the relevant conduct at issue here must fall short as well. See generally United States v. Rivalta, 892 F.2d 223, 230 (2d Cir.1989) (reviewing cases upholding use of preponderance standard at sentencing).
Appellants also contend that Application Note 5 to U.S.S.G. § lB1.2(d) requires that relevant conduct be found beyond a reasonable doubt. Section lB1.2(d) states that a “conviction on a count charging a conspiracy to commit more than one offense shall be treated as if the defendant had been convicted on a separate count of conspiracy for each offense that the defendant conspired to commit.” Application Note 5 in turn advises, in pertinent part, that
[p]articular care must be taken in applying subsection (d) because there are cases in which the verdict or plea does not establish which offense(s) was the object of the conspiracy. In such cases, subsection (d) should only be applied with respect to an object offense alleged in the conspiracy count if the court, were it sitting as a trier of fact, would convict the defendant of conspiring to commit that object offense.
The Sentencing Commission has indicated that the “if the court ... would convict” language of Application Note 5 requires a sentencing court to apply the reasonable doubt standard. See U.S.S.G.App. C, Amend. 75.
The problem with this argument is that U.S.S.G. § lB1.2(d) and Application Note 5 are not relevant to the sentences of these Appellants. That commentary “is provided to address cases in which the jury’s verdict does not specify how many or which offenses were the object of the conspiracy of which the defendant was convicted.” U.S.S.G.App. C, Amend. 75. Here, Appellants have pleaded guilty to a racketeering charge. Unlike a conspiracy count for which many objectives may be charged but only one need be found for conviction, Appellants’ pleas left no mystery regarding the predicate acts underlying their charge of conviction. Olivieri and Pa-lazzolo admitted in open court to participating in two kidnappings. The principal issue at sentencing was not whether their pleas were not coextensive with the conduct covered by the pleas but whether there was additional relevant conduct that should be taken into account under U.S.S.G. § 1B1.3. Nowhere do the Sentencing Guidelines suggest that the higher standard of Application Note 5 applies to an ordinary relevant conduct inquiry. See Concepcion, 983 F.2d at 388. Accordingly, we hold that the district court properly applied the preponderance of the evidence standard when determining the extent of Appellants’ relevant conduct.
II. The Sufficiency of the Evidence
Appellants next contend that, even if the district court applied the correct standard, the evidence was insufficient to support its factual findings as to the Mercedes or Goings kidnappings. A district court’s factual findings at sentencing “may not be overturned unless clearly erroneous.” United States v. Paccione, 949 F.2d 1183, 1208 (2d Cir.1991), cert. denied, 505 U.S. 1220, 112 S.Ct. 3029, 120 L.Ed.2d 900 (1992); see United States v. Echevarria, 33 F.3d 175, 178 (2d Cir.1994). “The court of appeals shall give due regard to the opportunity of the district court to judge the credibility of the witnesses,” 18 U.S.C. § 3742(e), and must consider the evidence in the light most favorable to the government as the respondent, Paccione, 949 F.2d at 1208. “Where there are two permissible views of the evidence, the district court’s choice between them cannot be deemed clearly erroneous.” United States v. Thai, 29 F.3d 785, 814 (2d Cir.), *292cert. denied, — U.S. -, -, 115 S.Ct. 456, 496, 130 L.Ed.2d 364, 406 (1994).
With respect to the Goings kidnapping, Augustine and Brown each testified that they personally observed Olivieri and Palazzolo take part in the attempted grab. Palazzolo’s employment records do little to contradict this testimony because they do not foreclose the possibility that the incident occurred while he was away from work. While his polygraph results may suggest the truthfulness of his denials, we have previously intimated that such “lie-detector” tests are generally not admissible in federal court because of their questionable accuracy. See United States v. Rea, 958 F.2d 1206, 1224 (2d Cir.1992); United States v. Bortnovsky, 879 F.2d 30, 35 (2d Cir.1989) (collecting cases). Olivi-eri’s evidence .as to the motives of Augustine, Brown, and Green and the circumstances of their identification of Olivieri, brought out in cross-examination, bears on their credibility but does not permit us to conclude that the district court’s finding in the government’s favor was clearly erroneous.
Palazzolo’s participation in the Mercedes kidnapping presents a closer question. Pa-lazzolo offered testimony from several witnesses to the effect that he was socially occupied at some distance from New York City for much of the day on which Mercedes was kidnapped. Palazzolo also presented a plausible and relatively innocent explanation for the use of his calling card that day. In the end, however, like the district court, we are faced with two contradictory accounts of Palazzolo’s activities that day, each feasible and each supported by eyewitness testimony and circumstantial evidence. We cannot fault Judge Schwartz’s resolution of this conflict in the government’s favor. See Thai 29 F.3d at 814 (“[W]e are particularly hesitant to disturb the court’s determinations when they are based on its evaluation of the credibility of witnesses.”). Olivieri, who offers no alibi and instead only attacks the credibility of the government’s witnesses, fares even worse than Palazzolo in challenging the district court’s findings as to the Mercedes abduction. We therefore affirm the district court’s factual findings as to the relevant conduct for sentencing.
III. Appellants’ Remaining Claims
The additional arguments raised by Olivieri and adopted by Palazzolo require little comment. First, Olivieri contends that the district court improperly treated the Mercedes, Goings, and Simmons kidnappings as separate counts of conviction and then combined them pursuant to the grouping rules in Chapter 3, Part D of the Sentencing Guidelines, with the result that those incidents, rather than the counts of conviction, determined his total offense level. Under U.S.S.G. § lB1.3(a), however, the district court is directed to consider all relevant conduct when computing “the base offense level where the guideline specifies more than one base offense level.” The guideline for Appellants’ count of conviction, U.S.S.G. § 2E1.1, specifies more than one offense level: it sets the base offense level as the greater of 19 or thé offense level applicable to the underlying racketeering activity. Because Appellants’ “underlying racketeering activity” included the three additional kidnapping incidents proven at sentencing, the district court properly determined the base offense level by taking those incidents into account.
It is also clear that the district court correctly applied Chapter Three’s grouping provisions. Under U.S.S.G. § 3D1.2, counts are to be grouped only if 1) they involve the same victim, 2) one count is a specific offense characteristic of another, or 3) the offense level is determined by quantity or “some other measure of aggregate harm,” or “if the offense behavior is ongoing or continuous in nature.” The five separate incidents of racketeering activity — the two attempted kidnappings that Appellants admitted during their plea allocutions and the three additional offenses proven at sentencing — did not qualify for grouping under this provision. Indeed, U.S.S.G. § 3D1.2(d) expressly provides, inter alia, that “all offenses in Chapter Two, Part A” and U.S.S.G. § 2B3.2 are “[specifically excluded from the operation of this subsection.” The district court’s decision not to group the offenses but to apply U.S.S.G. § 3D1.4 to each individually was thus proper.
Olivieri next contends that the district court relied on the ■wrong version of the *293Sentencing Guidelines in imposing the five-level enhancement for brandishing a firearm, which is assigned by the extortion provision. He argues that, because the offense conduct occurred in 1991 and U.S.S.G. § 2B3.2(b)(3)(A)(iii) of the 1991 Sentencing Guidelines imposes only a three-level enhancement for brandishing a firearm, application of a five-level enhancement under the 1993 Sentencing Guidelines violated the ex post facto clause of the Constitution. This argument is without merit.
In assessing whether a sentencing provision violates the ex post facto clause, a court must compare the two statutory schemes as a whole, rather than each provision, to determine “if the new [scheme] may be fairly characterized as more onerous.” Dobbert v. Florida, 432 U.S. 282, 294, 97 S.Ct. 2290, 2299, 53 L.Ed.2d 344 (1977) (evaluating new procedures for imposition of the death penalty); see also Miller v. Florida, 482 U.S. 423, 431, 107 S.Ct. 2446, 2451-52, 96 L.Ed.2d 351 (1987). In the context of the Sentencing Guidelines, the “whole scheme” to be evaluated includes all of the provisions applicable to a defendant’s conduct, not just one amendment or enhancement. See United States v. Stephenson, 921 F.2d 438, 441 (2d Cir.1990) (“Applying various provisions taken from different versions of the Guidelines would upset the coherency and balance the Commission achieved in promulgating the Guidelines.”). Because of changes to the kidnapping guideline that worked to Olivieri’s benefit, his total offense level after adjustments under the 1993 Sentencing Guidelines (before combining an adjustment for acceptance of responsibility) was actually lower than under the 1990 Sentencing Guidelines — 32 as opposed to 35.1 Under these circumstances, that the magnitude of a single enhancement of a multi-faceted sentencing provision increased between 1991 and 1993 does not constitute a constitutional violation.
Olivieri makes three additional arguments on appeal: that the imposition of multiple enhancements under the extortion guideline constituted impermissible double counting; that the district court erred in crediting the testimony of Augustine, Brown, and Green; and that Olivieri should not have been “strapped” with four grouping points for having committed five offenses. We have considered these arguments and find them to be without merit.
IV. The Denial of An Enhancement for Obstruction of Justice
In its cross-appeal, the government contests the district court’s decision, after reflection, not to impose an enhancement for obstruction of justice based on Palazzolo’s testimony at the Fatico hearing. The government argues that because Judge Schwartz found that the predicates for such an enhancement existed, he had no choice but to impose the enhancement. We disagree.
Under U.S.S.G. § 3C1.1, a two-level enhancement applies “[i]f the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the investigation, prosecution, or sentencing of the instant offense.” Perjury committed during a Fatico hearing qualifies as obstruction of justice, and once a district court has made specific findings that a defendant has committed perjury — that he has “give[n] false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of confusion, mistake or faulty memory” — an obstruction of justice enhancement must be imposed. Dunnigan, 507 U.S. at 93-95, 98, 113 S.Ct. at 1116, 1119; see United States v. Friedman, 998 F.2d 53, 58 (2d Cir.1993) (“The obstruction of justice enhancement ... *294is mandatory once its factual predicates have been established.”).
When Judge Schwartz issued his original factual findings, he found that the predicates for perjury existed and indicated his intent to impose the enhancement. At sentencing, however, Judge Schwartz expressed concern over the certainty of his findings that Appellants participated in the three additional kidnapping incidents. His doubt concerning Pa-lazzolo’s involvement in the Mercedes and Goings abductions translated into uncertainty as to whether Palazzolo had testified falsely when denying his involvement. Judge Schwartz observed that under decisions of this court a higher standard of proof than a preponderance of the evidence applies to perjury findings and concluded that, notwithstanding his finding that the government had proven Palazzolo’s participation, he did not have the firmness of conviction necessary to find the factual predicates for perjury. The government contends that this justification for failing to apply the enhancement is “simply insufficient and capricious.” We disagree.
Whether a higher standard of proof than a preponderance of the evidence applies to perjury findings is not a novel issue. Application Note 1 to U.S.S.G. § 3C1.1 cautions that “[i]n applying this provision in respect to alleged false testimony dr statements by the defendant, such testimony or statements should be evaluated in a light most favorable to the defendant.” We held in United States v. Cunavelis, 969 F.2d 1419 (2d Cir.1992), that the standard implicated by this language “is obviously different — and more favorable to the defendant — than the preponderance-of-evidence standard.” Id. at 1423 (reversing an automatic enhancement imposed without independent findings). In United States v. Onumonu, we disagreed with the defendant’s argument that this language required that the sentencing court find the predicates of perjury beyond a reasonable doubt, but concluded that it sounded “indistinguishable from a elear-and-convincing standard.” 999 F.2d 43, 45 (2d Cir.1993). These decisions may be distilled to the following proposition: a district court may make findings as to relevant conduct by a preponderance of the evidence yet properly refuse to find that the defendant, in testifying to the contrary, had committed perjury if the government’s proof did not sufficiently exceed the preponderance threshold.
The government argues that Application Note 1 to U.S.S.G. § 3C1.1 is inapplicable to this case. In United States v. Matos, we stated that the language in Application Note 1 “ ‘simply instructs the sentencing judge to resolve in favor of the defendant those conflicts about which the judge, after weighing the evidence, has no firm conviction.’ ” 907 F.2d 274, 276 (2d Cir.1990) (quoting United States v. Franco-Torres, 869 F.2d 797, 801 (5th Cir.1989)). The government argues that because the district court unequivocally found the predicates for perjury on September 17 and no new evidence was introduced to sway the court in defendant’s direction, there was no conflict that would trigger the operation of the application note.
We reject this argument for several reasons. First, the government ignores explicit language in Cunavelis and Onumonu which suggests that Application Note 1 does not simply provide a tool for resolving ambiguous evidence, but also heightens the burden of proof applicable to a perjury enhancement. Onumonu, 999 F.2d at 45; Cunavelis, 969 F.2d at 1423. Second, Judge Schwartz acted consistently with Matos. We stated in Ma-tos that evidence should be construed in the defendant’s favor if there is a conflict about which the judge “has no firm conviction,” 907 F.2d at 276 (emphasis added), not simply if the judge has no conviction. At sentencing, Judge Schwartz clarified that he found Appellants’ participation in the three additional incidents more - likely than not — sufficient to meet the preponderance standard — but could not characterize his belief as “firm.” It was thus appropriate to construe the evidence in Palazzolo’s favor and decline to impose the perjury enhancement. We will not attribute to Judge Schwartz’s findings a level of certainty that, after reflecting upon the matter, the judge himself did not believe he possessed.
V. The Reduction for Acceptance of Responsibility
The government also challenges the district court’s decision to grant Palazzolo a *295three-level reduction for acceptance of responsibility under U.S.S.G. § 3E1.1. While the court acknowledged in its original findings that Palazzolo’s false testimony east doubt on his acceptance of responsibility, it found that
Mr. Palazzolo, through his plea agreement, his confession on the witness stand to participation in the Simmons kidnapping, and his testimony regarding his feelings with respect to having participated in this conspiracy, has accepted responsibility for his criminal activities in a quite fundamental way.
The government contends that, in light of Palazzolo’s testimony at the Fatico hearing denying his involvement in the Mercedes and Goings affairs, it was error for the district court to find that “the defendant clearly demonstrate[d] acceptance of responsibility for his offense” under U.S.S.G. § 3E1.1. We disagree.
The government is correct in stating that conduct that amounts to obstruction of justice “ordinarily indicates that the defendant has not accepted responsibility for his criminal conduct,” U.S.S.G. § 3E1.1, comment. (n.4), and similarly that “a defendant who falsely denies, or frivolously contests, relevant conduct that the court determines to be true has acted in a manner inconsistent with acceptance of responsibility.” U.S.S.G. § 3E1.1, comment, (n.l(a)). That a reduction is not “ordinarily” appropriate under such circumstances, however, does not mean that it is never appropriate. Instead, we believe that a false denial of relevant conduct is simply one factor among many to be weighed by a district court considering whether a downward adjustment for acceptance of responsibility is warranted.
We find U.S.S.G. § 3E1.1, Application Note 3 instructive to the extent that it sheds light on how the Commission would have courts consider conduct inconsistent with acceptance of responsibility. Note 3 provides:
Entry of a plea of guilty prior to the commencement of trial combined with truthfully admitting the conduct comprising the conviction, and truthfully admitting or not falsely denying any additional relevant conduct for which he is accountable under § 1B1.3 (Relevant Conduct) ..., will constitute significant evidence of acceptance of responsibility.... However, this evidence may be outweighed by conduct of the defendant that is inconsistent with such acceptance of responsibility.
Note 3 thus appears to counsel weighing the evidence favoring the acceptance of responsibility adjustment against evidence of conduct inconsistent with acceptance. See United States v. Forte, 81 F.3d 215, 218 (D.C.Cir.1996) (language of Application Note 3 “strongly suggests ... that the Commission viewed the lies about ‘additional relevant conduct’ discussed in Application Note 1(a) as merely a factor in the trial judge’s decision, not a trump”). Vesting discretion in the district court to weigh these factors is appropriate, for, as Application Note 5 to U.S.S.G. § 3E1.1 states, “[t]he sentencing judge is in a unique position to evaluate a defendant’s acceptance of responsibility.”
Because “the determination of the sentencing judge is entitled to great deference,” id., we will not disturb it on appeal unless it was “without foundation,” United States v. Fredette, 15 F.3d 272, 277 (2d Cir.), cert. denied, — U.S. -, 114 S.Ct. 2119, 128 L.Ed.2d 677 (1994); United States v. Irabor, 894 F.2d 554, 557 (2d Cir.1990). We do not believe that Judge Schwartz’s careful determination — based on evidence such as the defendant’s remorse, his guilty plea, and his confession on the stand to an additional incident of relevant conduct — was without foundation, and thus, find no basis to disturb his decision to grant Palazzolo a three-level reduction for acceptance of responsibility under U.S.S.G. § 3E1.1.
CONCLUSION
For the foregoing reasons, we affirm the Appellants’ sentences in all respects.
. Olivieri also argues that the total offense level under the 1990 Guidelines was 31 — lower than that under the 1993 Guidelines — and that, therefore, the earlier version should have been applied. His computations ignore a four-level enhancement in the kidnapping guideline calculation because "the victim was ... abducted ... to facilitate the commission of another offense,” in this case extortion. U.S.S.G. § 2A4.1(b)(5) (1990). Application of this enhancement for the facilitation of extortion in combination with an enhancement for a ransom demand is permissible. See United States v. Rocha, 916 F.2d 219, 243-44 (5th Cir.1990) ("The district court did not err in ruling that section 2A4.1 permits an enhancement for a ransom demand and the offense of extortion.”), cert. denied, 500 U.S. 934, 111 S.Ct. 2057, 114 L.Ed.2d 462 (1991).