KANNE, Circuit Judge.

Charles Kroledge, his wife Kathleen Kroledge, Charles's brother Tony Kroledge and Tony's wife Ethel Juanita Kroledge were convicted on December 1, 1997, of conspiracy to participate in mail fraud. Ethel and Kathleen Kroledge were also convicted of mail fraud. The Kroledges' convictions resulted from the family's attempt to defraud its insurer by filing false claims in conjunction with a fire, allegedly set by Charles Kroledge, that damaged Charles and Kathleen's home. The four were indicted on the charge of using fire to commit a felony, but all were acquitted.

The Kroledges do not appeal the merits of their convictions. Instead, they contend that their sentences were wrongly enhanced, because the district court included the arson as relevant conduct for purposes of enhancing each of their offense levels, and ask us to reconsider the standard of evidence required to include acquitted offenses as relevant conduct for the purpose of sentence enhancement. They also claim that the district court erred in enhancing their sentences for obstruction of justice. Finding no errors, we affirm.

I. History

In May 1991, one of Charles and Kathleen Kroledge's children accidentally shot a hole in the family's television, causing it to spark. This accident led Charles's brother Gilbert to joke that Charles and Kathleen, who were under considerable financial pressure to keep up with the mortgage payments on their house, would be better off if the house did catch fire. These events allegedly spawned a plan in Charles's mind to burn down the house and use the insurance money to build a new house for the family. Shortly thereafter, Charles and Kathleen sought Gilbert and his wife Martha's help in planning the fire, and the four engaged in activities such as experimenting with ways to start a fire and packing up mementoes, photographs and records. Charles's brother Tony and his wife Ethel also became involved as Charles and Kathleen stored some of the boxes containing their possessions at Tony and Ethel's house.

On the morning of June 8, 1991, Charles told Martha that he and his wife intended to set fire to the house that night and that they would spend the evening with Tony and Ethel at the stock car races while the house burned. Sometime after 1:00 a.m. that night, the Hobart, Indiana fire department responded to a fire at Charles and Kathleen Kroledge's home. Although members of the Hobart Fire Department considered some of the damage to the house suspicious and worthy of arson investigation, the house was actually located in the jurisdiction of the neighboring town of Lake State, Indiana. Therefore, the Lake Station Fire Department was responsible for the investigation.

Lake Station's fire investigator Ken Corbeille who was inexperienced in arson investigation, focused on an electrical outlet rather than on other damage and determined that the fire was accidental. Corbeille then left the fire scene unattended for several hours. During this time, Gilbert Kroledge testified at trial that he and Tony Kroledge removed newspapers from inside the walls and among the furniture cushions of the couch where the fire started. These newspapers were allegedly planted by Charles to provide trailer for the fire.

Charles and Kathleen Kroledge declared that their entire house and all their valuables (including those that they had stored with Tony and Ethel) had been destroyed by the fire. In addition, Kathleen and Ethel Kroledge forged false receipts for an apartment where Charles and Kathleen were supposedly residing during the reconstruction of their house. Ethel Kroledge asked the owner of the apartment that Kathleen claimed to be renting, Annette Mathews, whether she could use Mathews's name on insurance claim forms and told Mathews to lie if anyone asked whether Kathleen and Charles were living with her. During this time, Charles, Kathleen and their family were actually living with Tony and Ethel Kroledge. When the fire was declared an accident, their insurer, State Farm Insurance Company ("State Farm"), reimbursed Charles and Kathleen for both their loss and their living expenses.

In October 1991, Martha and Kathleen Kroledge had a falling out because Kathleen informed Martha's husband Gilbert of an affair that Martha was having. Martha was enraged by this and told a relative about Charles and Kathleen's activities. This relative contacted State Farm's fraud investigators, who in turn contacted the FBI. The FBI contacted Martha, and the agency granted Martha and Gilbert immunity from prosecution in exchange for their cooperation in the investigation of the fire.

In August 1993, an FBI investigator spoke with Charles and Kathleen Kroledge about the events surrounding the 1991 fire. Charles and Kathleen told this investigator that they attended stock car races that night and did not return home until 1:00 a.m. In November 1993, the same investigator spoke to Tony and Ethel Kroledge about their involvement in the fire. Neither Tony nor Ethel mentioned that Charles and Kathleen stayed with them during the time that the Kroledges were rebuilding their house, but the two did verify that Charles and Kathleen had attended stock car races with them on the night of the fire.

During the 1993 investigation, Martha and Gilbert Kroledge secretly tape recorded conversations with Charles, Tony and Ethel. These conversations implicated each of the Kroledges in the scheme to defraud the insurer. Charles admitted that he burned his own house down. Tony and Ethel admitted that they had stored many of Charles and Kathleen's possessions for them.

On April 10, 1996, the four Kroledges — Charles, Kathleen, Tony and Ethel — were indicted on charges of conspiracy to commit mail fraud, mail fraud (on three counts) and using fire or an explosive to commit a federal felony. All four pleaded not guilty. After the return of a superseding indictment substituting certain mailings for which the mail fraud allegations would be based, trial commenced on November 17, 1997.

At trial, Charles Kroledge denied even discussing the possibility of starting a fire at his house. He also denied experimenting with ways to start a fire, and he testified that he attended stock car races on the night that the fire occurred. Kathleen admitted that she may have misrepresented her loss in her claim to State Farm but testified that she and Charles did not have financial problems. She denied lying to a State Farm investigator who asked her where she was living during the reconstruction of her house. State Farm claims adjuster Bob Bradley contradicted Kathleen's story, claiming that Kathleen never informed him that she was living with Tony and Ethel. In addition, Annette Mathews testified that Ethel told her to tell any person who asked that the Kroledges were living in her apartment.

Ethel Kroledge testified that she told the FBI investigator that she had lied about where Charles and Kathleen had lived during the rebuilding process, but the FBI investigator testified that she never admitted her lie prior to her testimony before a grand jury in 1994. Tony testified that he had no idea who lived in his house in 1991 because he worked nights. He also testified that Charles and Kathleen were with Tony at the stock car races on the night that the fire took place.

The jury found all four Kroledges guilty of conspiracy to commit mail fraud. The jury also found Kathleen Kroledge guilty of two counts of mail fraud and Ethel Kroledge guilty of one count. The jury acquitted the Kroledges of all remaining counts, including using fire to commit a federal felony. At sentencing, however, the court found by a preponderance of the evidence that the Kroledges used fire as a part of their conspiracy to defraud State Farm, and therefore, the court used evidence of the arson as relevant conduct and applied this conduct to each defendant's sentence. This evidence of relevant conduct led to a two-point enhancement of each defendant's base offense level for reckless risk of serious bodily injury and another two-point enhancement for more than minimal planning. In addition, the court found that Tony, Kathleen and Charles had each obstructed justice by providing false testimony and lying to FBI investigators about their role in the conspiracy. Because of medical problems that she experienced, Ethel was separately sentenced. At her separate sentencing, the district court adopted the same findings about her behavior except that the court made no finding of perjury, and she was given a similar sentence. Charles, Tony and Ethel Kroledge were each sentenced to twenty-seven months imprisonment with a three year term of supervised release. Kathleen Kroledge was sentenced to thirty-three months imprisonment with a three year term of supervised release. Each of the defendants was ordered to pay State Farm $78,344.85 in restitution.

II. Analysis

The Kroledges challenge the enhancement of their sentences on three grounds. First, they claim that the district court erred in enhancing each of their sentences for obstruction of justice. Second, they claim that the district court lacked sufficient evidence of arson to include it as relevant conduct for purposes of calculating their sentences. Third, they argue that the district court applied the wrong evidentiary standard in determining whether to include the arson as relevant conduct for the purpose of computing each of their sentences.

Both the challenge to the district court's enhancement to the Kroledges' sentences for obstruction of justice and the challenge to the court's inclusion of arson as relevant conduct are determinations made for the purpose of sentencing. We review sentence determinations for clear error. See United States v. Gwiazdzinski, 141 F.3d 784, 788 (7th Cir. 1998). We will reverse on clear error only if we are left with a definite and firm conviction that a mistake has been committed. See United States v. Garcia, 69 F.3d 810, 819 (7th Cir. 1995).

A. Obstruction of Justice

Each of the Kroledges challenges the enhancement of his or her sentence for obstruction of justice. Sentencing Guidelines § 3C1.1 authorizes a two-point enhancement for obstruction of justice if the sentencing court finds by a preponderance of the evidence that a defendant "willfully obstructed or impeded . . . the administration of justice during the course of the investigation, prosecution, or sentencing of the instant offense." U.S. Sentencing Guidelines Manual § 3C1.1 (1997). "To establish an obstruction of justice, the sentencing court must make an independent factual finding that the defendant engaged in a willful attempt to provide false testimony." United States v. Smith, 103 F.3d 600, 606 (7th Cir. 1996) (citation omitted). When a defendant objects to an enhancement for obstruction of justice, the district court must review the evidence and make an independent determination as to the existence of the willful obstruction of justice. See United States v. Menting, 166 F.3d 923, 929 (7th Cir. 1999). Since the court based its finding of obstruction against each Kroledge on different facts, we review each finding independently.

1. Charles Kroledge

The sentencing court based its finding of obstruction of justice against Charles Kroledge, among numerous other items, on his testimony that Tony and Ethel Kroledge had no involvement in the scheme to defraud State Farm. Charles claims that this finding, which was based on the pre-sentence report, was inaccurate and did not meet the required specificity for findings of fact as to the willfulness and materiality of Charles's testimony. We disagree.

Even if the district court did not explicitly address the willful and material nature of Charles's testimony, we may uphold the enhancement as long as the district court made a finding of obstruction that "encompasses all of the factual predicates for a finding of perjury." United States v. Craig, 178 F.3d 891, 901 (7th Cir. 1999) (quoting United States v. Dunnigan, 507 U.S. 87, 95 (1993)). Charles's testimony regarding Tony and Ethel Kroledge's involvement in the conspiracy speaks to the guilt of Charles's co-conspirators, Tony and Ethel, and is therefore a material obstruction. See Craig, 178 F.3d at 901. Thus, to enhance Charles's sentence for obstruction, Charles's inaccurate testimony must have been made willfully, rather than as a result of mistake, faulty memory or confusion. See Craig, 178 F.3d at 901. An enhancement authorized by § 3C1.1 may employ a defendant's perjurious testimony, but we construe the Guidelines in such a way as to avoid punishing defendants for exercising their right to testify. See Dunnigan, 507 U.S. at 96; United States v. Emerson, 128 F.3d 557, 563 (7th Cir. 1997). In this instance, we find that the court correctly met this standard by focusing on elements of Charles's testimony that did not reflect directly on his own guilt or innocence.

Charles testified that no one, including Tony, entered the house after the arson investigator left the premises. This statement seems to have been made with the intent to show that his brother Tony had no participation in his scheme. However, Gilbert Kroledge testified that he and Tony Kroledge entered Charles's house after the arson investigator left and removed newspaper from the couch and walls. Rather than claiming that his statements at trial were mistaken or the result of confusion, he still claims that his statements do not suggest that Tony and Ethel were not involved in the case. Because his statements were made to exculpate his family, we find no error in the court's determination that Charles's testimony formed the basis for a finding of obstruction.

2. Kathleen Kroledge

The district court based its finding of obstruction against Kathleen Kroledge on her testimony that Tony and Ethel Kroledge were not involved in the conspiracy. The court found that she obstructed justice both by her trial testimony and by pretrial statements that she made to investigators. In her opening statement, Kathleen Kroledge confessed lying to investigators when she and Charles misrepresented their living expenses to State Farm. She now claims that her earlier false statements were immaterial and the finding that she perjured herself at trial was inaccurate.

Kathleen Kroledge testified at trial that she told State Farm's claim adjuster that she was staying with Tony and Ethel, rather than at an apartment as she had claimed. She also testified that she was often away from Tony and Ethel's house, so Tony might not have been aware that she and Charles were living there. State Farm's claim adjuster Bob Bradley testified that Kathleen never informed him that Charles and Kathleen's family were residing with Tony and Ethel after the fire. In addition, Tony Kroledge testified that he told FBI investigators that he knew Charles and Kathleen Kroledge were living with his family while they rebuilt their house.

Kathleen Kroledge's testimony contradicts statements that she made to State Farm and to the FBI prior to trial and contradicts itself in several places. Given the testimony of the government's witnesses at trial, we find that the trial court had sufficient evidence to conclude that the statements by Kathleen about Tony's knowledge of her family's presence in their home, as well as many other contradictory statements, constituted an attempt to obstruct justice, and we will not second guess the district court on such questions of credibility. Kathleen's statements were material, as they would tend to influence the decisionmaking body to which they were addressed. See United States v. Wells, 519 U.S. 482, 483 (1997). Therefore, we find that the district court's finding was accurate on the ground of her perjurious testimony and that its enhancement must be upheld without regard to the materiality of her earlier false statements.

3. Tony Kroledge

The district court enhanced Tony Kroledge's sentence because he provided an alibi for his brother and sister-in-law. Tony Kroledge argues that this finding was in error because any misstatements that he made to investigators occurred early in the investigation and were therefore immaterial. Application Note 6 to Sentencing Guidelines § 3C1.1 defines materiality as "evidence . . . that, if believed, would tend to influence or affect the issue under determination." U.S. Sentencing Guidelines Manual § 3C1.1 application note 6. Although misstatements made to investigators that do not force investigators to expend additional resources are not material, see United States v. Barnett, 939 F.2d 405, 407 (7th Cir. 1991), pretrial statements that significantly obstruct or impede an investigation are material and may serve as the basis for an enhancement. See id.

Tony Kroledge provided an alibi for his brother and sister-in-law by testifying that the two accompanied him to the stock car races on the night of the fire. Further, he corroborated Charles's claim that Charles and Kathleen followed him home that night and did not find out about the fire until after 1:00 a.m. However, his own testimony and the testimony of some government witnesses suggest discrepancies in his story. Gilbert and Martha Kroledge both testified that they saw Charles and Kathleen Kroledge driving in the direction of the races on the night of the fire at an hour when Tony testified they were already with him. Tony Kroledge testified that it generally took thirty-five to forty minutes to return to his home from the races, yet he testified that on the night of the fire it took the Kroledges well over an hour to return home. In addition, Tony Kroledge testified on direct examination that he told the FBI investigator that Charles and Kathleen lived with him during the rebuilding of their home, but he also testified that he did not know at the time that they were living with him. Under cross-examination, Tony Kroledge admitted that he never told anyone that Charles and Kathleen lived with him until he testified so under oath before the grand jury.

On appeal, Tony Kroledge explains, through counsel, that these statements were mistakes made by a simple man confused by the proceedings who was attempting only to protect his family. However, the district court found instead that these statements were made willfully in an attempt to obstruct justice. We review such findings of credibility with great deference and will not reverse unless we find clear error. See United States v. Hall, 101 F.3d 1174, 1179 (7th Cir. 1996). As such, the obstruction enhancement to Tony Kroledge's sentence will remain undisturbed.

4. Ethel Kroledge

The district court enhanced Ethel Kroledge's sentence for obstruction of justice, but, unlike her co-defendants, the court based its enhancement on Ethel Kroledge's pretrial conduct rather than her testimony. On appeal, Ethel Kroledge argues that her pretrial conduct did not significantly impede the government's investigation into the fire and, therefore, was not material for the purposes of enhancing her sentence for obstruction.

In its finding that Ethel Kroledge obstructed justice, the court adopted the finding of fact contained in the pre-sentencing report that Ethel Kroledge had obstructed justice by attempting to influence the testimony of a witness. Ethel Kroledge admitted in her testimony that she told FBI investigators that Charles and Kathleen lived with Annette Mathews during the period when their house was being rebuilt. Annette Mathews testified that Ethel Kroledge asked her to lie to the FBI and State Farm investigators and claim that Charles and Martha lived in their basement apartment during that period. Ethel Kroledge admitted that she asked Annette Mathews whether she could use her name on receipts that the Kroledges presented to State Farm.

The presented testimony dispels any argument that Ethel Kroledge did not obstruct justice in an attempt to protect her brother and sister-in-law. However, she claims that her misstatements were not material because she later corrected them by telling the truth to FBI investigators. To determine the materiality of her conduct, we must review whether the district court correctly found that Ethel Kroledge's actions significantly impeded the investigation of the Kroledges' conduct. See Barnett, 939 F.2d at 407. In Barnett, we refused to uphold an enhancement for obstruction of justice based on a defendant's pretrial conduct when the defendant's only pretrial misstatement was that he denied committing the offenses about which he was questioned. See id.; see also United States v. Wells, 154 F.3d 412, 414 (7th Cir. 1998) (stating that obstruction of justice that "has no consequence . . . is not a permissible basis" for enhancement).

In this case, however, Ethel Kroledge's misstatements went well beyond a mere declaration of innocence. Instead, Ethel Kroledge concocted a false set of facts that led investigators toward a witness whom she had attempted to influence. As in Wells, Ethel Kroledge attempted to lead investigators on a "wild goose chase" in order to obscure evidence of her own criminal conduct. However, in this instance, unlike Wells, the evidence that Ethel Kroledge would obscure was not merely ancillary to questions of her (and her family's) guilt; the activities she concealed were exactly those which led to Kathleen Kroledge's and her own convictions for mail fraud. In circumstances such as these, we have found that such behavior was material, see United States v. Taylor, 135 F.3d 478, 483-84 (7th Cir. 1998), and we have no question that Ethel Kroledge's behavior significantly impeded the instant investigation. As such, her behavior was material for the purpose of determining whether her sentence should be enhanced for obstruction, and we will uphold the district court's enhancement of her sentence.

B. Use of Arson as Relevant Conduct

The Kroledges also argue that the district court erred when it found by a preponderance of the evidence that they had committed arson and that this arson could be used as relevant conduct for the purpose of computing their sentence. They argue that the district court lacked sufficient evidence to determine by a preponderance of the evidence that they committed arson, and in the alternative, they argue that under these circumstances the more rigorous "clear and convincing evidence" standard should have been applied instead of the "preponderance of the evidence" standard.

All four Kroledges were acquitted of the federal crime of arson — using fire in the furtherance of a federal felony. However, the district court determined, for the purposes of sentencing, that a preponderance of the evidence indicated that the Kroledges had committed arson, and the court decided to use the acquitted offense of arson as relevant conduct for the computation of their sentences. In United States v. Watts, 519 U.S. 148, 149 (1997), the Supreme Court held that acquitted offenses may be used as relevant conduct for the purposes of computing a defendant's sentence. The decision in Watts confirmed our own prior precedent, see United States v. Fonner, 920 F.2d 1330, 1332 (7th Cir. 1990), which allowed such conduct to be taken into account. See Watts, 519 U.S. at 149.

Sentencing judges may use all information that they possess in order to properly compute their sentence. See 18 U.S.C. § 3661 ("No limitation shall be placed on the information concerning the background, character, and conduct of a person . . . for the purpose of imposing an appropriate sentence."). Because the relevant burden at sentencing is the "preponderance of the evidence," we allow evidence of acquitted conduct to be considered as long as the government has met the burden of proving by a preponderance of the evidence that defendants have engaged in the relevant conduct, see United States v. Porter, 23 F.3d 1274, 1277-78 (7th Cir. 1994), rather than applying the more stringent standard "beyond a reasonable doubt" required to convict a defendant. See Fonner, 920 F.2d at 1333. Thus, we will uphold the sentences imposed by the district court whenever we determine that the government at trial met the applicable standard for proving that the defendants have engaged in the relevant conduct even if they were acquitted at trial under the stricter standard.

1. Relevant Burden of Proof

We have held that a preponderance of the evidence is all that is required under the Sentencing Guidelines for a finding of fact. See, e.g., Porter, 23 F.3d at 1277. Despite our clear precedent, the Kroledges urge us to consider the argument that a heightened standard of proof must be met under some instances "where a factual finding will result in a sentencing increase so great `that the sentencing hearing can fairly be characterized as a tail which wags the dog of the substantive offense.'" United States v. Corbin, 998 F.2d 1377, 1387 (7th Cir. 1993) (citations omitted). In support, the Kroledges cite United States v. Kikumura, 918 F.2d 1084, 1102 (3d Cir. 1990), in which the Third Circuit required the higher standard of proof in a case where the sentencing court raised the defendant's sentence from about thirty months to thirty years.

In Corbin, we acknowledged the possibility that a higher standard might be appropriate in those circumstances where the government appeared to use the sentencing hearing to retry the substantive offense. In such circumstances, the district court might use its discretion to depart from the Sentencing Guidelines in such a way as to effectively sentence a defendant to the term that would have been appropriate had she been convicted of the substantive offense. As we noted in United States v. Rodriguez, 67 F.3d 1312, 1322 (7th Cir. 1995), we have not yet been presented with an opportunity to consider whether, under a certain set of facts, such a heightened standard of proof may be appropriate. We are confident that these facts do not merit the imposition of the clear and convincing evidence standard.

Here, the Kroledges were each acquitted of the charge of use of fire in the furtherance of a federal felony, pursuant to 18 U.S.C. § 844(i), which provides that any person who "maliciously damages or destroys . . . by means of fire or an explosive, any building, vehicle, or other real or personal property . . . shall be imprisoned for not less than 5 years and not more than 20 years." Thus, if the Kroledges had been convicted of the federal arson charge, they would each serve between five and twenty years. Instead, by enhancing their sentences based on the relevant conduct of arson, each Kroledge is serving either twenty-seven or thirty-three months, which is roughly half of the minimum sentence that they would have received for the arson charge. As we noted in Porter, see 23 F.3d at 1277-78, we have in many instances refused to adopt the Kikumura standard in cases where the sentence enhancement was more drastic than the enhancement at issue here. See Rodriguez, 67 F.3d at 1323 (51-63 months enhanced to life imprisonment); Porter, 23 F.3d at 1276 (92-115 months enhanced to 137 months); United States v. Masters, 978 F.2d 281, 283-85 (7th Cir. 1992) (33-41 months enhanced to 40 years). Contrasting these cases with the facts of Kikumura, we find that this does not qualify as a rare instance where a higher standard might be justified.

2. Sufficiency of the Evidence

The Kroledges also argue that, even under the preponderance of the evidence standard, the sentencing court lacked sufficient evidence of the arson to include it as relevant conduct for the purpose of enhancing their sentences. Because there is ample evidence available in the record on which to base a finding of arson, we understand this claim actually to imply that the district court committed clear error by believing the government's witnesses and disbelieving the Kroledges' witnesses.

Determinations of credibility by the sentencing judge are entitled to great deference on review. See United States v. Anaya, 32 F.3d 308, 314 (7th Cir. 1994). When confronted with conflicting testimony, sentencing judges "are fully capable of considering the motivations of witnesses in weighing conflicting evidence and, because they have had an opportunity to assess the demeanor of the witnesses, are in a better position than this court to make credibility determinations." United States v. Griffin, 115 F.3d 1322, 1331 (7th Cir. 1997). For this reason, when a defendant asks only that we reassess a credibility determination, the argument is "wasted on an appellate court," United States v. House, 110 F.3d 1281, 1286 (7th Cir. 1997) (citation omitted), unless a challenged witness's testimony is shown to be inconsistent with contemporary documents or impossible. See, e.g., United States v. Grandinetti, 891 F.2d 1302, 1307 (7th Cir. 1989).

In this case, the Kroledges do not challenge any evidence presented by the government. Instead, they argue that the government's evidence should not outweigh the evidence that the Kroledges presented. The government's evidence of arson included testimony of at least three witnesses, each of whom told a consistent story, as well as such physical evidence as Charles and Kathleen Kroledge's possessions pre-dating the fire, which had been stored with their family to preserve them, and the tape recordings made by Gilbert Kroledge, which capture admissions made by the Kroledges about the nature of the fire. We consider this evidence sufficient to support the district court's determination.

III. Conclusion

We find that the sentencing court correctly enhanced Charles, Kathleen, Tony and Ethel Kroledge's sentences for obstruction of justice. In addition, we find that the district court's decision to include the arson that the Kroledges were accused of committing as relevant conduct for the purpose of computing their sentences was correctly based on a preponderance of the evidence. Therefore, we AFFIRM the decisions of the district court.