#### UNITED STATES of America, Appellee, v. Lin GUANG and Shi Yong Wei, Defendants-Appellants.

Docket Nos. 05-4724-cr(L), 05-6171-cr(CON).

United States Court of Appeals, Second Circuit.

Argued: March 12, 2007.

Decided: Dec. 13, 2007.

*113Paul A. Goldberger (Stacey Van Malden, of counsel on the brief), New York, NY, for Defendant-Appellant Lin Guang.

Alan M. Nelson, Lake Success, NY, for Defendant-Appellant Shi Yong Wei.

Jennifer G. Rodgers, Assistant United States Attorney, for Michael J. Garcia, United States Attorney for the Southern District of New York (Miriam E. Rocah, David Raskin, Celeste L. Koeleveld, Assistant United States Attorneys, of counsel), New York, NY, for Appellee.

Before: McLAUGHLIN and WESLEY, Circuit Judges, and SESSIONS, District Judge.*

*

 The Honorable William K. Sessions III, Chief Judge of the United States District Court for the District of Vermont, sitting by designation.

WILLIAM K. SESSIONS III, District Judge.

Following a fourteen-day trial, a jury found defendants-appellants Shi Yong Wei and Lin Guang guilty of conspiracy to commit extortion, in violation of 18 U.S.C. § 1951. Shi was also convicted of eight substantive counts of extortion, each involving a different victim, and Lin was convicted of three of the substantive counts of extortion, counts 2, 4 and 6. The United States District Court for the Southern District of New York (Berman, *J.)*entered judgment of conviction in Lin’s case on August 17, 2005, and sentenced him to 168 months’ imprisonment, to be followed by three years’ supervised release. The Court entered judgment of conviction in Shi’s case on November 9, 2005, and sentenced him to 235 months’ imprisonment, to be followed by three years’ supervised release. Both defendants were ordered to pay restitution. Shi and Lin now appeal their judgments of conviction and the sentences imposed upon them.

Lin raises five issues on appeal. Challenging his conviction, he argues that the district court abused its discretion in admitting evidence of Lin’s uncharged bad acts, and that trial counsel’s failure to object to the admission of tapes and transcripts amounted to ineffective assistance of counsel.1 Challenging his sentence, Lin *114argues that factors which determine a Sentencing Guidelines range must be proven beyond a reasonable doubt; that due process required an evidentiary hearing to resolve the dispute over the application of Guideline enhancements; and that the sentencing enhancements were not supported by sufficient evidence.

Shi raises four issues on appeal. Challenging his conviction, he argues that the district court should have granted his motion for new trial based upon ineffective assistance of counsel. Challenging his sentence, Shi argues that the district court’s determination that a victim sustained permanent injury was unsupported by the evidence; that its determination of the amount of loss was likewise unsupported by the evidence; and that as a result the order of restitution lacked a factual basis.

We find no merit in Shi and Lin’s challenges to their convictions. Their challenges to their sentences likewise fail to persuade, with one exception. We agree with the defendants that the district court lacked sufficient facts to make a finding of permanent bodily injury to one of the victims. Because this error could have affected both defendants’ sentences, their cases are remanded for further proceedings consistent with this opinion.

BACKGROUND

I. The Offenses

Between 1999 and 2003, Shi Yong Wei engaged in a campaign of extortion designed to generate business for his gift shop, which catered to Chinese tourists. The victims of the extortion scheme were a rival gift shop owner, a restaurant owner, and tour guides who were coerced by force and threats of force to steer business to Shi’s shop, known as the “No. 1 Gift Shop.” Shi enlisted Lin Guang and a gang of young men known as the “little brothers” to carry out the intimidation. Many of the gang members were younger than eighteen years old. Count 1, of which both Lin and Shi were convicted, charged them with conspiracy to commit extortion.

A. Zhang Qing Hai (Count 2)

Zhang Qing Hai came to the United States from China in 1997. He opened a gift shop in midtown Manhattan in 1999 that catered mainly to Chinese tourist groups, as well as students and workers at the United Nations and the Chinese consulate. Zhang typically paid tour guides a commission of between five and twenty percent of sales. The store, named Xin-hua, was located on 38th Street, less than a block away from Shi’s store, which opened in May 2000. The two stores directly competed for business.

Zhang’s store was doing well, generating profits of more than $10,000 a month during his best months. In January 2001 Shi called Zhang and complained that his prices were too low. Zhang paid no particular attention, and ended the call, but several minutes later he received an anonymous phone call that first asked: “You want to live or not,” and proceeded to threaten to break his legs if he came outside.

Zhang called Shi in an effort to resolve the problem, and they agreed to meet at a restaurant called the Jade Palace a little after midnight. Shortly after Zhang arrived, his table and the next table filled up with supporters of Shi, some of them teenagers. Shi identified them as his “brothers.” This group proceeded to ridicule him and threaten to shut down his store. Shi handed him a document and a member of the group told him that if he did not sign he would not be safe. Zhang refused to sign without reading it and everyone at the table stood up. Zhang was afraid that *115“something dangerous” was about to happen. Shi sent them out, and arranged that Zhang could go home safely that night, but told him to call and tell Shi what he intended to do.

Zhang received several threatening phone calls from one of Shi’s gang, and about a week later Zhang’s store was plagued by the daily presence of Shi’s gang in front of the store, taking photographs of the tour guides’ vehicles and disparaging Zhang’s wares. Business fell off. After approximately three weeks of this, Shi came to Zhang’s store and demanded $1,500 for his little brothers. Zhang paid. The youths stopped appearing in front of his store for approximately three months, then the youths reappeared and Shi demanded and received another $1,500 in protection money. Lin was involved in organizing the youths to harass Zhang.

In May 2002 Zhang opened a second store several blocks away, hoping to keep his ownership secret and escape Shi’s attention. In July a gang of the little brothers led by Lin assaulted Zhang near his second store. Shi was present. The gang punched and kicked Zhang, sprayed a blinding liquid in his face and left him bleeding and moaning in the street. Zhang was taken to a hospital for treatment of his injuries. At the hospital Zhang was able to rinse out his eyes and they felt better. Zhang testified that from that point on he found it difficult to read newspapers because it hurt his eyes. After the assault Zhang closed his second store. He stated that he lost $60,000 in reduced sales after Shi’s gang besieged his store, and $50,000 as a result of the opening and closing of the second store.

B. Xiao Yung Fei (Count 3)

Xiao Yung Fei came to the United States in 1989. He heads the Chinese-American Friendship Association, and conducted tours for delegations from China. As part of his tours Xiao would take his groups to gift shops, for which he would receive a commission.

In spring of 2001, Xiao twice encountered Shi at the Statue of Liberty. Both times Shi complained that Xiao was not giving him “face” by not bringing groups to Shi’s store. Shi embarrassed and frightened Xiao in front of his tour groups. Some time later the front window of his van was smashed. Tires were slashed on three different vehicles.

In June 2001 Xiao was giving a tour at the United Nations when Shi accosted him, insulted him and threatened to beat him up. Shi bragged that he had a gang of juveniles who wouldn’t face any penalties if they were to injure or kill someone. Shi proceeded to punch and attempt to choke him. The next day Xiao received an anonymous phone call telling him that he hadn’t been beaten enough and that the caller was going to break his legs. Xiao virtually stopped giving tours.

C. Peter Yuan (Count 4)

Peter Yuan came to the United States in 1988. He worked as a tour guide from 1993 to 2001, and currently wholesales tickets to tourist destinations in the New York City area. Shi invited Yuan to dinner at the Jade Palace in 1999 or early 2000 and told him he wanted Yuan to find investors for a new store Shi intended to open. Shi’s wife bragged about his underworld connections. Yuan, intimidated, said he’d think about it. He did not seek out investors, and over the next few weeks received phone calls from Shi asking about his progress in collecting money. Yuan tried to avoid him but eventually Shi took him again to the Jade Palace and confronted Yuan, telling him that with a phone call he could have ten or twenty “little broth*116ers” there. Yuan said he would try, but did not.

After Shi opened his gift shop, he told Yuan that he must bring his tours only to his store, and threatened to slash his tires if he refused. Yuan’s tires were slashed, and he began bringing his groups to the No. 1 Gift Shop. After Yuan was accosted and threatened by two of Shi’s young men, he stopped conducting tours.

Nevertheless, Shi demanded protection money if Yuan wanted to do business in New York. For seven months Yuan paid $300 each month. Yuan attended another dinner at the Jade Palace at Shi’s invitation, along with several other tour guides. Shi demanded that the tour guides accompany him to a karaoke bar, where he introduced Lin as one of his gang. Lin threatened to photograph the face and license plate of any tour guide who didn’t patronize Shi’s store.

In January 2002 Shi required Yuan to attend a Chinese New Year banquet at the Jade Palace along with about fifty other tour guides. While they were eating a group of thirty to forty youths dressed in black paraded into the restaurant and sat down at several tables. Lin was among the group. At one point one of the group began chanting a slogan, and all of the group stood up and began chanting together.

Shi continued to threaten Yuan once he began wholesaling tickets, telling him he would send his little brothers to his home to break his legs. In the fall of 2002 Yuan essentially did not leave his home for fear of what Shi and his gang might do to him.

At Zhang’s request Yuan made a digital recording of Shi and Lin on Xiao’s recorder. The Government and the defense stipulated to the admission of the recordings and accuracy of the English translation, with one exception, a phrase attributed to Lin, whose translation he disputed.

D. Lin Ji Tiang (Count 5)

Lin Ji Tiang came to the United States from China in 1994. He opened a restaurant in mid-town Manhattan called Sun East. Shi wanted Lin Ji Tiang to send customers to his gift shop. In 2002 Lin Ji Tiang held a small Chinese New Year’s party for tour guides at his restaurant. He invited Shi for the next day, but Shi showed up on the first day with six or seven of his little brothers. Lin Ji Tiang did not dare to charge them, although they were uninvited.

Shi tried to get Lin Ji Tiang to throw a bigger party for tour guides of Shi’s selection. When Lin Ji Tiang protested that he couldn’t afford this party, Shi got angry and left. On occasion Shi would arrive at the restaurant and treat the kitchen as his own, cooking meals for himself. One time Shi hauled Lin Ji Tiang up the stairs of his restaurant holding his arm behind his back. Twice Lin Ji Tiang found cement in the lock of his restaurant. Once he found a pen-knife on the floor while Shi was in his restaurant. Shi said such a knife is used on people who don’t listen, gesturing with the knife as though he would slip it between his ribs. Shi also said such a knife is used to slash tires. Lin Ji Tiang was scared.

Lin Ji Tiang’s restaurant displayed a sign advertising the No. 1 Gift Shop. When the sign fell down, Shi berated him and threatened to get his gang to beat him to death. He demanded $35 as the cost of the sign. The tour guides stopped coming to his restaurant because Shi was constantly there and they were afraid to come. The restaurant was losing money, and Lin Ji Tiang was scared all the time, so he decided to close the restaurant, in October 2003.

*117E. Xu Xin (Count 6)

Xu Xin came to the United States from China and worked as a tour guide in 1999. After Shi opened his store, he ordered Xu to bring his tours there exclusively. When Xu failed to do so, Shi began calling and threatening to have his little brothers beat him up. Xu was angry and frightened. He learned from Peter Yuan that Shi and Lin knew where he lived in New Jersey. Xu found his tires slashed and sugar poured in his gas tank. Lin left a message on his answering machine claiming credit for the damaged car. Xu left the tour business for awhile as a result of the threats and the harassment.

F. Wang Jun (Count 7)

Wang Jun came to the United States from China in 1996. He worked as a tour guide from 1998 to 2008. 'When Shi’s store opened, he took his tours there a few times, but stopped doing so after an employee of the store told him not to mess with Shi. About two weeks later the tires on Wang’s van were slashed. His tires were slashed three more times over the summer of 2000. During that time he received repeated telephone calls from Shi threatening to do worse than slash his tires. Wang also saw Shi at the United Nations and Statue of Liberty writing down the license plate numbers of tour guides’ vans.

G. Zhang Liang (Count 8)

Zhang Liang came to the United States from China in 1996. He began working as a tour guide in spring of 2000. On his first day on the job, Shi accosted him at the Statue of Liberty and told him to bring his business to the No. 1 Gift Shop. Some time later he was approached by two of Shi’s gang with the same message while he was at the United Nations. Zhang Liang complied with Shi’s demands out of fear of the consequences.

H.Zhang Fuchi (David Zhang) (Count 9)

David Zhang came to the United States in 1990. He worked as a tour guide in New York City from 1999 to 2001. After Shi opened up his store, he told Zhang to bring his tours there, and not to any other store. David Zhang continued to bring his tours to different stores, and Shi threatened to beat him up and break his legs. He was threatened again a few days later, in an anonymous voicemail. He recorded the message, and gave the tape to the police. Some days later the same individual called and threatened him again. Some time after that two individuals jumped him, pulled his T-shirt over his head, beat him up and ran away. After this David Zhang decided that he did not want to work as a tour guide anymore. He took a variety of much lower-paying jobs thereafter. He returned to the tour guide business when he learned that Shi had been arrested.

II. The Ineffective Assistance of Counsel Claim and Rule 33 Motion

Following the convictions on March 16, 2005, Shi’s attorney wrote to the district court, requesting that new counsel be appointed for Shi to pursue Shi’s claim that his trial counsel had been constitutionally ineffective in having failed to object to the admissibility of the recorded conversations and their transcripts. Shi obtained new counsel, who filed an ex parte request on May 27, 2005 for an expert to make a forensic examination of the two audio recordings to determine whether they had been altered or manipulated. Lin’s new counsel sought *to*join the motion.

The district court ordered the government to respond to the request, finding no *118basis for an ex parte discovery application post-trial. The government opposed Shi’s request for leave to hire an expert to analyze the recordings, pointing out first that Shi’s allegations of tampering with the recordings would have gone to the weight rather than the admissibility of the evidence, and second that any error in failing to object to the recordings would not have been prejudicial, given the testimony of eight victims of Shi’s extortion scheme and corroborating testimony of former members of Shi and Lin’s gang.

The district court denied the motion for a new trial on October 6, 2005. It found that the decision not to hire an expert was a strategic choice, that the defense had vigorously cross-examined Peter Yuan who made the recordings, that it found Yuan’s testimony credible, and that the evidence against the defendants was overwhelming despite the recordings. The district court concluded that defense counsel’s performance was not objectively unreasonable.

III. The Presentence Investigation Reports and the Sentencing Hearings

The United States Probation Office prepared presentence investigation reports for Lin and Shi, and calculated Guideline sentencing ranges for both according to the advisory United States Sentencing Guidelines.

For each conviction of violating 18 U.S.C. § 1951, the base offense level was 18, pursuant to U.S. Sentencing Guidelines Manual § 2B3.2(a) (2005). Two levels were added for the use of express or implied threats of death or bodily injury, pursuant to § 2B3.2(b)(l). With the exception of Count 7, the district court found that the extortions involved the use of minors, and added two levels pursuant to § 3B1.4.

For Count 2, the extortion involving Zhang Qing Hai, the district court concluded that Shi and Lin caused a loss of more than $50,000, and added two levels pursuant to § 2B3.2(b)(2) and § 2B3.1(b)(7). The district court also concluded that Zhang sustained permanent bodily injury from his beating, and added six levels pursuant to § 2B3.2(b)(4)(C).

A. Lin’s Sentencing

According to the Guidelines analysis, Lin’s adjusted offense level was 33, based on the upward adjustments for use of threats, minors, the loss and permanent injury suffered by Zhang Qing Hai, and an additional three-level increase for his role as a manager or supervisor of criminal activity involving five or more participants. *See*U.S.S.G. § 3Bl.l(b). Application of the grouping rules added two levels for a total combined offense level of 35. At Criminal History category I, Lin’s Guideline range was 168 to 210 months.

At Lin’s sentencing on August 17, 2005, the district court acknowledged the advisory nature of the United States Sentencing Guidelines, and that it was bound to consider the factors set forth at 18 U.S.C. § 3553(a) in determining a reasonable and appropriate sentence. The district court decided that a *Fatico*hearing to resolve disputed sentencing issues was unnecessary, given the extensive trial testimony and the parties’ submissions. *See United States v. Fatico,*579 F.2d 707 (2d Cir.1978).

The district court concluded that a sentence at the low end of the Guideline range was reasonable, in light of the § 3553(a) factors. Lin received a sentence of 168 months, plus three years of supervised release. The court ordered restitution to four victims: $113,000 to Zhang Qing Hai, $50,000 to Xiao Yung Fei, $2,000 to Peter *119Yuan, and $10,000 to David Zhang.2

B. Shi’s Sentencing

According to the Guidelines, Shi’s adjusted offense level was 34, based on the upward adjustments for use of threats, minors, the loss and permanent injury suffered by Zhang Qing Hai, and an additional four level increase for his role as an organizer or leader of criminal activity that involved five or more participants. *See*U.S.S.G. § 3Bl.l(a). Application of the grouping rules to Shi’s convictions added four levels for a total combined offense level of 38. At Criminal History category I, Shi’s Guideline range was 235 to 293 months.

At Shi’s sentencing on November 9, 2005 the district court followed a similar analysis to that performed in Lin’s case. The district court considered the Guideline determination, along with the sentencing factors listed at 18 U.S.C. § 3553(a), and concluded that a sentence at the low end of the Guideline range was reasonable and appropriate. Accordingly, the district court sentenced Shi to 235 months’ imprisonment, plus three years of supervised release. Restitution was ordered in the amount of $175,100, $113,000 to Zhang Qing Hai, $50,000 to Xiao Yung Fei, $2,100 to Peter Yuan, and $10,000 to David Zhang.

DISCUSSION

1. Denial of Motion for New Trial

Both Shi and Lin argue that the district court erred in denying motions for a new trial on the ground that trial counsel provided constitutionally ineffective representation by failing to challenge the admissibility of recordings made by one of the victims, and the transcripts of those recordings. Shi also argues that the district court erred in denying his post-trial ex parte request for funds to hire an expert to determine whether the recordings had been altered, and in forwarding the defense’s request to the government for a response.

Rule 33(a) of the Federal Rules of Criminal Procedure provides that a trial court “may vacate any judgment and grant a new trial if the interest of justice so requires.” “The test is whether ‘it would be a manifest injustice to let the guilty verdict stand.’ ” *United States v. Sanchez,*969 F.2d 1409, 1414 (2d Cir.1992) (quoting *United States v. Reed,*875 F.2d 107, 114 (7th Cir.1989)). For a trial judge to grant a Rule 33 motion, he must harbor “ ‘a real concern that an innocent person may have been convicted.’ ” *United States v. Parkes,*497 F.3d 220, 232 (2d Cir.2007) (quoting *United States v. Ferguson,*246 F.3d 129, 134 (2d Cir.2001)). Denial of a Rule 33 motion is reviewed for abuse of discretion. *Id.*

The trial judge refused to grant Shi and Lin a new trial, stating that he had no concern that an innocent party had been convicted, and that the defendants had not met either prong of the *Strickland v. Washington*standard. *See Strickland v. Washington,*466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

We review a claim of ineffective assistance of counsel de novo. *United States v. Finley,*245 F.3d 199, 204 (2d Cir.2001). Under *Strickland,*a “defendant must demonstrate ‘(1) that counsel’s performance fell below an objective standard of reasonableness, ... and (2) that there is a reasonable probability that, but for the *120deficiency, the outcome ... would have been different.’ ” *Id.*(alterations in original) (quoting *McKee v. United States,*167 F.3d 103, 106 (2d Cir.1999)).

A “ ‘strong presumption’ ” exists “ ‘that counsel’s conduct falls within the wide range of reasonable professional assistance,’ ” given that “ ‘[t]here are countless ways to provide effective assistance in any given case’ and that ‘[e]ven the best criminal defense attorneys would not defend a particular client in the same way.’ ” *United States v. Aguirre,*912 F.2d 555, 560 (2d Cir.1990) (alterations in original) (quoting *Strickland,*466 U.S. at 689, 104 S.Ct. 2052). Defense counsel have “a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” *Strickland,*466 U.S. at 691, 104 S.Ct. 2052; *accord Gersten v. Senkowski,*426 F.3d 588, 607 (2d Cir.2005).

In this case, however, even were Shi and Lin to establish that their counsel unreasonably failed to employ an expert to challenge the authenticity of the tapes, and unreasonably failed to object to the admission of the recordings and transcripts, they have failed to establish prejudice. As the district court accurately pointed out, the evidence against the defendants “was overwhelming.” The district court also found that Peter Yuan’s testimony, as the authenticating witness, was sufficient to support the admission of the recordings under Rule 901 of the Federal Rules of Evidence, and that disputes over the reliability of the recordings or the accuracy of the translation went to the weight rather than the admissibility of the evidence. Moreover, Lin’s counsel vigorously cross-examined Yuan on his identification of Lin as the speaker on portions of the tape. He presented an alternative translation for a particular portion of the recording attributed to Lin that was alleged to be a threat.

Given that the jury had more than sufficient evidence from which to find both defendants’ guilt without the admission of the recordings and transcripts, counsels’ failure to secure the services of an expert to investigate whether the tapes showed signs of tampering did not prejudice Lin or Shi. Their decision to stipulate to the admission of the recordings and translations was a strategic choice that could not have prejudiced them, given Yuan’s availability to authenticate the recordings, the translators’ testimony as to the accuracy of the translations, and the defense’s cross-examination of both Yuan and the government translator concerning disputed portions of the recordings and transcripts. Because the defendants cannot show prejudice, “this court need not consider the objective reasonableness of counsel’s actions.” *United States v. Birkin,*366 F.3d 95, 101 (2d Cir.2004); *accord Greiner v. Wells,*417 F.3d 305, 319 (2d Cir.2005) (“ ‘[Tjhere is no reason for a court deciding an ineffective assistance claim ... to address both components of the inquiry if the defendant makes an insufficient showing on one.’ ” (alterations in original) (quoting *Strickland,*466 U.S. at 697, 104 S.Ct. 2052)).

As we do not find the stipulation to the admission of the recordings and translations or the failure to obtain the services of a forensic audio expert to have caused prejudice to the defendants, the district court’s denial of their motions for a new trial was not an abuse of discretion. The failure to grant a post-verdict application for funds to hire such an expert likewise did not constitute an abuse of discretion, and there was no error in the district court’s refusal to consider ex parte the post-verdict request for funds.

II. Admission of Uncharged Bad Acts Against Lin

Lin argues that the trial court erred in admitting evidence of four inci*121dents of prior bad acts involving Lin. Specifically, the government offered evidence that one of the extortion victims observed Lin confront unruly customers at a massage parlor controlled by Shi with his hand inside his jacket as if he concealed a gun; that Lin and others assaulted a former confederate who had betrayed Lin; that Lin ran a gambling house owned by Shi; and that Lin became the leader of the gang because he reputedly beat up the leader of a Taiwanese gang. For three of the incidents the trial court gave a limiting instruction that the evidence was admissible to show a relationship of mutual trust between Shi and Lin.3 With regard to Lin’s reputation for having beaten up the Taiwanese gang leader, no limiting instruction was requested and none given. The trial court excluded several other incidents proffered by the government.

 A district court’s decision “to admit ‘other crimes’ evidence under Rule 404(b) ... will not be overturned on appeal absent abuse of discretion.” *United States v. Rosa,*11 F.3d 315, 333-34 (2d Cir.1993). In a conspiracy case, “other acts” evidence is admissible as background information, to demonstrate the existence of a relationship of mutual trust, or to “enable the jury to understand how the illegal relationship between the co-conspirators developed.” *United States v. Pipola,*83 F.3d 556, 566 (2d Cir.1996).

The Second Circuit’s “inclusionary approach” to the admission of other act evidence “allows such evidence to be admitted for any purpose other than to demonstrate criminal propensity.” *United States v. LaFlam,*369 F.3d 153, 156 (2d Cir.2004) (per curiam).

> To determine whether a district court properly admitted other act evidence, the reviewing court considers whether (1) it was offered for a proper purpose; (2) it was relevant to a material issue in dispute; (3) its probative value is substantially outweighed by its prejudicial effect; and (4) the trial court gave an appropriate limiting instruction to the jury if so requested by the defendant.

*Id.*Evidence of the four uncharged incidents was properly admitted. The evidence was not offered to show Lin’s criminal propensity, but to show the existence of the illegal relationship between Shi and Lin and how it developed. The trial court found that the evidence was not unfairly prejudicial, and gave limiting instructions as requested by the defendants. We find no abuse of discretion.

III. Sentencing Issues

Lin and Shi challenged the application of sentencing enhancements for their role in the offense, use of minors to commit the offenses, permanent injury to one victim, and the loss amounts. In addition, Lin argued that the enhancements could not be applied unless they were proven beyond a reasonable doubt, and both defendants argued that a *Fatico*hearing was necessary to determine challenged facts. *See United States v. Fatico,*579 F.2d 707 (2d Cir.1978).

Lin’s argument that the facts upon which a sentencing court calculates the applicable Guideline range must either be admitted or found by a jury beyond a *122reasonable doubt perished with this Circuit’s confirmation in *United States v. Salazar*that “the statutory requirement to determine a Guidelines range, and do so in the same manner as before *Booker,*necessarily means that facts relevant to sentencing must be found by a preponderance of the evidence.” 489 F.3d 555, 557 (2d Cir.2007) (per curiam).

Lin and Shi’s contention that the sentencing court was required to give them a *Fatico*hearing likewise lacks merit. “ ‘The district court is not required, by either the Due Process Clause or the federal Sentencing Guidelines, to hold a full-blown evidentiary hearing in resolving sentencing disputes. All that is required is that the court afford the defendant some opportunity to rebut the Government’s allegations.’ ” *United States v. Phillips,*431 F.3d 86, 93 (2d Cir.2005) (quoting *United States v. Slevin,*106 F.3d 1086, 1091 (2d Cir.1996)). Lin and Shi submitted letter briefs opposing the Probation Department’s calculation of their Guideline ranges in its presentence reports. At sentencing their attorneys argued against the enhancements that they currently challenge.

The district court stressed that it had heard extensive trial testimony, had observed the demeanor of the witnesses and assessed their credibility over a two-week trial. It had reviewed the submissions of all parties, as well as the presentence investigation report, and concluded that the challenged enhancements were warranted. Lin and Shi had notice of the proposed enhancements, including the evidence upon which the enhancements were based, and had an opportunity to dispute the evidence. The only issue is whether the challenged enhancements were based upon sufficient facts.

In reviewing a district court’s application of the Guidelines to the specific facts of a ease, we accord de novo review to issues of law, and accept its findings of fact unless they are clearly erroneous. *United States v. Gotti,*459 F.3d 296, 349 (2d Cir.2006). “ ‘A finding is clearly erroneous when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.’ ” *United States v. Cuevas,*496 F.3d 256, 267 (2d Cir.2007) (quoting *United States v. Hazut,*140 F.3d 187, 190 (2d Cir.1998)). “[F]aetual findings based on the testimony of witnesses [are] entitled to special deference,” because “assessing the credibility of witnesses is distinctly the province of the district court.” *United States v. Beverly,*5 F.3d 633, 642 (2d Cir.1993); *accord Cuevas,*496 F.3d at 267.

A. Use of Minors

Section 3B1.4 of the Sentencing Guidelines provides for a two-level increase “[i]f the defendant used or attempted to use a person less than eighteen years of age to commit the offense.” U.S.S.G. § 3B1.4. The Application Notes indicate that “ ‘[u]sed or attempted to use’ includes directing, commanding, .encouraging, intimidating, counseling, training, procuring, recruiting, or soliciting.” *Id.*cmt. n. 1. Lin argues that there is no record evidence that the “little brothers” were younger than eighteen years of age. The record demonstrates the contrary, as the district court noted in citing the government’s August 1, 2005 submission. Among the numerous witnesses who testified about Shi’s gang of “little brothers,” describing them as “kids,” was Steven Han, a member of the gang, who testified that the membership ranged in age “[fjrom 15-year-old until the 20s.” Shi himself told one of his extortion victims, Xiao Yung Fei, that the members of his gang were all juveniles because “in America, when a juvenile in*123jures or kills someone, they don’t face any penalty.” Extortion victim Zhang Qing Hai testified that the kids sent to loiter in front of his gift shop were “kids, around 14, 15, 16, teenager kids.” There was no error in adjusting Lin’s Guidelines offense level upward by two levels for use of a minor.

B. Loss Amount

Pursuant to U.S.S.G. §§ 2B3.2(b)(2) and 2B3.1(b)(7)(C), the district court imposed a two-level enhancement for a loss greater than $50,000 but less than $250,000 sustained by Zhang Qing Hai. Loss to a victim in an extortion case “means any demand paid plus any additional consequential loss from the offense.” *Id.*§ 2B3.2 cmt. n. 5. The district court based its determination of loss on Zhang’s testimony that he suffered $60,000 in lost sales, $50,000 in loss associated with the opening of a second store and paid $3,000 in protection money. The defendants argue that a district court may not rely upon the uncorroborated testimony of a victim as to amount of loss when that amount is disputed, and that the victim’s own testimony indicated that his estimate was unreliable.

A “district court need not establish the loss with precision but rather ‘need only make a reasonable estimate of the loss, given the available information.’ ” *United States v. Carboni,*204 F.3d 39, 46 (2d Cir.2000) (quoting *United States v. Jacobs,*117 F.3d 82, 95 (2d Cir.1997)).

Zhang testified that in good months he made more than $10,000 in profits, but in his worst months, for example after September 11, 2001, he lost money. He testified that the extortion began in early 2001, and he continued to feel the effects of the intimidation campaign in lost profits up to the trial. This was because many tour guides who used to frequent his shop stopped bringing their tours to his shop in spring of 2001, and never returned. Shi was arrested in November 2002. Zhang estimated that overall, as a result of the three-week intimidation campaign in spring of 2001, he lost at least $60,000. Zhang also estimated that he lost $50,000 as a result of closing his second store after Shi’s gang assaulted him.

The district court found Zhang’s testimony “entirely credible.” We give strong deference to findings based on credibility determinations. *United States v. Johnson,*378 F.3d 230, 239 (2d Cir.2004). Zhang’s estimate of $60,000 in lost sales at his first shop is not unreasonable, given the length of time that his business continued to suffer the effects of Shi and Lin’s intimidation campaign. The district court’s conclusion that the evidence at trial established that the extortion of Zhang caused a loss of more than $50,000 was likewise not unreasonable, given the added losses associated with closing the second store after six months of operation, and the protection money payments.

“[V]iew[ing] the evidence in the light most favorable to the Government,” *id.*at 238, the district court’s reliance on Zhang’s estimate of his losses was not clearly erroneous.

C. Permanent Injury

Section 2B3.2(b)(4) of the Sentencing Guidelines provides for an increase in offense level if any victim sustained bodily injury, according to the seriousness of the injury. “Bodily injury,” defined as “any significant injury; e.g., an injury that is painful and obvious, or is of a type for which medical attention ordinarily would be sought,” U.S.S.G. § 1B1.1, cmt. n. 1(B), receives a two-level increase. *Id.*§ 2B3.2(b)(4)(A). “Serious bodily injury,” defined as “injury involving extreme physical pain or the protracted impairment of a *124function of a bodily member, organ, or mental faculty; or requiring medical intervention such as surgery, hospitalization, or physical rehabilitation,” *id.*§ 1B1.1, cmt. n. 1(L), receives a four-level increase. *Id.*§ 2B3.2(b)(4)(B). “Permanent or life-threatening bodily injury,” defined as “injury involving a substantial risk of death; loss or substantial impairment of the function of a bodily member, organ, or mental faculty that is likely to be permanent; or an obvious disfigurement that is likely to be permanent,” *id.*§ 1B1.1, cmt. n. 1(J), receives a six-level increase. *Id.*§ 2B3.2(b)(4)(C). An injury whose degree of seriousness falls between the specified degrees may receive a three or five-level increase. *Id.*§ 2B3.2(b)(4)(D), (E).

The district court imposed a six-level increase on Shi’s and Lin’s base offense level, concluding that Zhang Qing Hai had sustained permanent injury to his eyes during the assault on him by members of Shi’s gang. The court reached this conclusion by applying the Guidelines definition of permanent injury to the facts as stated by Zhang in his trial testimony. Zhang described that he was accosted by a few people who began beating him. As he struggled, something went into his eyes that hurt tremendously. He could not open his eyes and he could not see. He described the substance as watery.4 He lost consciousness for a time, and was taken to a hospital. He received stitches for his wounds, but no medical treatment for his eyes. Zhang went to the lavatory and washed out his eyes with water, after which his eyes felt a little better. Zhang left the hospital after that. Zhang’s testimony concerning the permanency of his injury was as follows:

> Q. Mr. Zhang, did the beating that you received that evening affect your eyesight?

> A. Yes. Whomever knows me knew that I liked to read newspaper a lot in the past. After that occasion, it’s difficult for me to read newspapers. And so from that point on, I don’t even buy newspapers and I don’t even read newspapers.

> Q. Why is it difficult for you to read newspapers now?

> A. If I spend more time in reading, you know, it hurts my eyes.

Shi and Lin argue that these facts are insufficient evidence of permanent injury. We believe that the district court’s application of the permanent bodily injury enhancement to these facts presents a predominantly factual issue, which we review for clear error. *See Gotti,*459 F.3d at 349 (citing *United States v. Selioutsky,*409 F.3d 114, 118-19 (2d Cir.2005)); *see also United States v. Baggett,*342 F.3d 536, 540 (6th Cir.2003) (reviewing finding of permanent or life-threatening bodily injury under clearly erroneous standard); *United States v. Pandiello,*184 F.3d 682, 685 (7th Cir.1999) (conclusion that assailants inflicted bodily injury reviewed for clear error); *United States v. Jacobs,*167 F.3d 792, 798 (3d Cir.1999) (findings regarding permanent or life threatening injury reviewed for clear error); *United States v. Price,*149 F.3d 352, 353 (5th Cir.1998) (“severity of a victim’s injuries is a factual determination and thus reviewed for clear error,” construing permanent bodily injury). *But see Pandiello,*184 F.3d at 685 (applying de novo review to question whether welts fell within Guidelines’ definition of bodily injury).

*125For the injury to Zhang’s eyes to qualify as permanent or life-threatening bodily injury under the Guidelines’ definition, it must constitute “substantial impairment of the function of a bodily ... organ ... that is likely to be permanent.” U.S.S.G. § 1B1.1, cmt. n. 1(J). The district court clearly erred in finding that Zhang had sustained a permanent injury that would trigger a six-level enhancement. Where substantial impairment is not obvious, something more than the generalized and subjective impression of the victim is required in the way of proof. Here Zhang’s testimony that it hurts his eyes to spend more time reading did not afford a sufficient basis for the district court to find that he had sustained substantial impairment of his eyesight.

There is no question that Zhang suffered substantial impairment of his eyesight at the time of the assault. That Zhang currently has difficulty reading may constitute an impairment. There is, however, insufficient record evidence to warrant a finding that the assault resulted in substantial impairment that was likely to be permanent. The district court could not reasonably conclude on the state of the evidence that the impairment was both substantial and likely to be permanent.

Because the district court’s factual findings are insufficient to establish substantial impairment of Zhang’s eyesight that is likely to be permanent, we remand for consideration of the nature, severity and likely duration of Zhang’s impaired eyesight. *See United States v. Spinelli,*352 F.3d 48, 60 (2d Cir.2003).

D. On Remand

At their sentencing hearings, both Lin and Shi objected to the Guideline range adopted by the district court. Lin argued that he should receive a non-Guidelines sentence. The district court calculated an offense level of 35 and Criminal History category I, for a range of 168 to 210 months, and imposed a sentence of imprisonment at the low end of the range, 168 months, stating: “I am sentencing, however, in light of the factors set forth in 18 U.S.C. Section 3553(a), and believe that the sentence of 168 months and the other aspects of the sentence that I have described is appropriate, reflecting the seriousness of the offense and the need for punishment, deterrence and rehabilitation.”

Shi argued that his Guideline offense level should be 36, Criminal History category I, for a sentencing range of 188 to 235 months. He also argued for a non-Guidelines sentence. The district court rejected Shi’s Guidelines calculation, and his argument for a non-Guidelines sentence, and determined that Shi’s offense level was 38, Criminal History category I, for a sentencing range of 235 to 293 months. The district court indicated that it intended to impose a Guideline sentence, and imposed the low end of the Guideline range:

> in part based on the arguments of defense counsel. I was going to sentence at the high end of the guideline range because of the other factors that are pertinent here under 3553(a). But I will sentence at 235 months, which is the low end, which also has some overlapping with the sentencing guideline range computed by defense counsel.

The district court reasoned:

> I think the sentence is appropriate given the seriousness of the offenses, the need for punishment, deterrence, and rehabilitation. I have considered all of the factors at 3553(a), including the nature and circumstances of the offense and the history and characteristics of the defendant. I think this sentence does reflect the seriousness of those offenses. It *126would promote respect for the law, provide a just punishment, afford adequate deterrence, protect the public, and provide appropriate correctional treatment in the most effective manner.

An error in determining the applicable Guideline range may render a sentence unreasonable. *Selioutsky,*409 F.3d at 118. A reduction in the enhancement for degree of bodily injury would reduce the offense levels for both Shi and Lin, although Shi’s Guideline range might not be reduced below the range for which he argued, and there is of course overlap in the sentencing ranges. Because we do not know whether the district court would have imposed the same sentences of imprisonment had it calculated lower Guideline ranges based on facts supplying proof of a lesser degree of bodily injury, we remand for re-calculation of Lin’s and Shi’s Guideline ranges. Of course, the district court has discretion, on remand, to resen-tence at the low end of a re-calculated Guideline range based on evidence of the degree of Zhang’s bodily injury or anywhere within that re-calculated range, or to impose a non-Guideline sentence.

E. Restitution

Pursuant to U.S.S.G. § 5E1.1, the district court ordered that Shi pay restitution to four victims: $113,000 to Zhang Qing Hai; $50,000 to Xiao Yung Fei; $2,100 to Peter Yuan; and $10,000 to David Zhang, for a total of $175,100. Although Shi asserts that the district court erred in determining these amounts with respect to all four victims, his sole remaining argument5 concerns the loss to Zhang Qing Hai, and thus we address only that portion of the restitution order.

“[W]e review restitution orders deferentially,” *United States v. Porter,*90 F.3d 64, 68 (2d Cir.1996), and will not disturb a sentencing court’s determination absent abuse of discretion. *United States v. Ismail,*219 F.3d 76, 78 (2d Cir.2000). As discussed above, we do not find clear error in the district court’s determination of the amount of loss suffered by Zhang Qing Hai. The court did not abuse its discretion in ordering restitution in the amounts named.

CONCLUSION

The judgments of conviction are affirmed. The sentences imposed against Lin Guang on August 17, 2005 and against Shi Yong Wei on November 9, 2005 are vacated, and the cases remanded for re-sentencing.

1

. He also argues that the cumulative effect of trial errors requires retrial. Because we con-elude that the district court did not abuse its discretion in admitting evidence of the uncharged bad acts, and trial counsel's stipulation to the accuracy and authenticity of the recording was not ineffective, we do not consider this argument.

2

. Although Lin was not charged with or convicted of Count 9 involving David Zhang, the district court ordered Lin to make restitution based on Lin’s conviction on Count 1, the conspiracy count.

3

. The district court ruled pre-trial and prior to the testimony that the evidence that one of the extortion victims witnessed Lin intimidate unruly massage parlor customers was admissible to show the state of mind of the victim. In giving the limiting instruction, the district court mistakenly told the jury that the evidence was admitted to show Lin's slate of mind. When asked if the instruction was "agreeable to the lawyers,” however, Lin's attorney answered "yes.”

4

. A Government witness who participated in the assault, Henry Shen, testified that another gang member sprayed Zhang with pepper spray.

5

. Shi also argued that he should have been afforded a *Fatico*hearing to contest the loss amounts, an issue that we have already addressed.