
671 F.3d 149 (2011)
UNITED STATES, Appellee,
v.
Thomas ARCHER, Defendant-Appellant.
Docket No. 10-4683-cr.
United States Court of Appeals, Second Circuit.
Argued: May 2, 2011.
Decided: September 20, 2011.
*153 Jonathan I. Edelstein, Edelstein & Grossman, New York, N.Y., for Defendant-Appellant.
Soumya Dayananda, Assistant U.S. Attorney, of counsel, (Peter A. Norling, Andrew E. Goldsmith, Assistant U.S. Attorneys, of counsel, on the brief), for Loretta E. Lynch, United States Attorney for the Eastern District of New York, Brooklyn, N.Y., for Appellee.
Before: NEWMAN, CALABRESI, and HALL, Circuit Judges.
CALABRESI, Circuit Judge:
The Defendant-Appellant, Thomas Archer, requested specific jury instructions with respect to the government's burden of proof regarding his knowledge of the fraud for which he was indicted. The district court (Johnson, J.) denied these requests and instead gave a general instruction on acting "knowingly." Archer challenges those denials as well as the sufficiency of the evidence presented at trial. We find these challenges meritless.
*154 Accordingly, we affirm the defendant's conviction.
In calculating Archer's Guidelines sentencing range, the district court relied on four enhancements, three of which Archer challenges on appeal. Though the basis of the district court's application of the leader/organizer enhancement could have been more fully elaborated, we find the record supports its application here. Regarding the obstruction-of-justice and number-of-document enhancements, however, we agree with Archer that the evidence is insufficient to sustain their use in this case. We, therefore, vacate Archer's sentence.
Finally, Archer challenges the order of restitution imposed by the district court under the Mandatory Victim Restitution Act (MVRA), 18 U.S.C. § 3663A. Because we find the record evidence insufficiently specific to demonstrate that each client to whom the court ordered restitution was a "victim" of the fraud, we vacate the restitution order.
We remand the case for resentencing, including reconsideration of the restitution award.

I. BACKGROUND
Defendant-Appellant Thomas Archer was formerly an immigration lawyer in Jackson Heights and Jamaica, New York. The charges in this case arise out of Archer's filing of I-687 legalization applications on behalf of his clients. The Department of Homeland Security (DHS) created the I-687 program, which operated for a limited time in 2004 and 2005, as part of a court-approved settlement of a lawsuit that had alleged misconduct in the operation of a previous legalization program. Newman v. U.S. Citizenship & Immigration Srvs., No. 87-4757-cv, at 7-10 (C.D.Cal. Feb. 18, 2004) (order approving class settlement). Nationwide, a total of 79,000 applications were filed and about 3 percent were granted. Between 2004 and 2005, Archer filed between 230 and 240 applications, none of which were granted.
The government suspected that Archer was filing false I-687 applications. After investigation, Archer and his office manager, Rukhsana Rafique, were indicted on five counts: one count of conspiracy to commit visa fraud, 18 U.S.C. § 371, and four counts of visa fraud (one for each of three specific clients and one for a married couple), 18 U.S.C. § 1546(a). One of the substantive charges was dropped when that client declined to testify. Archer and Rafique were convicted on the indictment's remaining four counts.
Visa fraud, as charged here, has five elements: the defendant (1) knowingly (2) presented (3) an application or "document required by the immigration laws" (4) that contained a false statement (5) as to a material fact. 18 U.S.C. § 1546(a).[1] All agree that I-687 applications qualify as "document[s] required by the immigration laws," that Archer presented them by filing them with DHS, and that some of the applications that Archer filed did contain false material information. Therefore, Archer's key contention was, and continues to be, that he was unaware of these falsities and, by implication and extension as to the conspiracy count, that he never agreed to present false information.

A. Trial Evidence
At trial, the government presented the testimony of the three sets of clients *155 Gulistan,[2] Nizar Ahmad, and Iris and Mohammed Allywhose applications constituted the bases for the substantive fraud counts; a recording of two conversations, one between Gulistan, Archer, and Rafique and one between Gulistan and Rafique; and statistical evidence from an immigration officer.
To understand the import of all of this testimony, the I-687 program's details are important. In order to qualify for the program, the alien-applicant must both be a member of the class of the Newman settlement and have had limited travel outside the United States. In turn, to be a member of the class, the alien must have: (1) been in the country illegally on January 1, 1982; (2) applied for legalization under a prior program between May 1987 and May 1988; and (3) been turned down for that program because of travel outside the United States between 1981 and 1988. Applicants could meet the first of these sub-requirements in two ways, either (a) by having entered the country illegally or (b) by having entered legally and overstaying their visas. In addition to being a member of the Newman class, an eligible alien could not have traveled out of the country either (a) on any single trip longer than 30 days between 1986 and May 1988 or (b) on any single trip longer than 45 days between 1982 and the date of his or her application to the prior program and no more than 180 total days in all trips during that time. While an alien's I-687 application was pending, he could receive a temporary work permit to work in the United States.
Gulistan, a native of Pakistan, testified through a translator that he spoke only limited English and did not know, either at the time of his I-687 application or at the time of trial, the requirements of the program. He had gone to Archer's office on multiple occasions and had spoken with both Rafique and Archer. Rafique instructed him to sign an I-687 application, which was not translated for him and which he could not read. He paid Archer $1,500, and Archer submitted this application to DHS.
Gulistan testified that he arrived in the United States in 2000 on a work visa, but had previously visited for a short time in 1981 with his uncle. His I-687 application, however, stated that he had entered the United States illegally in 1981 and stayed until 1988, when he took a one-month trip to Pakistan. The application claimed that, thereafter, he had taken six trips to Pakistan between 1989 and 1999 (this was needed to account for the birth of Gulistan's seven children between the late 1980s and 2000). Gulistan also stated that Archer and Rafique gave him pre-filled affidavits for two U.S.-citizen friends to sign, falsely asserting that they had known him since 1981 and 1986, respectively. No one told him what the affidavits said, only that he needed to have his friends sign them. In a January 23, 2006, letter, DHS instructed Gulistan to attend an interview in connection with his I-687 application. Archer got the interview postponed until October 2006, at which time Gulistan attended alone.
In May and June 2007, after federal agents visited his home, Gulistan went to Archer's office on two occasions wearing a hidden recording device. On the first occasion, he spoke only with Rafique. On the second, he also spoke with Archer and protested that he did not have any proof of the travels his application claimed; Archer responded "so what?" They also discussed his interview with DHS, which Archer had told him to forgo. The government played both recordings at trial.
*156 Next, Ahmad, also a native of Pakistan, testified, also through a translator, that he, too, spoke little English and could not read. Rafique prepared his I-687 application, which he signed, but she did not read it to him, and he was unaware of what it said. He did not know the requirements of the program and paid Archer $2,000. Ahmad said he arrived in the United States in 1998 as a crewman on a ship. His application, however, stated that he had come to the country in 1981 and stayed until 1987, when he took a one-month trip to Pakistan. The application included employment and residency information that he agreed was false and that he said he had never provided to anyone. Rafique gave him two affidavits for his acquaintances to sign, both of which had "(1981)" pre-printed next to the blank where the witness should put the date on which he had met Ahmad. DHS sent Ahmad a letter, instructing him to appear for an interview, which Archer asked be postponed. When a new interview was scheduled, Archer withdrew Ahmad's application without Ahmad's permission.
The third set of witnesses was Iris and Mohammed Ally, a previously married couple from Guyana. Iris Ally said she had limited reading skills. She did not know the requirements of the program and had signed an application Rafique gave her without knowing what it said. Mrs. Ally had come to the United States in 2002 by sneaking across the Canadian border. Her application, on the other hand, claimed she had arrived in 1981 and stayed until 1987, when she took a one-month trip to Guyana. Her application also contained residency and employment information that was false and that she had never provided. Rafique gave her two affidavits similar to those described in Ahmad's testimony; she had her boss's children sign them and returned them to the office. DHS sent her an interview letter, and Archer got the interview postponed by having her get a note from her doctor falsely saying she was ill. The interview was rescheduled but neither she nor Archer attended it.
Mohammed Ally testified that he had met with both Archer and Rafique and paid them $2,500. Rafique filled out his I-687 application, which he signed. It showed an identical entry and travel pattern to that of Mrs. Ally. In reality, though, he entered the United States in 2000 by illegally crossing the Mexican border. His application also contained false employment and residency information that he had never supplied. When DHS sent him an interview letter, he brought it to Archer's office where Rafique told him they would withdraw his application. Though Mr. Ally protested and asked for a refund, he eventually relented and allowed Archer to withdraw his application.
A DHS officer, Mel Shatzkamer, presented some descriptive statistics about 175 of Archer's I-687 applications that were provided to him by the prosecutor. All of the applications claimed that the relevant alien entered the country illegally rather than that he or she overstayed a visa. Shatzkamer found this significant because the government has no way of verifying whether someone entered the country illegally on a certain date. A falsified I-687 application, he asserted, would be almost certain to claim eligibility through this method of entry rather than as a result of overstaying a visa, as overstaying a visa could be verified. Furthermore, 168(96%) of Archer's applications stated that the particular alien had arrived in the country in 1981 (rather than earlier)thereby just barely making the cutoff for the program. Nearly 90 percent claimed travel outside the country in the five-month interval from June to October of 1987, a coincidence Shatzkamer found *157 oddly duplicative given that the travel window for eligibility was the 29-month interval from January 1986 to May 1988. Finally, 45 of the 175 applications contained at least one fill-in-the-blank affidavit, mostly of the type described in Ahmad's testimony. Absent from Shatzkamer's testimony, as Archer pointed out on cross examination, was any reference to what the national pool of I-687 applications looked like in any of these particulars.

B. Jury Instructions
At the charge conference, Archer requested two jury instructions, both of which dealt with how the jury should interpret the evidence going to whether Archer acted "knowingly." First, he asked for an instruction based on United States v. Phillips, 543 F.3d 1197 (10th Cir.2008)the Phillips instruction. Phillips held that the fact that a defendant is a solo practitioner, without more, is an insufficient basis from which to infer his guilt because, even though he is the only lawyer in the office, he may not be aware of everything his staff is doing.[3]See id. at 1209. Second, he sought an instruction based on United States v. Maniego, 710 F.2d 24 (2d Cir.1983) (per curiam)the Maniego instruction. In Maniego, we said that attorneys are not held to a higher duty to investigate than non-lawyers and have no special obligation to verify independently information given to them by clients. See id. at 28. The district court denied both requested instructions.
On mens rea, the district court gave the following instruction:
To act "knowingly" means to act intentionally and voluntarily, and not because of ignorance, mistake, accident, or carelessness. In deciding whether a defendant acted knowingly, you should ask yourself whether the defendant knew that the visa application document you are considering contained a false statement? And did that defendant, nonetheless, present the document ...?
No evidence exists to indicate that Archer lodged an objectionas opposed to a request for specific supplemental instructionsto this instruction in particular or to the district court's final instructions as a whole, either at the charge conference or during trial. One further development on this point bears noting, though. During her rebuttal summation, the prosecutor argued that Archer knew of the scheme to falsify information because "it's his law firm. This isn't some huge midtown Manhattan law firm building where the law firm takes up a half a building of employees. It's two rooms. It's smaller than this courtroom." Archer objected, and the court instructed the jury that "whatever the lawyers say is not evidence in this case." Significantly, Archer did not, at that point, renew his request for a Phillips instruction or make any other objection.

C. Sentencing
After Archer's conviction, his pre-sentence report (PSR) recommended that the court impose four separate enhancements to his base offense level of eleven: a nine-level enhancement for conduct involving more than 100 fraudulent documents; a four-level enhancement for being the leader or organizer of criminal activity; a two-level enhancement for obstruction of justice; and a two-level enhancement for abusing a position of trust. The specific facts underlying each of the first three *158 enhancementsArcher has not challenged the fourthare set forth in the discussion of the sentence. The district court accepted all four enhancements and calculated Archer's Guidelines range to be 78 to 97 months. It then imposed a below-Guidelines sentence of 60 months' imprisonment, three years' supervised release, and a special assessment.
The court also entered an order of restitution in the amount of $309,500, payable to 234 of Archer's former clients. This amount represents a refund of $1,500 per client, roughly the full fee the clients usually paid Archer in connection with their I-687 cases.
The district court entered the final judgment of conviction and sentence on November 1, 2010. Archer timely appealed.

II. DISCUSSION
Archer raises four issues on appeal: whether (1) the district court properly denied his requested Phillips and Maniego jury instructions, (2) the evidence is sufficient to sustain his convictions, (3) the first three sentencing enhancements listed above properly apply to him, (4) the district court erred in ordering restitution. We address each issue in turn.

A. Jury Instructions
A defendant challenging the district court's rejection of his proposed jury instructions "must show that his proposed charge accurately represented the law in every respect, and that the charge actually given, viewed as a whole, prejudiced him." United States v. Feliciano, 223 F.3d 102, 116 (2d Cir.2000) (internal quotation marks omitted). More specifically, the defendant can prevail by showing that his requested "instruction is legally correct, represents a theory of defense with basis in the record that would lead to acquittal, and the theory is not effectively presented elsewhere in the charge." United States v. Quattrone, 441 F.3d 153, 177 (2d Cir.2006) (internal quotation marks omitted). We address each challenged instruction in turn.

1. The Phillips Instruction

Though Phillips is a Tenth Circuit case dealing with the sufficiency of the evidence rather than jury instructions, the government does not dispute that it correctly states the law, and we agree. Furthermore, because the proposed instruction focused directly on Archer's defense (that he was unaware of the false statements) and because, had the jury believed that defense, it would have been required to acquit him, the only issue before us is whether the charge the court actually gave adequately represented the requirements of "knowledge" as an element of the crime. See Quattrone, 441 F.3d at 179-80 (vacating and remanding for failure to instruct regarding lack of knowledge); United States v. Dove, 916 F.2d 41, 45 (2d Cir. 1990) (holding that "unbalanced" instructions, which explain how certain evidence may be inculpatory but not exculpatory, are insufficient, especially when the defendant's theory of defense is that the government failed to prove an element of the crime). Put another way, for Archer to show that the substance of his requested charge was not effectively presented elsewhere, he must show that the jury could have convicted him under the instructions given by the court even if it believed his defense of lack of knowledge. Quattrone, 441 F.3d at 180.
To resolve this issue, we compare the requested charge with the one given. Phillips involved a solo practitioner charged with immigration fraud. The defendant and his assistant, who was also his wife, were convicted of forging documents. On appeal, the defendant challenged the *159 sufficiency of the evidence establishing his knowledge of the forgeries. The court said that without some evidence showing how the attorney supervised his office, the mere fact that he was a solo practitioner was insufficient to support the inference that he was aware of the fraud. To find otherwise, it said, would be to hold such lawyers to "something approaching strict criminal liability for the acts of their employees," contrary to what the law requires.[4] 543 F.3d at 1209. The Phillips court, however, found sufficient evidence to sustain the conviction in the case before it for two reasons: (a) the employee in question was also the attorney's wife, which enabled the jury to infer that a closer-than-typical office relationship existed between them, and (b) the government had direct proof that he had forged one of the many documents involved. Id. at 1209-10.
Relying on Phillips, Archer asked that the court instruct the jury that "[t]he fact that one of the defendants is the sole attorney in a small firm in and of itself is not sufficient to determine that the attorney was aware of each and every act that took place in the office or that he approved or encouraged such actions." The court declined, opting instead to give the following instruction with respect to mens rea:
To act "knowingly" means to act intentionally and voluntarily, and not because of ignorance, mistake, accident, or carelessness. In deciding whether a defendant acted knowingly, you should ask yourself whether the defendant knew that the visa application document you are considering contained a false statement? And did that defendant, nonetheless, present the document ...?
On its face, the district court's instruction accurately describes the "knowingly" element of the charged offense. See, e.g., United States v. Doyle, 130 F.3d 523, 540 (2d Cir.1997); United States v. Hopkins, 53 F.3d 533, 541 (2d Cir.1995). And that instruction leaves no room for the jury to convict Archer if it believed that he merely ran an office from which fraudulent documents were filed.
Resisting this conclusion, however, Archer claims that the court's refusal to give the Phillips instruction prejudiced him because the government, in its rebuttal summation, asserted that Archer had to have known about the fraud because the office was small and "it's his law firm." This, he says, is precisely the type of reasoning against which the Phillips instruction would have cautioned the jury. Archer's argument, however, goes too far: the Phillips instruction, properly construed, does not prohibit the jury from considering the fact that an attorney is a solo practitioner as one piece of circumstantial evidence from which, along with other evidence, it can infer the attorney's knowledge. What it does do is prohibit the jury from relying on that fact in isolation. Here, the prosecutor did not ask the jury to rely only on Archer's status as a solo practitioner. Rather, immediately thereafter, she recounted the contents of the audio tapes and the testimony of the trial witnesses; that is, she pointed to other evidence that, together with his being *160 a solo practitioner, might lead the jury to find that Archer did have actual knowledge.[5] In this respect, the government's case has much in common with that upheld in Phillips, where the attorney's status as a solo practitioner was also just one piece of the evidentiary pie. 543 F.3d at 1210.

2. The Maniego Instruction

Maniego involved two attorneys who operated a sham-marriage scheme to secure lawful permanent resident (LPR) status for aliens. At trial, their defense was that they were unaware that their clients' marriages were fraudulent. A client testified that she told them about her prior marriage, which made her LPR-qualifying marriage invalid. The trial court instructed the jury that "an attorney is not held to a higher standard of conduct, or legal obligation, to verify independently the truth of the information given by a client." 710 F.2d at 28. This court found that instruction "proper" and affirmed the convictions. Id. Archer requested, nearly verbatim, the same charge as given in Maniego. Def.'s Am. Req. to Charge 3-4, United States v. Archer, No. 08-cr-288 (E.D.N.Y. Mar. 21, 2010), ECF No. 147.
As with the Phillips instruction, there is no dispute that Maniego accurately states the law or that, if the jury had believed that Archer's clients provided him with false information and Archer was unaware of its falsity, it would have had to acquit him. Thus, as above, the only issue before us is whether the mens rea instruction given by the district court adequately represented the requirements of "knowledge" as an element of the crime. As we said above, it did. The jury could not have convicted Archer if it both believed his defense and followed this instruction. Therefore, Archer has failed to show reversible error.

B. Sufficiency of the Evidence
Archer argues that the evidence before the jury was insufficient to demonstrate beyond a reasonable doubt that he had knowledge of the fraud. A defendant challenging the sufficiency of the evidence underlying a criminal conviction bears a "heavy burden" because this court "must review the evidence in the light most favorable to the government, drawing all reasonable inferences in its favor." United States v. Gaskin, 364 F.3d 438, 459 (2d Cir.2004). We also "resolve all inferences from the evidence and issues of credibility in favor of the verdict." United States v. Howard, 214 F.3d 361, 363 (2d Cir.2000). In short, "[r]eversal is warranted only if no rational factfinder could have found the crimes charged proved beyond a reasonable doubt." Gaskin, 364 F.3d at 459-60. Moreover, "the jury's verdict may be based on circumstantial evidence," United States v. D'Amato, 39 F.3d 1249, 1256 (2d Cir.1994), and the government is not "required to preclude every reasonable hypothesis [that] is consistent with innocence," United States v. Chang An-Lo, 851 F.2d 547, 554 (2d Cir.1988). The government must, however, show "more than evidence of a general cognizance of criminal activity, suspicious circumstances, or mere association with others engaged in criminal activity." United States v. Samaria, 239 F.3d 228, 233 (2d Cir.2001), abrogated in part on other grounds by United States v. Huezo, 546 F.3d 174, 180 n. 2 (2d Cir. 2008).
All four client-witnesses testified that they spoke little English and did not read well in any language. They all said they *161 did not know the requirements of the program when they came to Archer's office. They also all testified that their I-687 applications contained false information and that they did not provide this information to anyone at the office. A "reasonable inference" to draw from this combined testimony is, as the government argued, that they could not have fabricated the dates and other information on their applications in such a way that the fabrications would match up with the program's requirements.
Accepting this inference, Archer protests that the evidence shows only that someone in his office, not he himself, fabricated their information. He contends that Rafique, who spoke the clients' languages and who met with them in the office while Archer was in court, is a more logical candidate. Yet, three of the client-witnesses said they spoke with Archer about their applications. And one of the two taped conversation with Gulistan also could well be interpreted as Archer responding "so what?" when confronted with accusations of false information in Gulistan's application.
In all four clients' cases, Archer requested adjournments of the DHS hearings that were scheduled for his clientsapparently attempting to postpone them indefinitely and in two cases, Archer withdrew the applications when DHS insisted on the interviews. From these actions, it could reasonably be inferred that Archer was attempting to avoid having clients answer DHS's questions about the applications in ways that would uncover their falsity.
The jury was entitled to credit this testimony and was not required to see it as Archer urged. See Chang An-Lo, 851 F.2d at 554. Together, this evidence was enough for a reasonable jury to conclude beyond a reasonable doubt that Archer was aware that the visa applications contained false statements and that he filed them anyway. This is so, moreover, apart from whatever additional weight Phillips permits giving to the fact that Archer was a solo practitioner. We, therefore, reject Archer's challenge to his conviction on this ground.

C. Sentencing
We review a sentence for both procedural and substantive reasonableness. United States v. Friedberg, 558 F.3d 131, 133 (2d Cir.2009). Among other things, the district court commits procedural error when it "makes a mistake in its Guidelines calculation." United States v. Cavera, 550 F.3d 180, 190 (2d Cir.2008) (en banc). The district court's interpretation of the Guidelines is a question of law, which we review de novo. United States v. Zagari, 111 F.3d 307, 323 (2d Cir.1997). As to the facts that support the application of a Guideline, the burden of proving such facts is on the government, the standard for proving such facts is a preponderance of the evidence, and we review the district court's factual conclusions for clear error. Id. Clear error exists when "we [are] `left with the definite and firm conviction that a mistake has been committed.'" Cavera, 550 F.3d at 204 (quoting Anderson v. City of Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985)). On this point, we note that a conclusion that factual findings are not clearly erroneous is more easily reached when the district court makes those findings explicitly and on the record.
Archer contends that the district court committed procedural error in calculating his Guidelines range by inappropriately applying three enhancements to that calculation. First, he argues that the government presented insufficient evidence to sustain a nine-level enhancement for conduct that involved more than 100 fraudulent *162 documents. Second, he claims that the district court erred in imposing a four-level enhancement for being the leader or organizer of criminal activity, because the government presented insufficient evidence to show either that five or more people joined the conspiracy or that the criminal scheme was "otherwise extensive." Third, he challenges a two-level enhancement for obstruction of justice, imposed for threatening a witness, because his conduct toward the potential witness was, he asserts, not threatening. We address these arguments in this order.

1. 100 or More Documents

Archer received a nine-level enhancement for an offense involving 100 or more fraudulent documents. See U.S. Sentencing Guidelines Manual (U.S.S.G.) § 2L2.1(b)(2)(C). At sentencing, the government proffered nothing beyond what it offered at trial. And there, the only evidence as to the number of false documents involved was immigration officer Shatzkamer's statistical summary of 175 of Archer's cases. See PSR ¶ 6.
To sustain quantity-based enhancements for relevant conduct, the court must base its findings on "specific evidence" that the offense involved the requisite quantity of items. This evidence can, however, be circumstantial. United States v. Shonubi ("Shonubi II"), 103 F.3d 1085, 1090 (2d Cir.1997). This requirement has two parts: (a) there must be evidence regarding the quantity of illicit or fraudulent goods and (b) it has to be specific to the defendant. See id.; United States v. Shonubi ("Shonubi I"), 998 F.2d 84, 89 (2d Cir.1993). Shonubi I and Shonubi II each dealt with one of these two prongs, respectively. Over a number of years, the defendant in the Shonubi cases made eight trips to Nigeria. On returning to the United States from the last of these trips, he was arrested because officials found 427.4 grams of heroin in him. Shonubi I, 998 F.2d at 86, 89. The district court, multiplying the amount found in the defendant on this one trip by the total number of trips he had made, sentenced him based on eight times that quantity. This court vacated and remanded. We explained that "specific evidencee.g., drug records, admissions or live testimony[is required] to calculate ... quantities for sentencing purposes," and we concluded that the government instead provided "only speculation." Id. at 89-90.
On remand, the district court held "an elaborate hearing," collecting a great deal of statistical evidence about the amount of heroin carried by other Nigerian smugglers in similar circumstances. Shonubi II, 103 F.3d at 1088. It then re-imposed the same sentence. Id. This court again vacated the sentence. Id. at 1093. This time, we faulted the district court for not evaluating evidence specific to the individual defendant. Id. at 1090 ("By mentioning `drug records' and `admissions' as examples of specific evidence we thought it reasonably clear that we were referring to the defendanthis admissions and records of his drug transactions. And by `live testimony' we were referring to testimony about his drug transactions."). In so vacating, our court was careful to point out that "specific" evidence need not be "direct" and, when correctly considered, circumstantial evidence could be sufficient. Id. For example, the court approved of statistical extrapolation to arrive at an estimate of drug quantity when the sample was randomly selected from a known population. Id. at 1092 (approving of the method of testing four randomly selected heroin balloons to estimate the quantity of heroin contained in 103 balloons found inside the defendant's body).
*163 Unlike most of the cases that follow the Shonubi decisions, the case before us does not involve the second prong of the test; there is no doubt that the evidence presented is specific to the defendant. Cf., e.g., United States v. Jones, 531 F.3d 163, 175-77 (2d Cir.2008); United States v. Moreno, 181 F.3d 206, 214 n. 3 (2d Cir. 1999). No one disputes that Archer filed all 175 I-687 applications at issue. Any analysis of those applications is, therefore, sufficiently "specific" to Archer.
What is at issue here is whether the statistics the government relied on satisfy the first prongthe "specific evidence" requirement. The government contends that Shatzkamer's report, which demonstrates striking similarities between the four applications presented at trial, all of which the jury, in convicting Archer on the substantive counts, must have found to be false, and the remaining 171, constitutes adequate specific evidence. These statistics, the government asserts, permit a sentencing judge to find by a preponderance of the evidence (the relevant standard under Zagari) that at least 96 of those applications were fraudulent, thus supporting the nine-level enhancement under § 2L2.1(b)(2)(C) for an offense involving 100 or more fraudulent documents. The contention fails for two reasons.
The first and most obvious flaw in the government's reasoning is that it has presented no evidence that the four applications proven false at trial were, in Shonubi's relevant way, a representative slice of the 175 applications on which the government relies. Unlike the representative sampling of heroin balloons in Shonubi, the four applications presented at trial were not randomly selected from the population. If they had been, Shatzkamer's report might well be sufficient. If fewer than 100 of the 175 applications were false, the likelihood of randomly selecting four applications that were all false would be, at most, 10 percent.[6] It follows then that if four randomly selected applications were all found to be false, this finding could form the basis of a reasonable conclusion that, more likely than not, at least 100 of the applications from which the four were drawn were false. Cf. United States v. Duong-Cam Tran, 519 F.3d 98, 106-07 (2d Cir.2008) (affirming random representative sampling as a valid method of estimating drug quantity).
There is, instead, good reason to think that the applications presented at trial were not random, but were instead the most egregious cases. They look like the easiest ones for agents to identify as fraudulent, both because the clients who were most badly misrepresented were most likely to complain and because those applications involved assertions that were easiest to prove false. In this respect, what happened here would be as if the chemist mentioned in Shonubi had selected the four balloons with the most pungent vinegar smell, which indicates heroin, tested the chemical composition of those four and then extrapolated the result to the population of 103 balloons whose odor was less pungent.
The second flaw is that the government's statistics, without more, tell us very little that is helpful to determining whether *164 any of the other 171 applications were false. The government notes that 100 percent of the applications involved aliens who claimed to have entered the country illegally, that 96 percent of these aliens allegedly did so in 1981, that 90 percent of the applications claimed travel outside the country between June and October 1987, and that 26 percent involved one or more fill-in-the-blank affidavits. That information is interesting, but without a baseline as to what the national pool of I-687 applications (filed by, we must assume, honest lawyers) looked like to compare it toand Shatzkamer admitted he had no such baselinethe data tell us nothing about the truth or falsity of the applications. It is like saying that Dr. Jones's patients died, on average, a year after their initial visit with her: if most of her patients were healthy people coming for a check-up, this information suggests a finding that Dr. Jones is a terrible physician; if, on the other hand, Dr. Jones is an oncologist, all of whose patients had terminal cancer of a sort that had a national average life expectancy of two months, the same information makes her look very good indeed. Context is essential; but the government did not take the time and make the effort to provide any.
This deficiency might, nonetheless, have been cured if the government had explained why the similarities in the applications are, in themselves, incriminating. And we certainly do not foreclose the possibility that, in some circumstances, the incriminating character of similarities is sufficiently obvious that no further explanation is needed. For example, in an immigration fraud case in which the government offered an INS agent's summary of "regular patterns" contained in 1365 applications filed by the defendants, the similaritiesnamely repeated stories of allegedly personal persecution, given in great, often "word-for-word" detailwere deemed too unlikely to be accidental, and the incriminating character of those similarities was held to be obvious. United States v. Walker, 191 F.3d 326, 331, 333 (2d Cir.1999).[7] But the facts heredates of entry and of travelare not so peculiar. Without some further explanation or context, the conclusion that many of the applications must be false is no more than supposition.
In the end, this case is unlike those in which we have upheld this enhancement and more like those in which we have not. In all of these, some evidence was required to show that the court was sentencing the defendant not based on his characterin this case, his guilt with respect to four false applicationsbut on his actionsin this case, his filing of more than a hundred applications that were in fact false. Thus, we have held that a court may not assume that because the defendant was convicted of dealing drugs, all the money that he has is drug money, see Jones, 531 F.3d at 177 (finding the money to be drug money only, in part, because the defendant had "no other means of employment that could be a legitimate source of the money"), and we have held that simply because a defendant was convicted of cashing forged checks, it was error to conclude that every check he cashed was fraudulent, United States v. Spitsyn, 403 Fed.Appx. 572 (2d Cir.2010) (summary order) (remanding for resentencing because no evidence existed that 545 of the 578 checks defendant cashed were forged). Conversely, where the defendant's *165 assistant testified that he had personally "processed thousands of false applications" for the defendant, we upheld an enhancement. See Walker, 191 F.3d at 339.
When the Guidelines allow for punishment of relevant conduct as though it were convicted conduct, we have a special obligation to ensure that the evidence of relevant conduct is solid. See Shonubi II, 103 F.3d at 1089. The absence of such evidence here renders the district court's factual findings clearly erroneous.

2. Leader or Organizer

Archer received a four-level enhancement for being an organizer or leader of the criminal operation. See U.S.S.G. § 3B1.1(a). This enhancement applies when the criminal activity "involved five or more participants or was otherwise extensive." Id. The government argued, and the district court agreed, that Archer qualified for this enhancement on both grounds.
Before we examine Archer's contention about the sufficiency of the government's evidence on either ground, we pause to note that before applying this enhancement, the district court is required to make specific factual findings regarding either the number of participants or the extent of the criminal activity. United States v. Skys, 637 F.3d 146, 156 (2d Cir. 2011); United States v. Espinoza, 514 F.3d 209, 212 (2d Cir.2008) (per curiam). We have repeatedly said that it is not enough for the court to make implicit findings or "`merely to repeat or paraphrase the language of the guideline and say conclusorily that the defendant meets those criteria.'" Skys, 637 F.3d at 157 (quoting United States v. Ware, 577 F.3d 442, 452 (2d Cir.2009), and collecting cases).
Here, the district court simply said, "I find that there was a conspiracy involving five people, and even if there were not five people, that this activity was otherwise extensive." It did, however, adopt the PSR, which provided some factual support. See PSR ¶ 39 (noting that the fraud "involved not just [Archer, Rafique, and Sarvjit Singh, but also] the knowing and unknowing services of many outsiders (including a number of victim applicants who were aware of the fraudulent nature of the applications but signed them anyway, and a number of individuals who fraudulently attested to the truth of those applications in signed affidavits)"). We will review this enhancement in light of the PSR's finding.
For a defendant to qualify for the enhancement on the five-or-more ground, the government must show four people other than the defendant who were "criminally responsible for the commission of the offense." U.S.S.G. § 3B1.1 cmt. n. 1. Because the PSR mentions only Archer, Rafique, and Sarvjit Singh, a former employee of Archer's who solicited clients for him and who was convicted on one count of visa fraud, the evidence is insufficient to sustain the enhancement on this ground.
To qualify on the "otherwise extensive" ground, however, the government can include "the unknowing services of many outsiders" in tallying the scope of the fraud. U.S.S.G. § 3B1.1 cmt. n. 3; see also United States v. Carrozzella, 105 F.3d 796, 803-04 (2d Cir.1997), abrogated in part on other grounds by United States v. Kennedy, 233 F.3d 157, 160-61 (2d Cir. 2000). Three factors weigh in determining the extensiveness of the fraud: "(i) the number of knowing participants; (ii) the number of unknowing participants whose activities were organized or led by the defendant with specific criminal intent; (iii) the extent to which the services of the unknowing participants were peculiar and necessary to the criminal scheme." Carrozzella, *166 105 F.3d at 803-04; accord United States v. Rubenstein, 403 F.3d 93, 99 (2d Cir.2005).
Here, the uncontested number of knowing participants is at least three. This number is on a par with prior cases where we have sustained application of the enhancement. E.g., Rubenstein, 403 F.3d at 99 (two knowing participants). Next, we count as unknowing participants in the overarching conspiracy a fair number though probably not all of Archer's clientsthe precise number being impossible to determine from the record before us for the reasons stated suprawho signed the I-687 applications and who sought affidavits from third parties in support of those applications. The same evidence that was sufficient to convict Archer, as discussed supra Part II.B, is sufficient to show that "[t]he organization of, and direction given to, [at least some of the clients was] done with the specific intent of" filing false visa applications.[8]Carrozzella, 105 F.3d at 804. Finally, though it is logically possible that Archer could have filed false applications simply by pulling information from thin air, that was not what the evidence indicated he did. Cf. Rubenstein, 403 F.3d at 96-97 (describing defendants' conviction for violating the work-practice standards of the Clean Air Act, a violation that can occur only if one has actual workers). Under his scheme, Archer needed real clients to provide some of their own information and to secure the supporting affidavits that his office prepared. In the actual scheme before us, these clients were "peculiar and necessary to the criminal scheme." Carrozzella, 105 F.3d at 804; cf. id. (explaining that "the taxi driver who brought a leader of the fraudulent scheme to work on a single occasion" would not count).
All this is sufficient to support the PSR's finding, and we, accordingly, affirm the application of the four-level enhancement under § 3B1.1(a).

3. Obstruction of Justice

Archer received a two-level enhancement for obstruction of justice for sending two text messages to Sarvjit Singh. U.S.S.G. § 3C1.1.[9] In early 2009, Archer called Singh repeatedly, and Singh did not answer. On April 17, 2009, Archer texted Singh, "Sarvjit. If ur a government witness signal me by not responding to this message. But if ur a friend call me." PSR ¶ 42. Singh did not respond. Ten days later, Archer texted him again, "Pussy." Id.[10] Singh was, apparently, "very threatened" by these messages. Id.
An obstruction-of-justice enhancement is warranted, inter alia, when the defendant threatens, intimidates, or otherwise unlawfully influences a potential witness with the intent to obstruct justice. *167 U.S.S.G. § 3C1.1 cmt. n. 4(a). An intent to deter cooperation with the government is sufficient. United States v. Shoulberg, 895 F.2d 882, 885 (2d Cir.1990).
Most cases where we have upheld the application of this enhancement involve clear and direct threats against cooperating witnesses or government agents. E.g., United States v. Hertular, 562 F.3d 433, 443 (2d Cir.2009) (upholding the enhancement where the defendant told agents "it was in their `best interest to back down' from their investigation and warned them that `hit men from Colombia or Mexico' would be hired to `take [them] out'") (alteration in original); United States v. Agudelo, 414 F.3d 345, 348, 351 (2d Cir.2005) (affirming the district court's interpretation of the defendant's statement to a witness that if the witness were to testify against him in a drug case, he would "make a case against [the witness] for kidnapping" as a threat designed to intimidate the witness). But the district court may draw inferences from context and must determine what the defendant "meant by his words, and how a listener would reasonably interpret those words." Shoulberg, 895 F.2d at 883-84 (sustaining the enhancement where a drug dealer with a violent history known to all parties asked for a potential witness's address saying, "If he is fucking[,] I got a trick for his ass").
Where the defendant's statements are ambiguous, "we generally defer to a sentencing court's findings" on the speaker's meaning and intent. United States v. Gaskin, 364 F.3d 438, 466 (2d Cir.2004) (upholding a § 3C1.1 enhancement where the defendant threatened the life of one witness in front of a second witness and the district court found that he did so in order to intimidate that second witness). Here, however, the district court made no findings with respect to the meaning of Archer's messages. And we are, in any event, unpersuaded that a reasonable reading of these messages evidences sufficient intent to support an obstruction-of-justice enhancement.
The most obvious reading of Archer's texts is (1) that he wished to know whether Singh would testify for the government and (2) that he was displeased that Singh would do so. The district court made no attempt to explain why these interpretations were incorrect under the circumstances or in what way Archer's words manifested any intent to obstruct justice. With no explicit threat of violence and no history between the two men to suggest that the insult was code for a threat, see Shoulberg, 895 F.2d at 885-86 (finding that an ambiguous statement could be interpreted against the defendant where his violent history indicated that his statement would be understood as a threat), this case seems very similar to United States v. Hernandez, 83 F.3d 582, 585-86 (2d Cir. 1996). In Hernandez, the defendant had spoken to the cooperating witness before trial, called her "the devil," and said she would "stare [the witness] down" at trial. Id. at 585. The Hernandez court found the district court's finding of obstructive intent clearly erroneous, even though the witness was "scared"; the statement was not a threat but was merely an expression of an understandable feeling of betrayal.[11]*168 Id. at 586 ("Fury may be exceedingly unpleasant, but alone, it bespeaks no intent to obstruct justice.").
As in Hernandez, the defendant called the witness an unpleasant name upon learning that the witness would cooperate with the government, and the witness was subjectively afraid. But also as in Hernandez, and unlike Shoulberg, no evidence exists from which one could conclude that the defendant's statement was a threat. Therefore, like the Hernandez court, we find clearly erroneous the district court's conclusion that Archer's texts were threats and hence find the enhancement improper.

4. Remand

For the reasons given in Parts II.C.1 and II.C.3, we vacate the sentence imposed and remand the case for resentencing. This raises the question of whether the government should, or can, be allowed to present additional evidence on remand as to one or more of the matters as to which we found the current record evidence to be inadequate.[12] This is an open question in our circuit. But see Shonubi II, 103 F.3d at 1092 ("Since the Government has now had two opportunities to present the required `specific evidence' to the sentencing court, no further opportunity is warranted." (emphasis added)).
The consensus among our sister circuits is that generally where the government knew of its obligation to present evidence and failed to do so, it may not enter new evidence on remand. Nonetheless, there are cases (a) where the government's burden was unclear, (b) where the trial court prohibited discussion of the issue, or (c) where the evidence was, for a good reason, unavailable, in which the district court was permitted, in its discretion, to hear new evidence. To put it more broadly, where special circumstances make the prohibition on new evidence unfair, the district court may admit it. United States v. Noble, 367 F.3d 681, 682 (7th Cir.2004) (holding that the "the government is not permitted on remand to try again and submit new evidence in a belated effort to carry its burden" where the "government knew what it was required to introduce"); United States v. Matthews, 278 F.3d 880, 885-86 (9th Cir.2002) (adopting a policy of remand "without limitation on the evidence that the district court may consider" unless, inter alia, "there was a failure of proof after a full inquiry into the factual question at issue"); United States v. Hudson, 129 F.3d 994, 995 (8th Cir.1997) ("Because we have clearly stated the governing principles as to when and how disputed sentencing facts must be proved, we direct that resentencing on remand be conducted on the existing sentencing record, with no opportunity for either party to reopen or add to that record."); United States v. Leonzo, 50 F.3d 1086, 1088 (D.C.Cir.1995) ("see[ing] no reason why [the government] should get a second bite at the apple [where n]o special circumstances justified, or even explained, the government's failure to sustain [its well-established] burdens"); United States v. Dickler, 64 F.3d 818, 832 (3d Cir.1995) ("perceiv[ing] no constitutional or statutory impediment to the district court's providing the government with an *169 additional opportunity to present evidence on remand if it has tendered a persuasive reason why fairness so requires"); United States v. Parker, 30 F.3d 542, 553-54 (4th Cir.1994) (holding that double jeopardy prevents the government from offering new evidence when it "has already been given one full and fair opportunity to offer whatever proof about [the disputed issue] it could assemble").
We now join that consensus. We leave to the district court to consider in the first instance whether the justifications outlined above for allowing the government to present new evidence on remand exist in this case. Thereafter, if it has admitted no new evidence, the district court should recalculate Archer's Guidelines range without using the enhancements in §§ 2L2.1(b)(2)(C) and 3C1.1. If it chooses to consider new evidence, it should calculate Archer's Guidelines range based on its findings with respect to that evidence. In either case, it should then, of course, impose the sentence it finds warranted by the sentencing factors set forth in § 3553(a).

D. Restitution
Under the Mandatory Victim Restitution Act (MVRA), 18 U.S.C. § 3663A, the district court ordered Archer to pay $309,500 in restitution to 234 clients, representing a refund of the estimated fees paid by those clients to Archer for their I-687 cases. We review restitution orders for abuse of discretion. United States v. Ojeikere, 545 F.3d 220, 222 (2d Cir.2008). A court abuses its discretion when it rests its decision on an error of law. United States v. Fernandez, 443 F.3d 19, 27 (2d Cir.2006).
The MVRA requires restitution where (a) the offense was "committed by fraud or deceit" and (b) "an identifiable victim or victims has suffered a physical injury or pecuniary loss." 18 U.S.C. § 3663A(a)(1), (c)(1)(A)(ii), (c)(1)(B). There is no dispute that Archer's crime qualifies as to the first element. With respect to the second, the government contends that Archer's clients are victims of the fraud and that they suffered the pecuniary loss of paying him "for a servicehelping them obtain legal statusthat he did not provide." Appellee's Br. 56. Archer resists the classification of his clients as victims and argues that, in any event, not all of them are victims.
A "`victim' means a person directly and proximately harmed as a result of the commission of an offense ... including, in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person directly harmed by the defendant's criminal conduct in the course of the scheme, conspiracy, or pattern." § 3663A(a)(2).[13] Determining whether Archer's clients qualify *170 as "victims," therefore, is in large part about whether their losses were caused by Archer's offense, namely his conspiracy to commit visa fraud.[14] Critically, "the district court's statutory authority to award restitution under the MVRA is limited to awards to victims of the offense of conviction." In re Local # 46 Metallic Lathers Union, 568 F.3d 81, 85 (2d Cir.2009) (per curiam) (citing Hughey v. United States, 495 U.S. 411, 416-19, 110 S.Ct. 1979, 109 L.Ed.2d 408 (1990)).
The government's argumentthat Archer took his clients' money "for a service... he did not provide"might be taken as referring to an entirely separate consumer fraud rather than to the immigration fraud it charged. This raises the possibility that the government is seeking restitution for losses caused by an unprosecuted offense rather than by the offense of conviction, something it may not do. Id. (holding that a victim of a fraud count in the indictment to which the defendant did not plead guilty was properly denied restitution). For a number of years, our court determined whether a loss was part of the offense of conviction by reference to the elements of the crime: restitution was proper only if the conduct that caused the loss was an element of the crime. Id. at 86; id. at 84 (rejecting the plaintiff's argument that the district court erred by "defining a victim according to the elements of the crime or offense of conviction" (internal quotation marks omitted)).[15]
For example, in the Local 46 case, the defendant, a business owner, developed a scheme in which he issued business checks to fictitious vendors, forged endorsements on those checks, cashed them, and then used the proceeds to pay his employees in cash, thereby avoiding obligations to the IRS and the employees' union. Id. at 82. He was charged with conspiracy to launder money and defrauding the union, but pleaded guilty to the former charge as part of a plea agreement in which the government agreed to drop the latter charge. Id. at 83. The union sought restitution, claiming that it was a victim of the money laundering scheme because paying the employees with cash, and thus avoiding paying the union as required under the collective bargaining agreement, was the purpose of the money laundering scheme. Id. at 83-84. The court affirmed the magistrate judge's determination that the money laundering scheme was complete when the defendant received the cash and so what he intended to do (or did) with it after that moment was irrelevant to the crime of conviction. Id. at 86-87. As a result, the court held that the union was not a victim under the MVRA. Id. at 88.
Our recent decision in United States v. Paul, 634 F.3d 668, 670 (2d Cir.2011), however, expands this test somewhat. In that case, the defendant committed securities fraud by trading a stock between multiple accounts he controlled, called "nominee accounts," thereby artificially increasing the liquidity of the stock and, hence, its price. *171 In the process, he secured margin loans from several banks based on his holdings of this stock. These loans were how he profited from the schemesimultaneously inflating the stock price while continuing to hold the shares, something he could do only because of the loans he had secured. Id. Eventually, the scheme was uncovered, the stock price fell dramatically, and given the worthlessness of the shares, he was unable to repay the loans. Id. He pleaded guilty to securities fraud but contended that the court could not order restitution to the banks because their losses were caused by his fraudulent creation of the nominee accounts, which he argued was bank fraud, and not the securities fraud of which he was convicted. Id. at 676-77. We rejected this argument and found that the loans were part of the larger securities fraud for two reasons. First, because Paul "explicitly admitted that ... [he] concealed from the investing public that [he] was leveraging and, in effect, liquidating a substantial part of [his stock] holdings" through the use of the margin loans, that conduct itself was an element of securities fraud. Id. at 677. Second, and more broadly, because the loans were part of the scheme Paul actually devised for profiting from his crime and because "[t]he brokerage houses would not have made the loans to [the defendant] had they known that the collateral for the loans was the stock he manipulated through the nominee accounts," their losses were caused by his overall scheme. Id. at 677.
Paul's reasoning echoes the statute, which provides that "in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person [who is] directly harmed by the defendant's criminal conduct in the course of the scheme, conspiracy, or pattern [is a victim]." § 3663A(a)(2). This same reasoningthat victims are those who "would not have made the [payments to the defendant] had they known [about the fraudulent scheme]," Paul, 634 F.3d at 677also explains the well-established rule that co-conspirators, who, by definition, know of the scheme, are not victims and may not receive restitution, see United States v. Reifler, 446 F.3d 65, 127 (2d Cir.2006) (disallowing restitution for those individuals whose stock lost value but who bought it knowing the defendant intended to inflate the price artificially).
The government is correct that this rule is not about denying benefits to those with unclean hands. See Ojeikere, 545 F.3d at 223 (allowing restitution to those whose money the defendant had stolen despite the fact that they had conspired with him to commit a different fraud on third parties). It is a rule about causation in the fundamental and not simply "but for" meaning of the word: if a person gives the defendant his money to bet, knowing that the bet might lose, his later loss, for purposes of restitution, is, in this fundamental sense, caused not by the defendant accepting his money but by the outcome of the bet.[16]
In the instant case, the first question is whether the clients' payments to Archer were part of the visa fraud conspiracy or, instead, were only part of an entirely separate consumer fraud scheme for which he was not prosecuted. It is certainly possible for one to commit visa fraud without accepting any money from the visa applicantsthe crime is "complete" with the knowing presentation of a false document *172 to the government.[17]See In re Local # 46, 568 F.3d at 86. Archer's receipt of money from his clients was, therefore, not an element of the crime. But, in this case, the fraud was not by any means entirely separate; hence, restitution might nonetheless be available. Here, the clients' payments, like the margin loans in Paul, were the mechanism through which Archer profited from his conspiracy and, thus, were an integral part of the single scheme he devised. Under Paul, such payments could qualify as part of the offense for which he was convictedand hence his clients could be victims under the MVRAif, but only if, "[the clients] would not have made the [payments] had they known that [Archer would file false applications]." See Paul, 634 F.3d at 677. That is, if Archer's clients thought they were buying his honest legal services, they may well have been victims of his visa fraud conspiracy. On the other hand, if they thought (and a fortiori if they in fact knew) that they were buying the cover that his law practice gave to their false visa applicationseither because they wanted the temporary work permits issued to I-687 applicants or because they thought the government might be duped and grant their applicationsthen they suffered no loss that was proximately caused by Archer's visa fraud.
The showing required to satisfy the government's burden on this point varies depending on the circumstances of the fraud. In some cases, it will be clear that no reasonable person would have given the defendant her money if she had known of his planas in the fraud in Ojeikere where the defendant's plan was to abscond with his co-conspirators' funds as soon as he got hold of their money. 545 F.3d at 223. See also United States v. Marino, 654 F.3d 310 (2d Cir.2011). In those cases, a generalized description of the fraudulent scheme is enough to support restitution. But where it is plausible that some individuals would have paid the defendant even if they had been informed of his fraudulent plan, then the government must proffer some individualized evidence to meet its burden of showing that each alleged "victim" was actually a victim. Cf. United States v. Gonzalez, 647 F.3d 41, 65-67 (2d Cir.2011) (vacating a restitution award where the district court failed to calculate individualized and actual losses).
Two facts lead us to conclude that the case before us is of the latter kind. First, the record reflects that in several instances, applicants did in fact know that their papers contained falsehoods. For example, Mr. Ally admitted that he knew one of the affidavits for his application was false but that he "begged" his co-worker to sign it anyway. Rahul Gupte, a client who was deposed but did not testify, said that he signed his I-687 application knowing it contained false statements, including a false address he provided. Another client, Manzoor Ahmad, had previously submitted a similar application for legalization with the same false information that was later included on his I-687 form.
Second, filing a false but plausible I-687 application was anything but a sure loser. While the alien's application was pending, the alien could obtain a temporary work permit, and all four clients who testified at trial said they in fact did receive such a permit. There also remained the possibility, however small, that DHS would be fooled by their false applications and grant *173 them visas. Of course, a knowing applicant might well realize that the application would likely have to be withdrawn eventually or would be denied and that he or she could face the possibility of future sanctions. But it is an unfortunate fact that criminals take that kind of risk every day.
The upshot is that, in the instant case, the government bore the burden of demonstrating by a preponderance of the evidence, 18 U.S.C. § 3664(e), that each individual it claims is entitled to restitution was actually a "victim." The government undertook to satisfy that burden only by showing that 234 clients paid Archer a fee. Although Archer's receipt of these fees was part of his scheme, such receipt created at most only a prima facie case that each client was a victim entitled to restitution. As we have pointed out, a client would not have been entitled to restitution if the client paid a fee with knowledge of the fraud (and thereby became a co-conspirator) or if the client would have paid a fee had the client known of Archer's plan to submit a fraudulent visa application. To show that a fee-paying client was a victim, the government's burden, therefore, was to show that a fee-paying client did not know of the fraud and would not have paid a fee had the client known of the fraud.
These further aspects of the government's burden obliged it to prove two negatives, a circumstance that requires some refinement in the proper allocation of the parties' evidentiary obligations. It is familiar ground that where the prosecution's burden of proof would require it to prove a negative and the facts at issue are more readily ascertainable by the defendant, the defendant is often obliged to assume a burden of production of evidence that presents at least a triable issue as to the fact at issue, at which point the burden of persuasion must be assumed by the prosecution. See Model Penal Code § 112 (Proposed Official Draft 1962); Weinstein's Federal Evidence § 303.06[2] (2011). That is how burdens are allocated, for example, when a defendant accused of crime asserts the affirmative defenses of duress or coercion. See United States v. Bakhtiari, 913 F.2d 1053, 1057-58 (2d Cir. 1990) (defendant's evidence insufficient to raise a triable issue of duress or coercion); see also Mullaney v. Wilbur, 421 U.S. 684, 701 n. 28, 95 S.Ct. 1881, 44 L.Ed.2d 508 (1975) (noting that many states require defendant to show that there is some evidence that he acted in heat of passion before requiring prosecution to negate this element by proving the absence of passion beyond a reasonable doubt); Grey v. Heckler, 721 F.2d 41, 45 (2d Cir.1983) (relying on Illinois law that party alleging that divorce was not obtained must present evidence sufficient to afford reasonable ground for presuming allegation is true, at which point "onus probandi will be thrown on his adversary"); United States v. Vardine, 305 F.2d 60, 63 (2d Cir.1962) (assigning to defendant in tax fraud prosecution burden of production to furnish leads to explain net worth bulge with burden of proof of tax evasion on government).
That allocation of burdens is appropriate in this case. Archer, having been found guilty of conspiracy to submit fraudulent visa applications for his clients, is more likely than the government to ascertain whether a client knew of the fraud or would have paid a fee even if the client had known of the fraud. A client's knowledge would have come from Archer or someone in his firm, and the client's willingness to pay a fee had the client known of the fraud would likely have come to light in conversations between the client and Archer or someone in his firm.
In this case, Archer's burden of production was fully discharged as to some alleged *174 victims, such as Mr. Ally and Rahul Gupte, by some evidence that they knew of the fraud. The government then had to persuade the trier by a preponderance of all the evidence that these clients did not know of the fraud. The present record does not indicate that Archer has yet satisfied his burden of production on the issue of knowledge of the fraud with respect to other clients.
Archer endeavored to satisfy his burden of production on the issue of whether a client would have paid a fee had he known of the fraud by evidence of attorney-shopping on the part of some of the clients. That evidence, however, does not suffice to raise a triable issue of whether such clients would have paid a fee had they known of the fraud. Attorney-shopping is explicable by many reasons, the most likely of which is attempting to find an attorney who charges a more reasonable fee. With respect to a client like Manzoor Ahmad, however, Archer's evidence that Ahmad had previously submitted a similar application for legalization with the same false information later included on his I-687 form satisfied Archer's burden of production with respect to this client. The burden was therefore on the government to prove by a preponderance that Ahmad would not have paid a fee had he known of the fraud. With respect to other clients, Archer has not yet satisfied his burden of production to raise a triable issue as to whether they would have paid a fee had they known of the fraud.[18]
Because the determination of victim status was not made with the evidentiary burdens allocated as set forth above, we will remand to afford the district court an opportunity to reconsider which of Archer's clients are entitled to restitution. And because restitution is a matter of sentencing, 18 U.S.C. Pt. II, Ch. 232 (containing the MVRA and entitled "Miscellaneous Sentencing Provisions"), the analysis articulated supra in Part II.C.4 regarding new evidence applies here as well, although the lack of clarity as to the parties' respective burdens on the restitution issue, in the circumstances of this case, would seem to favor allowing additional evidence on this issue. Regardless of whether the district court decides to admit new evidence on this point, the parties are, of course, free to make new arguments based on the evidence already in the record.

III. CONCLUSION
We hereby AFFIRM the defendant's conviction. We VACATE his sentence, including the restitution order, and REMAND for further proceedings as outlined above.
NOTES
[1]  The conspiracy charge required (a) an agreement between two or more persons to commit visa fraud and (b) an overt act by at least one of the participants in furtherance of that agreement. See 18 U.S.C. § 371. There is no dispute that if an agreement existed, the overt-act requirement has been met.
[2]  Gulistan does not have a last name.
[3]  The precise text of the requested instruction was: "The fact that one of the defendants is the sole attorney in a small firm in and of itself is not sufficient to determine that the attorney was aware of each and every act that took place in the office or that he approved or encouraged such actions."
[4]  In general, the law does not impute criminal liability to those who are unaware of the criminal activity. See, e.g., United States v. Applins, 637 F.3d 59, 75 (2d Cir.2011) (holding that to be liable for a criminal conspiracy's acts, one must have knowingly joined the conspiracy and been aware of its basic contours). We find it troubling, therefore, that the pre-sentence report prepared by the Probation Office seemed to apply tort-like respondeat superior liability of the type rejected by the Phillips court to Archer as an employer. PSR ¶ 39 ("As a sole practitioner, Archer was responsible for the actions, both legitimate and criminal, of those he employed and supervised....").
[5]  Whether such other testimony by itself would be sufficient to support a conviction or whether it becomes sufficient only when combined with Archer's status as a solo practitioner is a question we advert to infra.
[6]  The likelihood of randomly drawing four false applications is determined by multiplying the likelihood of drawing a false application on each of four successive selections. In this example, the likelihood of drawing the first false application would be 56.6 percent (99 false applications out of 175 total applications). The likelihood of drawing a second false application would be 56.3 percent (98/174); the third, 56.1 percent (97/173); and the fourth, 55.8 percent (96/172). The total likelihood of drawing four false applications in a row, then, would be 10.0 percent (.566 x .563 x .561 x .558).
[7]  Even there, however, the court ultimately rested its conclusion that more than 100 false documents were involved on direct testimony regarding the number of documents: the lawyer-defendant's clerk said at trial that "he processed thousands of false applications" for the defendant. Walker, 191 F.3d at 339.
[8]  This is so without regard to the statistical evidence discussed supra in Part II.C.1. The trial testimony established that four clients and eight other individuals (two affidavit-signers for each client) could be counted as unknowing participants in the conspiracy. See Rubenstein, 403 F.3d at 99 (approving the "otherwise extensive" finding where the scheme involved two knowing participants and seven unknowing participants whose work was necessary to the scheme).
[9]  This section provides: "If (A) the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice with respect to the investigation, prosecution, or sentencing of the instant offense of conviction, and (B) the obstructive conduct related to (i) the defendant's offense of conviction and any relevant conduct; or (ii) a closely related offense, increase the offense level by 2 levels."
[10]  Note that the PSR calls this second message an "email." The photograph in the record, however, clearly shows it to be a text message. [A 1272]
[11]  Though the Hernandez court took the defendant's words in the light most favorable to her, as it was required to do by a now-repealed Guideline note then in effect, see U.S.S.G. § 3C1.1 cmt. n. 1 (1995) (requiring the court to take the defendant's statements "in a light most favorable to" her), repealed by U.S.S.G. App'x C, amd. 566 (1997), its conclusion was largely based on the total lack of evidence showing any intent to obstruct justice. Hernandez, 83 F.3d at 585 ("[T]here is no evidence that Hernandez made the statements with the requisite intent to obstruct justice."); id. at 586 ("Without some showing of evil intent as to that attempted contact, however, this fact cannot constitute any evidence at all of obstruction."). So too here: our conclusion is based not on reading Archer's statement in the light most favorable to him, but rather on the lack of evidence in the record either on the face of the statements or in their contextdemonstrating any intent to keep Singh from helping the government.
[12]  Of course, if the government is allowed to introduce new evidence on remand, the defendant must be allowed to answer it by presenting new evidence of his own.
[13]  Our court recently decided United States v. Aumais, 656 F.3d 147 (2d Cir.2011). In Aumais, restitution arose under § 2259; the current case is under § 3663A. As noted above, § 3663A defines a victim as "a person directly and proximately harmed as a result of the commission of an offense," and it is that statutory definition of victim, requiring proximity of causation, that we apply in this case. Aumais was decided in the absence of the same definition of victim. Nevertheless, Aumais held that proximate cause was needed for restitution. It did this by reading § 2259 as mandating that the victim's claimed losses be proximately caused by the defendant's action. There is nothing, of course, inconsistent with the requirement of proximate cause that Aumais reads into § 2259, and that which we find to be statutorily required under § 3663A. The two cases, therefore, can exist in harmony. But, notably, even had Aumais not read into § 2259 a requirement of proximate cause with respect to the loss, § 3663A by its language, would require proximate cause in its definition of victim in the case before us.
[14]  The substantive counts of visa fraud could only have victimized the four clients whose applications were covered by those charges. For the overwhelming majority of the alleged victims, therefore, their losses must be tied to the conspiracy count.
[15]  A slightly different rule applies in cases where the conviction is for an inchoate crime like possession of an illicit item with intent to defraud. See United States v. Oladimeji, 463 F.3d 152, 159 (2d Cir.2006). In those cases, we have held that carrying out the fraudulent scheme is sufficiently encompassed within the "intent to defraud" element of the crime so as to allow for restitution caused by the defendant's use of the prohibited item even though he was convicted only for its possession. Id. Even in these cases, however, the critical point of reference remains the elements of the crime of conviction.
[16]  The requirement of causation here is akin to the well-established requirement that there be "loss causation" in securities-fraud cases and not merely transaction ("but for") causation. See Lentell v. Merrill Lynch & Co., 396 F.3d 161, 172 (2d Cir.2005).
[17]  Unlikely though it may seem, a defendant might aid an alien in preparing a false visa application out of friendship to a particular alien or beneficence to aliens in general. Under the statute, that defendant would be just as guilty of visa fraud as Archer. See 18 U.S.C. § 1546(a).
[18]  With regard to fees paid to Archer by clients who participated in the efforts to obtain visas with knowledge that those efforts were fraudulent, while those clients may not be entitled to restitution, that is not to say that the funds themselves would not be forfeitable. We offer no opinion in that regard, and whether to proceed down that track is, of course, up to the government in the first instance.
