
658 F.3d 1 (2011)
UNITED STATES of America, Appellee,
v.
Robert L. NEWELL and James J. Parisi, Jr., Defendants, Appellants.
Nos. 09-1590, 09-1614.
United States Court of Appeals, First Circuit.
Heard September 16, 2010.
Decided July 11, 2011.
*3 Mary A. Davis, with whom Tisdale & Davis, P.A. was on brief, for appellant Newell.
George T. Dilworth, with whom David M. Kallin and Drummond Woodsum & MacMahon were on brief, for appellant Parisi, Jr.
Margaret D. McGaughey, Appellate Chief, with whom Paula D. Silsby, United States Attorney, was on brief, for appellee.
Before TORRUELLA, RIPPLE,[*] and LIPEZ, Circuit Judges.
TORRUELLA, Circuit Judge.
This case stems from extensive financial mismanagement at the Passamaquoddy Tribe Indian Township Reservation (the "Tribe") in Down East Maine. Defendants Robert Newell, the former governor of the Tribe, and James Parisi, Jr., the Tribe's former finance director, were convicted for conspiracy to defraud the United States under 18 U.S.C. § 371, as well as violations of 18 U.S.C. §§ 287, 666 and 669, involving the misuse of federal grant and tribal monies. On appeal, Newell and Parisi raise a host of issues related to the *4 federal court's jurisdiction over "internal tribal matters," the sufficiency of the evidence, the lower court's jury instructions, sentencing, and the restitution order entered against them. For the reasons explained below, we vacate Parisi's conviction on count five and remand for clarification of certain issues related to the restitution order, but otherwise affirm.

I.
The following facts are drawn from the parties' filings supplemented by the record as necessary, and are presented in the light most favorable to the verdict. See United States v. Poulin, 631 F.3d 17, 18 (1st Cir.2011).

A. Background
The Passamaquoddy Tribe is a federally recognized Indian tribe located in northern Maine.[1] The Tribe is relatively small, with fewer than seven hundred residents. It relies in large part on federal grant and contract money for its financial survival. During the period of time at issueroughly, September 2002 to September 2006, i.e., Newell's tenure as tribal governorthe Tribe received between five and eight million dollars annually in federal grants and contracts.
The Tribe's political leadership consists of a governor and tribal council. In addition, the Tribe shares a 12-member joint tribal council with its sister reservation in Princeton, Maine. Council members receive no official salary, but many are employed by the tribal government in other capacities, are reimbursed for travel expenses, and receive "honoraria" that approximate a salaried employee's vacation pay. The tribal government provides administrative services to the tribal programs, including bookkeeping and accounting services.
The Tribe receives funding from the Bureau of Indian Affairs ("BIA") and the Department of Health and Human Services ("HHS") through the Indian Self-Determination and Education Assistance Act. These grants are used to fund myriad tribal services, including the police, fire, child welfare and wildlife and parks departments, the housing authority, the Tribe's courts and schools, and the Indian health center. The Tribe additionally receives funding from HHS's Substance Abuse and Mental Health Services Administration ("SAMHSA") for an HIV awareness and substance abuse prevention program. The Tribe received a Department of Justice ("DOJ") COPS program grant for police equipment and training, as well as funding from the Environmental Protection Agency ("EPA") for its environmental department and from the Department of Housing and Urban Development ("HUD") for its housing authority. Each of the federal contracts and grants included terms and conditions specifying how they were to be used. Generally, the contracts required the Tribe to use the funds to pay for allowable direct costs of the identified programs, as well as specified amounts of the indirect costs incurred by the tribal government for administrative services. The awarded funds generally could not be diverted for non-contract or grant purposes without a contract amendment or agency approval.[2]
*5 In addition to the federal grants and contracts, the Tribe had income from its ownership interests "in three companies [Dragon Cement, Creative Apparel and Northeast Blueberry Company] that it purchased with money it received under the Indian Claims Settlement Act." This income was on the order of "several million dollars . . . annually."
Newell served as the Tribe's governor from 1986 to 1993, and again from 2002 to 2006. Newell served as his own finance director for the first year of his most recent term, but in the fall of 2003 he hired Parisi to fill the position. Parisi had worked as a banker but did not have experience with federal contracts. In addition to Parisi, the finance department was composed of several bookkeepers and a federal grant compliance officer, Linda Lewey. Despite his official job title, Parisi appeared to have had little actual authority, and would refer most questions to Newell. There is also evidence that Parisi may have been somewhat ostracized by at least some of his co-workers as he was not a member of the Tribe.
During his tenure as governor, Newell exercised extensive control over tribal governance in general, and the Tribe's finances in particular. Newell would transfer funds between the various accounts to pay for unauthorized expenses, including salaries for individuals who did not actually work for the programs that were funding them. Newell also caused the Tribe's various programs to "loan" hundreds of thousands of dollars each year to the Tribe which he then disbursed in the form of "general assistance" to Tribe members, including friends, family and political supporters.[3] These loans were by and large never repaid.
We now sketch briefly the details of the transactions relevant to the current appeals, leaving aside those uncontested on appeal. Our discussion is somewhat condensed in light of the large multitude of transactions, which were spread over a number of years, involved a large cast of supporting characters, several distinct funding sources, and the arcana of accounting practices for federal grants and contracts.

B. The financial mismanagement
In 2003, the Tribe received a three-year, $350,000-per-year grant from SAMHSA to fund its HIV and substance abuse program, known as the Wonahkik program. The Wonahkik program ramped up slowly. Roger Paul, the Wonahkik program coordinator, testified at trial that the program did not "get a staff to start getting things actually done" until January of 2004. As of October of 2003, the program had only spent $86,354 of the $350,000 grant. In September, Newell and Elizabeth Neptune, the director of the health center, wrote to SAMHSA requesting permission to carry over the remainder into the next fiscal year. In October, Faye Socobasin, the Tribe's SAMHSA bookkeeper, filed a "269" form with SAMHSA showing that the Tribe had $236,645 in unspent grant funds. Lewey, the Tribe's federal grant compliance officer, signed off on the form. Parisi was hired at around this time.
In February 2004, before SAMHSA had responded to the request, Newell directed that the unspent funds be used to reimburse the Tribe for salaries it had paid to three tribal councilors despite the fact that they did not actually work for the Wonahkik *6 program.[4] Newell insisted that the grant money "had to be spent," and that if the Wonahkik program wasn't going to spend it, "the Tribe would." Socobasin, at Lewey's instruction, then prepared a journal entry form for the Tribe's records indicating that the three individuals had been paid out of the SAMHSA grant on or before September 30, 2003, the last day of the fiscal year. Parisi signed the journal entry.
When SAMHSA notified the Tribe in April 2004 that it would not permit the unused funds to be rolled over, Newell wrote back, stating, among other things, that the Tribe's initial 269 report had been in error, and that the Tribe had spent an additional $129,044 of the SAMHSA grant in salary expenditures in FY 2003. Subsequently, Socobasin prepared a revised 269 form reflecting the additional $129,044 expenditures, again dated to appear as if they had occurred in September of 2003. Socobasin refused to backdate the charges unless either Parisi or Newell approved it. Parisi, rather than Lewey, subsequently signed the revised 269 form. Newell told Socobasin that Parisi should sign the revised 269 "so we can blame it all on him." In June 2004, SAMHSA relented, and approved the Tribe's request to roll over the unused grant funds.
It was during this time that the tribal council learned that the Tribe's budget had been overspent to the tune of $1.6 million. At a contentious council meeting, Newell admitted he had been using SAMHSA funds to pay council members, but insisted he had the authority to do so. The council voted to strip Newell of administrative authority, but backtracked when it came out that this meant they would no longer receive general assistance payments. The council insisted that subsequent checks, with the exception of payroll and housing authority checks, be signed by two council members. Undeterred and largely unimpeded, Newell was able to secure the cooperation of sympathetic council members or, in other cases, circumvent the council entirely by transferring funds through online or wire transfers.
The Tribe continued to pay the salaries of council members and other non-health center "ghost" employees with the health center's funds throughout FY 2004. Wonahkik was not the only program that saw its budget raided. Funds were "loaned" to the tribal government from the Indian Health Services ("IHS") contract, state Medicaid payments, and EPA and BIA grants. Several of the tribal health services administrators objected, but Newell and Parisi continued to authorize the payments. Parisi promised that the non-employees would be taken off the health center's payroll, and that the funds would be restored. When pressed by Paul about the missing funds, Parisi replied that it was "normal" for Tribes to use incoming grant money to pay pressing non-grant related bills, and to replenish the funds later with other income, an explanation that Paul conceded he found "reasonable."
Despite the earlier troubles, SAMHSA approved funding for the Wonahkik grant for a second year. This time around, however, SAMHSA required that the Tribe submit itemized claims for approved expenses. Thus, when Parisi requested $81,779 in reimbursement from SAMHSA in February of 2005, the claim was denied because it was not correctly itemized. Parisi resubmitted correctly itemized forms to SAMHSA in March, but because the requested amount included the salaries *7 of individuals who did not work for Wonahkik, SAMHSA ultimately refused to pay for those claims.
Neither Newell nor Parisi was accused of lining their own pockets. (Parisi appears to have been motivated mostly by a desire to retain his employment with the Tribe). Newell, however, did improperly redirect federal grant money to help friends and family. For instance, shortly after Newell took office in the fall of 2002, he refused to release funds that the BIA had awarded the Tribe through its Housing Improvement Program. Instead, he spent the money on his friends, family, and tribal council members and their families, including William Nicholas, the Tribe's current governor. Similarly, in June of 2004, Newell had Carol Roehrich, the Tribe's BIA bookkeeper, issue his son, Roger, a check for $1020, ostensibly to reimburse Roger for the costs of attending training in Boston. Alex Nichols, Roger's supervisor, knew that Roger did not attend training in Boston and asked Roger to return the money. Newell insisted that Roger needed help, and the funds were never repaid. On other occasions, Newell dipped into Housing Authority funds for wedding donations, unspecified small loans, travel reimbursement for his son, Eric, and "general assistance" for two other Tribe members.
Despite his efforts to keep the political wheels well-greased, by the spring of 2005, Newell was facing increasing opposition to his leadership. Several of the health center administratorsincluding Roger Paul, the head of Wonahkik, and Elizabeth Neptune, the health center's directorparticipated in an anti-Newell protest and went to federal investigators with their complaints. Newell responded by cleaning house, firing Paul, Neptune and three other health center administrators. Bookkeepers who protested the interfund "loans" found themselves suspended. Newell then reassured Don Payne, the new head of the health center, that although health center funds were being used for other purposes, the funds would be restored.
The misapplication of funds continued apace, and the Tribe's financial situation deteriorated further. As of the fall of 2005, the Tribe owed $866,000 to the BIA and IHS grants. The Tribe had budgeted $621,000 in "tribal assistance" in FY 2005, but had spent nearly three times that amount. Newell continued to try to cover the Tribe's costs by "borrowing" money from the incoming federal grants, and Parisi continued to offer assurances to the affected programs that the funds would be repaid. Although some of the non-employees who had been drawing salaries from the grants were finally removed at this point, some remained, and others were added on.
Newell and Parisi received multiple warnings at around this time that their conduct was of questionable legality. In early 2005, the Tribe's outside auditor warned them that "pooling" federal funds was permissible, but that the funds should only be used for allowable purposes, a point reiterated by Lewey, the federal grant compliance officer, and Roehrich, the BIA bookkeeper.[5] Harry Schade, a former finance director for the Tribe, was brought back in June of 2005 to help Newell *8 and Parisi sort out the Tribe's increasingly desperate finances. However, Schade's repeated demands that non-approved employees be taken off the health center's payroll were ignored.
Newell and Parisi were also put on notice by warnings from various federal officials. IHS officials confronted Newell and Parisi in August 2005 about delinquent audits and interfund transfers. Despite the fact that Schade and Payne had asked the IHS not to release the funds because Newell and Parisi were raiding the accounts, the IHS was satisfied with Newell and Parisi's assurances that the funds would not be misused and that they would conduct an audit. IHS then agreed to a lump sum wire transfer of $2,000,000 for FY 2006. Within a week, over $400,000 had been diverted to the tribal government at Newell's direction. Newell and Parisi directed the health center to "loan" the tribal government a further $200,000 over the next two months. In a by-now-familiar scene, Schade protested and was subsequently fired. IHS officials began inquiring as to why so little of the grant funds remained, but were rebuffed by Newell.
One of the "loans" in question occurred in November of 2005. At this point in time, the Tribe, together with its sister Pleasant Point reservation, was engaged in an effort to place a referendum question on the 2007 ballot asking for approval of a combined race track and casino, otherwise known as a Racino. The Joint Tribal Council hired an outside firm to solicit the necessary signatures to ensure that the question was placed on the ballot. Newell realized that the Tribe lacked the funds to pay for its share of the expenses and so decided once again to dip into his federal slush fund, a/k/a the health center budget. Parisi transmitted Newell's request to Frances Neptune, the IHS bookkeeper, who drew up a check for $33,000. After the payment was approved by two tribal council members, it was picked up by Joseph Socobasin, the Tribe's lieutenant governor and delivered to the Joint Tribal Council. This money was never returned to the health center.
As he neared the end of his term, Newell must have realized that the game was up, as the Tribe's financial situation had become increasingly precarious at the same time that federal investigators were closing in on him. In the spring of 2006, the situation had become so dire that in order to meet the Tribe's payroll obligations, Newell directed Parisi to transfer funds from the tribal employees' 401K account, and directed the account bookkeeper not to file the mandatory report with the company that managed the 401K program. Parisi also directed the payroll clerk to pay only net salaries, meaning that state and federal tax withholdings, 401K contributions, state garnishments for child support or back taxes, and rent (for those employees who lived in HUD housing) were not paid. Among the sources tapped to cover payroll was a DOJ COPS grant for the Tribe's police department. The grant's remaining $30,000 of unspent funds was pressed into service to meet the Tribe's payroll obligations. When Newell left office in September, after losing the election to William Nicholas, the Tribe only had enough money left to pay one person's salaryNewell's.
When Newell stepped down as governor, "the Tribe's employees had not been paid in two weeks, worker's compensation payments had not been made, vendors and programs were owed over $3 million, and the Tribe owed federal programs $1.7 to $1.8 million." In addition, the health centerregularly raided by Newellhad outstanding debts of approximately $850,000. An audit subsequently revealed that the Tribe had no cash available, owed other *9 funds approximately $1.6 million, lost $2 million from its general fund, and had once again overspent its general assistance budget by approximately $1.1 million.
In the spring of 2008, Newell and Parisi were charged by indictment with thirty counts of misapplying federal funds, making false statements to federal agencies, submitting false claims, and misapplying retirement, police, housing authority and other program funds, as well as conspiracy to defraud the United States.[6]

C. Trial
At trial, Newell argued that he believed in good faith that he had the authority to act as he did, and that his intent had been to help the Tribe's impoverished and needy residents. Parisi argued that he was an outsider who simply did as Newell instructed. The jury found Newell guilty of all counts except count 10, and found Parisi guilty of counts 1, 5, 8, 9, 11-15, 29 and 30. Both defendants moved for acquittal, and Parisi moved for a new trial. Both defendants' motions were denied by the district court.
Newell's guideline range was determined to be 151 to 188 months. The court sentenced him instead to concurrent 60 month terms on counts 2, 3, 7-9, 11, 29 and 30, and concurrent 31 month terms on counts 1, 4-6 and 12-28, followed by three years of supervised release. Parisi's guidelines range was determined to be 51-63 months. The court sentenced him to a year and a day, also followed by three years of supervised release. In addition, under the Mandatory Victim Restitution Act (MVRA), codified at 18 U.S.C. § 3663, the court imposed a restitution order of $1,741,876.18 on Newell and $1,602,516.13 on Parisi, payable jointly and severally.[7]
This appeal followed.

II. Did the district court have jurisdiction?
Newell, joined by Parisi, first contends that counts 1, 2, 29 and 30 fall outside the jurisdiction of the federal courts. Essentially, the appellants argue that the Passamaquoddy Tribe has negotiated agreements with the state of Maine and the federal government granting them exclusive jurisdiction over "internal tribal matters," and that the conduct charged in counts 1, 2, 29 and 30 should be understood as such.
We note that the parties appear to have conflicting understandings of the nature of the claim being raised. The government appears to construe the claim as one of "tribal sovereign immunity," and contends that Parisi, at least, has waived any such claim. Parisi, for his part, insists that the argument instead concerns our subject matter jurisdiction, and hence avoids the "[o]rdinary raise-or-waive rules" which the government seeks to enforce against him. See Caban Hernandez v. Philip Morris *10 USA, Inc., 486 F.3d 1, 5 (1st Cir.2007).[8]
As we have noted, an "objection to subject matter jurisdiction is not waivable and may be raised for the first time on appeal." F.A.C., Inc. v. Cooperativa de Seguros de Vida de Puerto Rico, 449 F.3d 185, 189 (1st Cir.2006). Even if the same claims were presented below as a sovereign immunity defense, this does not preclude the defendants from appealing to them, now, to challenge our jurisdiction. Our review is de novo. Miller v. Nichols, 586 F.3d 53, 58-59 (1st Cir.2009) ("The existence of federal subject matter jurisdiction . . . [is a] question[] of law, subject to de novo review in this court.").
Relations between the Tribe and the state and federal government are governed by an agreement that the parties arrived at after the Passamaquoddy filed suit in the 1970s, asserting claims to nearly two-thirds of Maine's land mass. The Tribe and the state of Maine eventually reached a settlement, in which the Tribe "in many respects gained the powers of a municipality under Maine law." Akins v. Penobscot Nation, 130 F.3d 482, 484 (1st Cir.1997). The settlement granted the Tribe recognition under federal law as a tribe, as well as entitlement to a portion of the income from an $81.5 million settlement fund established by Congress. See 25 U.S.C. §§ 1723-24. In exchange, the Tribe's claims to Maine's territory were extinguished, and the Tribe agreed that "with very limited exceptions," it was "subject to the laws of Maine." Akins, 130 F.3d at 485; see also Penobscot Nation v. Fellencer, 164 F.3d 706, 708 (1st Cir.1999) (noting that "Maine was permitted to extend its jurisdiction over the Nation to a greater degree than most states exercise over other Indian Tribes"). The agreement between the Tribe and the state of Maine was memorialized in the Act to Implement the Maine Indian Claims Settlement, 30 M.R.S.A. §§ 6201-14 (the "Implementing Act"). The Implementing Act was subsequently ratified by Congress in the Maine Indian Claims Settlement Act, at 25 U.S.C. §§ 1721-35 (the "Settlement Act").
Section 6206 of the Implementing Act states, in material part, that "internal tribal matters, including . . . tribal organization, tribal government, tribal elections and the use or disposition of settlement fund income shall not be subject to regulation by the State." 30 M.R.S.A. § 6206. This limitation on state jurisdiction was incorporated into the federal Settlement Act by reference. See 25 U.S.C. § 1725(f) ("The Passamaquoddy Tribe . . . [is] hereby authorized to exercise jurisdiction, separate and distinct from the civil and criminal jurisdiction of the State of Maine, to the extent authorized by the Maine Implementing Act, and any subsequent amendments thereto."). We have interpreted the Settlement Act to interpose a bar to federal jurisdiction over "internal tribal matters." See Akins, 130 F.3d at 485 ("[T]he Nation in certain capacities functions as a municipality of Maine and is reachable under state and federal law in that capacity, but when it functions as a tribe as to internal tribal matters, it is not.").
The operative question is, accordingly, whether the conduct alleged in counts 1, 2, *11 29 and 30 constitute "internal tribal matters." Newell's argument is that the government's attempt to enforce 18 U.S.C. § 666(a)(1)(A) against him reaches "internal tribal matters" because "the allocation of tribal money amongst tribal accounts only affects tribal members, not nonmembers" and concerns only matters of "tribal organization, tribal government, and the use or disposition of settlement fund income."[9] He argues that "[f]ederal jurisdiction over these allegations would be contrary to the purpose of the Settlement Acts, which is to allow the Tribe to handle internal tribal matters, particularly internal government matters."
Not surprisingly, Newell neglects to mention that Congress specifically exempted the Tribe from several federal criminal statutes in the Settlement Actbut that § 666 is not one of those exempted. See 25 U.S.C. § 1725(c). Indeed, Congress specifically included Indian Tribes within the ambit of § 666(a), which explicitly applies to agents of "Indian tribal government." These observations suggest that assertion of federal jurisdiction over counts 1, 2, 29 and 30 was not improper.[10]
Although "tribes generally retain the right to self-government, [they] are nonetheless subject to federal criminal jurisdiction of both a specified and more general nature." United States v. Boots, 80 F.3d 580, 593 (1st Cir.1996) (internal citations omitted). In Boots, the defendants were accused, inter alia, of defrauding the Passamaquoddy Reservation of the honest services of their police chief by attempting to bribe him. One of the defendants claimed that he should have been acquitted *12 "in deference to tribal sovereignty." Id. at 592. We rejected this claim, noting that the violations he was charged with "are not specific to Native Americans, but rather are of general applicability," and that even if such crimes "may involve `an independent federal interest to be protected,' . . . it is unclear that one is required." Id. at 593 (internal citations omitted).
Conspiring to defraud the United States and misapplying federal funds are, like the crimes defined by the wire fraud statute at issue in Boots, crimes of general applicability. Therefore, even were we to accept Newell's claim that there is no federal interest in how the Tribe transfers its money between its accounts, it is not clear that any "peculiarly federal interest" is in fact required for such a statute to apply to the Tribe. Id., 80 F.3d at 593. Moreover, a less tendentious description of Newell's conduct would in any case suggest that there may well be a relevant federal interest, viz. an interest in ensuring that federal grants and contracts are spent in the way the government intends them to be spent. As the Supreme Court has held, when federal agencies spend taxpayer dollars, Congress has an interest in ensuring that this money is "not frittered away in graft or on projects undermined when funds are siphoned off." Sabri v. United States, 541 U.S. 600, 605, 124 S.Ct. 1941, 158 L.Ed.2d 891 (2004) (rejecting claim that § 666(a)(2)the anti-bribery portion of the statute at issue hererequired proof of a nexus between the federal funds received and the alleged bribe). When "money can be drained off here because a federal grant is pouring in there . . . [i]t is certainly enough that the statutes condition the offense on a threshold amount of federal dollars defining the federal interest." Id. at 606, 124 S.Ct. 1941. Congress presumably agreed that there was such an interest when it made § 666(a) explicitly applicable to Indian tribal governments. Moreover, despite rather mysterious invocations of tribal self-governance, Newell has not managed to explain how holding him, qua governor of a Tribe that received millions of dollars a year in federal financial assistance, criminally responsible for extensive misuse of federal funds would interfere with a "right integral to self-government." Boots, 80 F.3d at 593.
Finally, in Akins, a case about a tribe's timber harvesting policies, we emphasized five factors that were "strong considerations" to take into account in deciding whether a dispute about tribal practices constitutes an internal tribal matter. Akins, 130 F.3d at 486-87. These factors are (1) whether the practice in question "purports to regulate only members of the tribe," or if "the interests of non-members" are "at issue"; (2) whether it "regulates the very land that defines the territory of the Nation"; (3) whether it concerns the use of a natural resource derived from the land; (4) whether it "implicate[s] or impair[s] any interest of the state of Maine"; and (5) whether construing the challenged practice as an internal tribal matter "is consistent with prior legal understandings." Id. at 486-87. Applying these factors to the current case reveals the following. First, the interests of non-membersat the very least, those of the federal agencies in ensuring that the funds they award are properly spentare clearly implicated. Second, the funds at issue include state funds (count 10 alleged misuse of state Medicaid funds). Finally, as our discussion has just indicated, prior legal understandings support our finding that the challenged conduct does not constitute an internal tribal matter.[11]
*13 Because the conduct alleged in counts 1, 2, 29 and 30 involves mismanagement of federal grants and contracts, which are subject to regulations that the Tribe is not free to ignore, we hold that the conduct alleged in these counts do not constitute internal tribal matters. We emphasize that the case before us rests on malfeasance involving federal grant money, in which the federal interest is clear. It would be a different case if the counts attempted to apply § 666 to mismanagement of settlement fund income. We express no opinion as to whether such a prosecution would or would not implicate the internal tribal matters exception to federal jurisdiction under the Implementing and Settlement Acts.

III. Was the evidence sufficient?
We now turn to Parisi's contentions that the evidence failed, in several key respects, to sufficiently support the jury's verdict. "We review a sufficiency claim de novo, drawing all reasonable inferences in favor of the verdict to determine whether a rational jury could find each element of the crime beyond a reasonable doubt." United States v. Scott, 564 F.3d 34, 39 (1st Cir.2009).

A. Count 1
Parisi challenges the sufficiency of the evidence supporting his conviction under count one, for conspiracy to misapply government property in violation of 18 U.S.C. § 666(a)(1)(A), and to misapply the funds and assets of a health care program, in violation of 18 U.S.C. § 669.[12] To prove its case, the government had to show beyond a reasonable doubt that "(1) a conspiracy existed; (2) the defendant knew of and voluntarily participated in the conspiracy; and (3) there was an overt act in furtherance of the conspiracy." United States v. Munoz-Franco, 487 F.3d 25, 45 (1st Cir.2007).
Parisi challenges his conspiracy conviction under heading (1). Parisi argues that a conspiracy consists of an agreement between two or more individuals to disregard or disobey the law, United States v. Drougas, 748 F.2d 8, 15 (1st Cir.1984), and that simply doing what his employer asked of him was insufficient to establish such an "agreement." The question is thus whether the evidence was sufficient to allow a rational jury to conclude, beyond a reasonable doubt, that Parisi and Newell came to an agreement to "disregard or disobey" §§ 666(a)(1)(A) and 669, i.e., the statutes prohibiting the misapplication of government funds generally and the funds and assets of a health care benefit program specifically.
We have noted in similar circumstances that "[a] formal agreement [between co-conspirators] is not required; rather `[t]he agreement may be shown by a concert of action, all the parties working together understandingly, with a single design for the accomplishment of a common purpose.'" Munoz-Franco, 487 F.3d at 45-46 (internal citation omitted) (quoting Am. Tobacco Co. v. United States, 147 F.2d 93, 107 (6th Cir.1944)). In that case, employees of a bank and a development company were convicted for conspiring under 18 U.S.C. § 371 to commit bank fraud, misapply bank funds and make false entries in the books and records of the bank. Id. at 45. We dismissed their sufficiency of the *14 evidence challenge, noting that the two bank officials "directly supervised" and "worked closely with" the developer's loans, that the developer and his employee "submitted many certifications for work not yet completed," that one of the bank officials "repeatedly approved" those certifications, that the same bank official "met frequently" with the developer's employee regarding the status of their business ventures, and that the bank officials failed to disclose material information to the bank's Board of Directors. We held that this was sufficient to allow a jury to infer an agreement among the four defendants to defraud the bank. Id. at 46.
The nature of the evidence in this case is similar. The evidence presented at trial showed, for instance, that Newell channeled money from the accounts of various federally funded programs into non-approved uses. These "interfund transfers" were recorded as "loans," and while some were ultimately repaid, others were not. Some of these expenditures went toward paying payroll and general assistance, as well as the salaries of "ghost employees," individuals who either no longer worked at the various grant-funded programs, or did not work for the time claimed. Parisi signed off on financial status reports filed with the federal agencies that were funding the programs, certifying that the money was spent in accordance with the grant's terms. Parisi was well aware that the grant money could not be used indiscriminately; indeed, he was repeatedly told as much by the fund administrators themselves. Nevertheless, Parisi continued to divert federal grant funds, including funds provided by SAMHSA intended for the Tribe's health center, to payroll and tribal government expenses. Parisi promised bookkeepers at these federally-funded programs that the ghost employees would be removed from payroll, but that did not happen. Similarly, Parisi assured the manager of the Tribe's health center (funded by federal SAMHSA grants) that the diverted funds would be repaid, although very little ultimately was. This conduct persisted for a period of nearly three years.
The evidence presented against Parisi was sufficient to establish that even if there was no express agreement with Newell, nonetheless there was an implied or tacit agreement. Newell ordered that federal funds be misapplied and Parisi saw that they were. This was the requisite "concert of action" evincing a "common purpose." See Munoz-Franco, 487 F.3d at 45-46. We will not disturb the jury's verdict as to count one.[13]

B. Count 5
Parisi next contends that he was improperly convicted under count five, which alleged that he made a materially false statement with regard to how $215,599.43 of a SAMHSA grant intended for the Tribe's Wonahkik substance abuse and HIV prevention programs was spent. Parisi signed and submitted a "financial status report" with HHS claiming this amount was spent in accordance with grant purposes. In reality, $129,044.67 was spent to pay "ghost employees"Dennis Tomah, Sr., Dana Newell, and John Stevenswho did not work for those programs during the relevant time period. Parisi's claims on appeal are, first, that the government's evidence did not prove that *15 his submission was "knowing[] and willful[]" as required by 18 U.S.C. § 1001(a)(2) and, second, that the form was in any case not "material" as it was improperly filled out.[14]
"To establish a violation of 18 U.S.C. § 1001, the government must prove that the defendant knowingly and willfully made or used a false writing or document, in relation to a matter within the jurisdiction of the United States government, with knowledge of its falsity." United States v. McGauley, 279 F.3d 62, 69 (1st Cir.2002). "Willfulness . . . means nothing more in this context than that the defendant knew that his statement was false when he made it or . . . consciously disregarded or averted his eyes from its likely falsity." United States v. Gonsalves, 435 F.3d 64, 72 (1st Cir.2006).
Parisi contends that the government produced no evidence showing that he knew that Tomah, Newell and Stevens had not worked in the Wonahkik program during the specified time. The form referenced a period of time prior to Parisi's employment at the reservation, and the jury acquitted Parisi of actually misapplying those particular funds (count three).
An examination of the trial transcript reveals the following: at trial, Faye Socobasin (the tribal bookkeeper who actually filled out the form that Parisi later signed) was asked by the prosecutor if she had conversed with "either" Parisi or Newell about the inappropriate use of the funds. She said she had, and the prosecutor continued, "so you did have a conversation with Robert Newell about this?" to which she replied, "Yes." The prosecutor then asked if she discussed the matter with Parisi, and she replied that "with Jim Parisi, Iwhat I can remember is I just did the 269 [the financial status report] and told him that it had to be signed." The prosecutor then went on to establish that Parisi in fact signed the 269 form.
Three days later, Linda Lewey, the Tribe's federal grant compliance officer, testified that Parisi was present at two meetings during which the issue of what to do about the unused money in the SAMHSA grant was discussed. The first meeting was apparently in December of 2003, when the decision was taken to request permission from HHS to "roll over" the unused money into the next fiscal year's budget. Lewey appears not to have been questioned as to what, specifically, transpired at the second meeting. As before, the prosecutor moved immediately to discuss whether Parisi had in fact signed off on the fraudulent financial reports.
The most specific testimony on the issue of Parisi's knowledge of the falsehoods contained in the 269 form appears to have been provided by Roger Paul, the Wonahkik program coordinator. The prosecutor asked Paul whether he ever discussed payment of non-program employees with Parisi. His reply was: "I don't remember that issue exactly. There were many occasions I spoke to Mr. Parisi, and there was one occasion I spoke to Mr. Parisi about the finances, and I remember Mr. Parisi saying, well, that's what Governor Newell wants done, and that's why we're doing it this way." However, this statement is ambiguous in at least two key respects. First, Paul testified only that he discussed "finances" with Parisi. And, second, it is unclear when Paul had this conversation *16 with Parisi. Even if Paul's testimony is sufficient to show that Parisi knew of the unauthorized use of SAMHSA funds, if the revelation occurred after the false 269 form had already been filed, it would shed little light on the crucial question of whether Parisi knew the form to be false at the time of filing.
The evidence the government amassed as to Parisi's guilt on count five clearly establishes that Parisi signed the 269 form, and that the 269 form misrepresented that certain expenses were properly charged to the SAMHSA grant. However, the evidence as to whether Parisi at this point knew that the information he was filing was materially incorrectthat Tomah, Newell and Stevens had not worked for Wonahkik in FY 2003appears to be skimpy at best. The time period in question was prior to Parisi's employment with the Tribe, and we see no reason to believe that he knew, within a few months of his arrival, where every tribal member had worked in the previous fiscal year. Conversely, of course, the inference of knowledge becomes increasingly pressing as Parisi became more and more deeply involved with, and received warning after warning about, Newell's on-going financial tomfoolery.
Perhaps one could conclude from the evidence presented that it was possible that Parisi knew the 269 form to contain false statements. But we do not see how a reasonable person could view the evidence as establishing such knowledge beyond a reasonable doubt. Accordingly, we find that the evidence was not sufficient to convict Parisi under count 5.[15]

C. Counts 12-15
Parisi was convicted of counts 12-15, which assert that Parisi filed fraudulent claims for reimbursement to SAMHSA officials in the fiscal year ending on September 30, 2005, in violation of 18 U.S.C. § 287.[16] Parisi challenges his convictions on these counts because he claims that the government failed to prove that the forms at issue were material. They were not material, Parisi claims, because one of themthe form underlying count 12was returned to him "because it was not in a format in which [HHS] was willing to review it," and because the government did not pay the claims listed on the forms underlying counts 13-15.
The plain language of § 287 makes no mention of materiality as an element of the offense. Parisi argues that we should nevertheless read materiality into the statute, as the Eighth and Fourth Circuits have done. See United States v. Adler, 623 F.2d 1287, 1291 n. 5 (8th Cir.1980); United States v. Snider, 502 F.2d 645, 652 n. 12 (4th Cir.1974). In contrast, the Fifth, Ninth, Tenth and Second Circuits have held that § 287 does not require proof of the materiality of the false statement. See United States v. Upton, 91 F.3d 677, 685 (5th Cir.1996); United States v. Taylor, 66 F.3d 254, 255 (9th Cir.1995); United States v. Parsons, 967 F.2d 452, 455 (10th Cir. 1992); United States v. Elkin, 731 F.2d 1005, 1009-10 (2d Cir.1984), overruled on *17 other grounds by United States v. Ali, 68 F.3d 1468 (2d Cir.1995). Finally, the Third Circuit has split the difference and concluded that materiality sometimes is, and sometimes is not, an element under § 287. See United States v. Saybolt, 577 F.3d 195, 200 (3d Cir.2009).
This case does not require us to express a view as to whether materiality is an element under 18 U.S.C. § 287. This is because Parisi's claim cannot succeed either way. As we have noted in other statutory contexts, a statement need not actually deceive to qualify as "material." Rather, "materiality requires only that the fraud in question have a natural tendency to influence, or be capable of affecting or influencing, a government function. The alleged concealment or misrepresentation need not have influenced the actions of the Government agency, and the Government agents need not have been actually deceived." United States v. Corsino, 812 F.2d 26, 30 (1st Cir.1987) (citing United States v. Markham, 537 F.2d 187, 196 (5th Cir.1976)); see also United States v. Moran, 393 F.3d 1, 13 (1st Cir.2004).[17]
It is thus clear that Parisi's claims would be unavailing even were we to read materiality into § 287. The forms Parisi submitted were expressly designed to cause the SAMHSA administrators to pay on claims that were not authorized by the terms of the SAMHSA grant. Although the 270 form at issue in count twelve was returned to Parisi because it was improperly formatted, it contained the substance of the relevant false claims, which substance was re-submitted several days later in the correct format.[18] As our precedent on materiality makes clear, that SAMHSA administrators were not ultimately deceived into paying out on the fraudulent claims at issue in counts 12-15 does not bear on the materiality of the fraudulent misrepresentations. Corsino, 812 F.2d at 30. For these reasons, the evidence was sufficient to show that the misrepresentations contained on the forms underlying counts 12-15 were "material."[19]


*18 D. Counts 1, 8, 9, 11, 29, 30
Finally, Parisi attacks his conviction under counts 1, 8, 9, 11, 29 and 30 on the grounds that the government failed to prove "the necessary criminal intent of acting willfully." The relevant statutes are §§ 666(a)(1)(A) and 669; the former alleges that Parisi "intentionally misapplie[d]" property, whereas the latter alleges that he "knowingly and willfully" embezzled, stole or converted the assets of a health care benefit program. Parisi insists that he had "no motive to disobey or disregard the law, as he gained no benefit from the transfers."
Parisi's argument is that in order to obtain a conviction under either of these statutes, the government needed to show that he acted "willfully," meaning that the government had to show that he acted with an illicit motive. See Bryan v. United States, 524 U.S. 184, 192 n. 12, 118 S.Ct. 1939, 141 L.Ed.2d 197 (1998) (explaining that the term "willful" in a criminal statute "generally means an act done with a bad purpose."). Parisi supports his contention by suggesting that when allegedly fraudulent acts are not "themselves wrongful," then the government must additionally show illicit motive. See Fed. Deposit Ins. Corp. v. Elder Care Servs., 82 F.3d 524, 527 (1st Cir.1996) (noting that "[n]ormally, a party suggesting fraud or bad faith is expected to point to the misconduct (lies, rigged account books, self-dealing by a fiduciary) that reflects the bad faith or constitutes the fraud," but acknowledging that "on some occasions the inference of fraud or bad faith might be compelled by the combination of motive and outcome.").
There appears to be scant law on the necessary mens rea under either §§ 666(a)(1)(A) or 669, and we do not attempt here to define the precise criminal intent required by these statutes. In particular, we do not express any view as to whether the government is required to prove a self-interested motive under either § 666(a)(1)(A) or § 669. It is sufficient for our purposes to note that, even if Parisi's argument were correct, the evidence presented was sufficient to support a finding of illicit motive. After all, Parisi evidently did have a "motive to disobey or disregard the law," and derived a very concrete benefit from doing so: continued employment with the Tribe. Although not the direct beneficiary of the financial maneuvers he executed on Newell's behalf, Parisi benefitted indirectly by avoiding the fate of others who protested and subsequently found themselves out of a job. Thus, even if proof of an illicit motive or personal benefit was requiredan issue we do not resolve todaythe existence of such a motive or benefit was supportable from the facts. We discern no error in the jury's verdicts on this score.

IV. Were the Pinkerton instructions misleading?
Both appellants contend that the district court erred in twice giving the *19 jury a Pinkerton instruction because doing so could have misled the jury. When an appellant claims that a jury instruction would "tend[] to confuse or mislead the jury on the controlling issues," we review for abuse of discretion. United States v. Silva, 554 F.3d 13, 21 (1st Cir.2009) (quoting United States v. Ranney, 298 F.3d 74, 79 (1st Cir.2002) (internal quotation marks omitted)). In assessing a challenge to a trial court's jury instructions, we must bear in mind that "[a] trial judge has broad discretion in deciding how best to communicate complicated legal rules to a lay jury." DeCaro v. Hasbro, Inc., 580 F.3d 55, 63 (1st Cir.2009). In addition, "[w]hen reviewing a district court's instructions to the jury, we look at the charge as a whole, not in isolated fragments." United States v. Taylor, 54 F.3d 967, 976 (1st Cir.1995); United States v. Garcia-Pastrana, 584 F.3d 351, 385 (1st Cir.2009).
A Pinkerton instruction tells the jury that they may hold a defendant liable for a criminal offense in which the defendant did not personally participate if it was committed during the course of and in furtherance of the conspiracy of which he was a member. See Pinkerton v. United States, 328 U.S. 640, 645-48, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946); United States v. Hansen, 434 F.3d 92, 103 (1st Cir.2006). The district court gave the jury a Pinkerton instruction once when instructing on counts 29 and 30, and again when instructing on counts 3, 7, 8, 9, 10 and 11. Both Newell and Parisi objected before the court instructed the jury, and Parisi objected again after the instructions were given.
Appellants argue that by giving the Pinkerton instruction twice, the court created an undue risk that the jury would draw the inference that a person who had committed the substantive offense must have been a conspirator as well. See United States v. Sanchez, 917 F.2d 607, 612 n. 4 (1st Cir.1990) (cautioning against automatically providing a Pinkerton instruction in cases "where the jury is being asked . . . to infer, on the basis of a series of disparate criminal acts, that a conspiracy existed"). But see United States v. Wester, 90 F.3d 592, 597 (1st Cir.1996) (rejecting challenge to Pinkerton instruction on grounds that in some cases "some interplay between the jury's assessment of guilt on the substantive counts and the conspiracy charge is both natural and appropriate," and that "the fact that substantive crimes were carried out by the defendants, following discussions between them, may well make the fact of agreement more likely").
As the government notes, the two Pinkerton instructions were not duplicative, but rather were addressed to two distinct sets of offensesthe misapplication of tribal funds in counts 29 and 30 and the misapplication of government and health care funds in counts 3, 7, 8, 9, 10 and 11. Even if giving the instruction twice created a risk that the jury would improperly infer the existence of a conspiracy, there was a converse risk that failing to adequately instruct the jury that vicarious liability was available on these distinct sets of charges would itself have misled the jury. (The appellants do not contend that Pinkerton liability was in fact impermissible on either set of charges). Moreover, it is worth bearing in mind that the appellants were facing a thirty-count indictment, alleging violations of five separate statutes in dozens of transactions occurring over the span of approximately four years. The trial took eleven days, and the jury instructions alone occupy approximately forty pages in the trial transcript. Under these circumstances, it was well within the court's discretion to decide whether providing the Pinkerton instruction twice would serve to clarify or to confuse.


*20 V. Were specific unanimity instructions required?
Many of the counts in the indictmentspecifically, counts 2, 7, 8, 9, 11, 29 and 30alleged multiple fraudulent transactions. Each of these counts listed multiple instances of the misapplication of funds occurring within discrete one-year windows. The appellants now object that the structure of the indictment was duplicitous and violated their right to a unanimous verdict. See Fed.R.Crim.P. 31(a). The gist of the appellants' complaint is that counts 2, 7, 8, 9, 11, 29 and 30 of the indictment allowed the jury to vote to convict even though they may have disagreed as to which specific acts of intentional misapplication were proven beyond a reasonable doubt. Some of the jurors could have thought, for instance, that the appellants had intentionally misapplied funds on only a particular subset of occasions, whereas other jurors could have thought that they had misapplied funds on a different subset of occasions. Despite this disagreement, the jurors could still have all agreed that the government had proven that appellants had intentionally misapplied at least some funds, and voted to convict on that basis. The question is whether unanimity on that proposition would be sufficient to sustain the convictions.
Normally, "[a] party's entitlement to a unanimity instruction presents a question of law," meaning that "the district court's answer to that question engenders de novo review." United States v. Lee, 317 F.3d 26, 35 (1st Cir.2003). However, in this case, neither Newell nor Parisi raised the issue below, so we review for plain error. United States v. Pagan-Santini, 451 F.3d 258, 267 (1st Cir.2006); United States v. Puerta, 38 F.3d 34, 40-41 (1st Cir.1994). Plain error is established by showing not only that error occurred, but that it was plain or obvious, violated substantial rights, and "seriously affected the fairness, integrity, or public reputation of judicial proceedings." United States v. Perez-Montanez, 202 F.3d 434, 442 (1st Cir.2000) (quoting United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)).
The characterization of the issue as one of jury "unanimity" is in some respects misleading. No one disputes that conviction requires unanimous agreement amongst the jurors. The issue is rather what it is that they must be unanimous about. This question is subtle and difficult, and raises two closely related sets of issues. The first is: when is a disputed facte.g., whether the crime occurred on a Monday or a Tuesday, with a knife or a gun, against this or that victimone that the jury must unanimously agree upon, and when is it merely dispensable detail? And the second is: when is a defendant's conduct one violation of a statute, and when is it many?
Although the basic issue raised in this portion of the appeal concerns the second questionpotential duplicity in the indictmentthe government devotes substantial energy to resisting the appellants' argument on grounds that proof of a specific transaction is not an element under the relevant statutes. But, as we now explain, even if not always in the most perspicuous manner, our cases have distinguished between unanimity as to a crime's elements and unanimity as to a crime's instances.

A. Unanimity as to a crime's elements
The government points us toward United States v. Lee, 317 F.3d 26 (1st Cir. 2003). In Lee, the defendant was convicted under 18 U.S.C. § 1029(a)(3), which prohibited possession of "fifteen or more. . . counterfeit or unauthorized access devices." Lee claimed that the jury was *21 required to agree on which fifteen unauthorized credit cards he actually possessed. After considering the statutory text, relevant legal traditions, the structure of the law, its legislative history and implications for unfairness, see Lee, 317 F.3d at 37, we, on de novo review, rejected the claim and held that "the identity of the particular devices possessed by a defendant is not an element" under 18 U.S.C. § 1029(a)(3). Id. at 40. We cautioned, however, that "[a]scertainment of the level at which unanimity is required . . . tends to be offense-specific." Id. at 37.
The government insists that Lee controls the outcome here as well. If so, then the appellants' claims are doomed. If a claim fails under de novo review, then it must of course also fail under plain error review. So the question is whether Lee governs. It does not.
The government fails to appreciate that the appellants are not contending that the jury had to be given a specific unanimity instruction because proof of a specific transaction is an element of § 666(a)(1)(A), i.e., that the government must in every prosecution under § 666(a)(1)(A) show a single, unambiguous qualifying transaction. What the appellants are claiming is rather that the indictment brought against them bundled multiple discrete violations of the statute under single counts, meaning that, in the absence of a specific unanimity instruction, it is unclear which (if any) of the referenced crimes commanded the jury's unanimous assent. This claim is fundamentally not about the "elements" of § 666(a)(1)(A); it is about the structure of the indictment. See United States v. Holley, 942 F.2d 916, 927 (5th Cir.1991) (distinguishing alternative mentes reae for a single killing from "the situation where a single count as submitted to the jury embraces two or more separate offenses, though each be a violation of the same statute").[20]
This latter issue was not broached in Lee. The statute at issue in Lee, 18 U.S.C. § 1029(a)(3), defined the crime in terms of possession of "fifteen or more" unauthorized credit cards. The text of the statute thus supported our finding that the statute did not consist of "fifteen acts of possessing an unauthorized credit card, but, rather, a single act of possession of fifteen such devices." Lee, 317 F.3d at 39-40. As we noted, the starting point of the analysis was the text of the statute, and the statute in that case made it reasonably clear that "Congress's emphasis was not on the identity of the actual items . . . but, rather, on the possession thereof." Id. at 38.
Because § 1029(a)(3) defined an offense in terms of possession of "fifteen or more" unauthorized credit cards, it was clear that even if some of the jurors thought that Lee possessed this pile of cards while other jurors thought he possessed that pile, either way Lee could have committed no more, and no less, than a single violation of § 1029(a)(3). The same cannot be said of the indictment brought against Newell and Parisi.
The government claims that the elements of an offense under § 666 are:
1) the defendant was an agent of an Indian tribal government; 2) who embezzled, stole, fraudulently obtained or willingly converted property worth at least $5000 of tribal property [sic]; and 3) did so during a time when the tribal government received more than $10,000 in any one year from a qualifying federal assistance program.
*22 Counts 2, 7, 8, 9, 11, 29 and 30 of the indictment each contained descriptions of numerous transactions. With a few exceptions, each of these transactions would seem, on its face, to be enough to make out an independent violation of § 666(a)(1)(A). For instance, count two claimed that Newell was "an agent" of the Tribe, that the tribe "received benefits in excess of $10,000 through contract, grants, and cooperative agreements with U.S. Departments and agencies," and that he "intentionally misapplied" the following funds: (1) approximately $50,130 from the BIA Housing Improvement Program, and (2) approximately $44,000 from the Indian Township Housing Authority. In light of the government's characterization of the elements of § 666(a)(1)(A), it appears that proof of either (1) or (2) would have been sufficient to make out a complete violation. It thus appears that the appellants have a point when they complain that the challenged counts presented "two or more distinct violations of the same statute . . . lumped together in a single count," an allegation that the government, for its part, does not deny.
But if it is true that, for instance, misapplying $50,130 in BIA funds and misapplying $44,000 of Indian Township Housing Authority funds constitute discrete violations of the statute, then count two did not allege two different ways of committing one and the same crime, as in Lee, but rather alleged two entirely distinct crimes. Under these circumstances, an undifferentiated guilty verdict on count two would leave it entirely unclear whether the jurors unanimously agreed (a) that Newell had misapplied the $50,130 in BIA funds; (b) that he had misapplied the $44,000 in Indian Township Housing Authority funds; (c) that he had misapplied both; or (d) that he had misapplied either the BIA or the Housing Authority funds, although they were not in agreement as to which. In short, if a specific unanimity instruction was required, it was not because proof of which specific funds were misapplied is an "element" under § 666(a)(1)(A), but because this indictment was duplicitous in consolidating multiple complete offenses under single counts. Lee did not address this issue, and does not govern this case.
The government has insisted in this appeal that the bundled allegations merely specify "alternate means of committing a crime," and therefore no specific unanimity instruction was required. As we have noted, it is true that a jury does not need to agree upon "a single means of commission" of a crime. See Schad v. Arizona, 501 U.S. 624, 631, 111 S.Ct. 2491, 115 L.Ed.2d 555 (1991); see also Fed.R.Crim.P. 7(c) ("A count may allege that the means by which the defendant committed the offense are unknown or that the defendant committed it by one or more specified means."). However, it does not follow from the fact that unanimity is not required with respect to alternative means of committing one and the same criminal act that unanimity is not required with respect to multiple instances of the same type of criminal act.[21]


*23 B. Unanimity as to a crime's instances
The transactions detailed in counts 2, 7, 8, 9, 11, 29 and 30 occurred on various dates and involved misapplications from various sources. Count two, for instance, merely specifies that at some point between October 1, 2002 and September 30, 2003, Newell misapplied some funds from the BIA and also some other funds from the Indian Township Housing Authority. The question now is how many statutory violations the alleged conduct states.
We cannot evade this question because the Supreme Court has indicated, on at least two separate occasions, that the jury is required to unanimously agree as to which instances of a crime the defendant committed. In Schad, the Supreme Court rejected a challenge to Arizona's murder statute, which permitted conviction on a theory of either premeditation or felony murder. In his concurrence, Justice Scalia concurred with the plurality largely on grounds of legal tradition, and disavowed the plurality's explanation for why "it is permissible to combine in one count killing in the course of robbery and killing by premeditation." Schad, 501 U.S. at 651, 111 S.Ct. 2491 (Scalia, J., concurring). After all, despite their "moral equivalence," Justice Scalia noted that "[w]e would not permit . . . an indictment charging that the defendant assaulted either X on Tuesday or Y on Wednesday."[22]
Later, in Richardson v. United States, 526 U.S. 813, 815, 119 S.Ct. 1707, 143 L.Ed.2d 985 (1999), the Court held that a jury must agree unanimously as to the individual violations making up the "series of violations" element under the federal continuing criminal enterprise statute ("CCE"), 21 U.S.C. § 848(a). The majority specifically cited Justice Scalia's warning in Schad as authority for the proposition that "the Constitution itself limits a State's power to define crimes in ways that would permit juries to convict while disagreeing about means, at least where that definition risks serious unfairness and lacks support in history or tradition." Id. at 820, 119 S.Ct. 1707.
We have described the type of indictment singled out by Justice Scalia in Schad, and subsequently emphasized in Richardson, as duplicitousthat is, as one that "join[s] in a single count . . . two or more distinct and separate offenses." United States v. Canas, 595 F.2d 73, 78 (1st Cir.1979). We must, therefore, now turn our attention squarely to the question of whether the transactions bundled under counts 2, 7, 8, 9, 11, 29 and 30 were duplicitousthat is, whether they described distinct violations of §§ 666(a)(1)(A) and 669. If they did, then the failure to give specific unanimity instructions was error. If not, then not.
Determining whether the challenged counts were duplicitous is no easy matter.[23] In some cases the standard for individuating *24 crimes is obviouswe count murders, for instance, by counting bodies. But in other cases, determining how many crimes were committed is much less clear. See, e.g., United States v. Rivera Ramos, 856 F.2d 420, 422-23 (1st Cir.1988). The text of § 666 offers little guidance. Section 666(a)(1)(A) refers to "property that is valued at $5000 or more and is owned by, or is under the care, custody or control of" qualifying institutions. Section 669 refers to "any of the moneys, funds, securities, premiums, credits, property, or other assets of a health care benefits program." Neither clearly specifies the baseline unit of prosecution. Although the statute is conditioned upon the organization's receipt of over $10,000 in benefits from a Federal program "in any one year period," § 666(b), this is consistent with either (a) treating all qualifying transactions within a one-year period as aggregated together to state one offense under § 666(a)(1)(A), or (b) treating each qualifying transaction as an independent offense. The text of the statute thus fails to specify the allowable unit of prosecution.
The legislative history of § 666 indicates that it was enacted as part of the Comprehensive Crime Bill of 1984, and that it was
designed to create new offenses to augment the ability of the United States to vindicate significant acts of theft, fraud, and bribery involving Federal monies which are disbursed to private organizations or State and local governments pursuant to a Federal program.
United States v. Cicco, 938 F.2d 441, 444 (3d Cir.1991) (citing S.Rep. No. 98-225, at 369 (1983), reprinted in 1984 U.S.C.C.A.N. 3182, 3510). This history does not illuminate Congress's preferred unit of prosecution.
There is a "surprising paucity of federal case law identifying the unit of prosecution for § 666." United States v. Nystrom, No. 07-30100-03, 2008 WL 4833984, at *10 (D.S.D. Nov. 4, 2008). We have previously held that the government may aggregate transactions occurring within a one-year time period in order to meet the $5000 jurisdictional minimum of § 666(a)(1)(A). United States v. Cruzado-Laureano, 404 F.3d 470, 484 (1st Cir.2005). Cruzado-Laureano relied on a case from the Sixth Circuit, United States v. Sanderson, 966 F.2d 184, 189 (6th Cir.1992), which concluded that aggregation to meet the jurisdictional minimum is permissible when the transactions are part of a single scheme. See also United States v. Hines, 541 F.3d 833, 837 (8th Cir.2008) (interpreting aggregation of transactions for purpose of § 666 generally); United States v. Webb, 691 F.Supp. 1164, 1168 (N.D.Ill.1988) ("[A]ggregation is permissible where the thefts are part of a single plan.").
These cases are not dispositive of the present controversy. These cases were concerned with the propriety of aggregation when the transactions involved sums which fell below the jurisdictional minimum and hence did not make out independent violations of § 666. However, one of the rationales for allowing aggregation under such circumstances is to ensure that poorly motivated officials do not evade liability under § 666 simply by stealing less than $5000 at a time. See Webb, 691 F.Supp. at 1168; Sanderson, 966 F.2d at 189. Worries about opportunistic evasion of liability do not apply to transactions that involve sums larger than the statutory minimum. Since most of the bundled transactions in this case involved sums *25 greater than $5000, it is not clear whether this line of precedent would support the aggregation that occurred in this case. But see United States v. Urlacher, 784 F.Supp. 61, 64 (W.D.N.Y.1992) (holding that the unit of prosecution under § 666(a)(1)(A) is "`$5,000 or more,' from whatever source, in any one year period in which the government or agency at issue receives more than $10,000 in Federal aid.").
Fortunately, we are not completely without compass. We have previously given more general consideration to the individuation of criminal transactions. See United States v. Verrecchia, 196 F.3d 294, 297-301 (1st Cir.1999). In Verrecchia, an undercover sting caught the defendant attempting to fence stolen firearms. When he was arrested, the police discovered weapons in both his truck and in the adjacent barn. Verrecchia was subsequently charged with (among other things) one count related to the two weapons found in the truck and another for the twenty-one weapons found in the barn, under the auspices of the federal felon-in-possession statute, 18 U.S.C. § 922(g)(1). Id. at 296. Verrecchia contended that the counts were duplicitous insofar as they each alleged multiple crimes, and that it was plain error not to instruct the jury that they had to agree on which gun or guns he was shown to have possessed. Id. at 297.
We rejected the claim under plain error review, and held that "[c]ontrary to Verrecchia's contention, . . . the government could not have properly charged him with twenty-three separate crimes for the twenty-three different guns he allegedly possessed." Id. at 298. We relied in part on the Supreme Court's decision in Bell v. United States, 349 U.S. 81, 75 S.Ct. 620, 99 L.Ed. 905 (1955), and in part on the overwhelming consensus from other courts of appeals that "the simultaneous possession of multiple firearms . . . constitutes only one crime." Verrecchia, 196 F.3d at 297.
In Bell, the Supreme Court emphasized the "presupposition of our law to resolve doubts in the enforcement of a penal code against the imposition of harsher punishment." Bell, 349 U.S. at 83, 75 S.Ct. 620. Therefore, "if Congress does not fix the punishment for a federal offense clearly and without ambiguity, doubt will be resolved against turning a single transaction into multiple offenses." Id. at 84, 75 S.Ct. 620. Accordingly, after finding that the language of § 922(g)(1) (referring to "any firearm") was, like the language of the Mann Act at issue in Bell (18 U.S.C. § 2421, referring to "any woman or girl"), ambiguous as to the allowable unit of prosecution, and finding no indication of Congress's clear intent "to treat each possession of a firearm as a separate violation," we applied Bell in holding that the government properly charged him with two offenses rather than twenty-threeone for the two guns found in the truck and the other for the twenty-one guns found in the shed. Verrecchia, 196 F.3d at 298.
The government cites Verrecchia for the proposition that "[w]here separate instances of the same act are grouped in a single count . . . there is no duplicity." This is a serious misunderstanding of Verrecchia. After all, on this view, the indictment in Verrecchia should have contained only one count, encompassing all twenty-three guns. But we quite clearly held that "the indictment here correctly grouped the firearms into counts based on the place of possession." Id. at 298. Moreover, Bell, on which we relied, did not say that every instance of the same type of criminal act could be lumped together under one count. It said that, for the sake of lenity, a single transaction should not be split up into multiple offenses. The focus on the transaction as the unit of prosecution explains *26 why there were two counts in Verrecchia, rather than either one or twenty-three: possession of the guns in the truck counted as one transaction, and possession of the guns in the shed counted as another. Thus, Verrecchia permitted bundling of guns by transaction, not simply qua instances of the same type of criminal act. See also United States v. Waldman, 579 F.2d 649, 654 (1st Cir.1978) (identifying appropriate unit of prosecution under 15 U.S.C. § 77(q)a to be "separate transactions accompanied by the use of the mails"). But see United States v. Campbell, No. 90-1130, 1990 WL 151318, at *1-2 (1st Cir. July 19, 1990) (treating unit of prosecution under 26 U.S.C. § 5861(d) as possession of the "individual firearm").[24]
But if, as we held in Verrecchia, the fact that some guns are stored in a shed and others in a truck parked next to it is sufficient to constitute two distinct transactions, then there is a compelling claim that misapplying funds from agency A in March and misapplying funds from agency B in July is also sufficient to constitute two distinct transactions. Thus, far from supporting the government's position, Verrecchia appears to seriously undermine it. In light of Verrecchia, insofar as the conduct aggregated under counts 2, 7, 8, 9, 11, 29 and 30 involved distinct transactions, the counts must be deemed to bundle within their ambit multiple distinct violations of § 666(a)(1)(A).
There is thus reason to believe that the indictment brought against Newell and Parisi was constitutionally infirm. For the only sense in which it is true that a duplicitous count merely specifies "alternate means of committing" some crime is in the sense in which it is true that an indictment that alleges that A killed B on Monday, C on Tuesday and D on Wednesday specifies "alternate means" of committing a single instance of the crime of murder. The Supreme Court has made quite clear that this form of indictment violates a defendant's right to a unanimous verdict. See Richardson, 526 U.S. at 820, 119 S.Ct. 1707; Schad, 501 U.S. at 651, 111 S.Ct. 2491 (Scalia, J., concurring).
Other circuits have come to similar conclusions. In United States v. Holley, the Fifth Circuit held that an indictment that charged counts of perjury on the basis of multiple statements required a specific unanimity instruction, as the "government was required to prove dissimilar facts to show the knowing falsity of each statement." Holley, 942 F.2d at 928-29. The Holley court specifically relied on Justice Scalia's warning against duplicitous indictments in Schad. Id. at 927; see also Bins v. United States, 331 F.2d 390, 393 (5th Cir. 1964) (noting that a two-count indictment, each count of which alleged multiple acts of uttering and publishing false documents in violation of 18 U.S.C. § 1010, was duplicitous, as "[t]he filing of each false document would constitute a crime, and each should be alleged in a separate and distinct count of the indictment."). The Third Circuit has held that the unanimity requirement extends to an indictment that includes "several transactions or occurrences, *27 any of which could constitute one of the acts proscribed by the charged statutes." United States v. Beros, 833 F.2d 455, 460-61 (3d Cir.1987). The Beros court noted that "just as the sixth amendment requires jury unanimity in federal criminal cases on each delineated offense that it finds a defendant culpable . . . it must also require unanimity regarding the specific act or acts which constitutes that offense. Absent such certainty, the unanimity requirement would provide too little protection in too many instances." Id. at 461. The Seventh Circuit came to the same conclusion in a case very similar to Holley. See United States v. Fawley, 137 F.3d 458, 471 (7th Cir.1998). But see United States v. Margiotta, 646 F.2d 729, 733 (2d Cir.1981) (holding that the "policy" considerations behind the unanimity requirement suggest "that a single count of an indictment should not be found impermissibly duplicitous whenever it contains several allegations that could have been stated as separate offenses . . . but only when the failure to do so risks unfairness to the defendant.").
The risks of serious unfairness presented by a duplicitous indictment are apparent. In conditions where jurors disagree among themselves as to just which offenses the evidence supports, the defendant may nevertheless wind up convicted because the jurors agree that the evidence showed that he had committed an offense, even if it was ambiguous as to which one. See United States v. Valerio, 48 F.3d 58, 63 (1st Cir.1995). In other words, although a jury may return a guilty verdict even if the jurors disagree about how a specific crime was committed, this is quite different from allowing a jury to return a guilty verdict when they disagree even as to which crime or crimes were committed. The Supreme Court emphasized just this kind of danger in Richardson, warning that the lack of a unanimity instruction could cover up "wide disagreement among the jurors about just what the defendant did, or did not, do." Richardson, 526 U.S. at 819, 119 S.Ct. 1707; see also Beros, 833 F.2d at 460 (observing that a general unanimity instruction is likely to be inadequate "where the complexity of the case, or other factors, creates the potential that the jury will be confused.").
Secondly, in criminal cases, the government is still ostensibly required to prove the defendant's guilt beyond a reasonable doubt. See United States v. Ayewoh, 627 F.3d 914, 930 (1st Cir.2010) (Thompson, J., dissenting). In aggregating multiple instances of the same crime, the prosecution may bundle together alleged offenses that are strongly supported by the evidence with ones that are only moderately, or even weakly, supported by the evidence. If a jury does not specifically indicate that it has assented to each alleged offense, then by assenting to the bundle it has done no more than indicate its agreement with the proposition that the defendant is guilty of some, though perhaps not all, of the charged conduct. (And it may not have even indicated that much, if the jurors did not agree which offense was committedwhich, again, we simply do not know without an specific jury instruction). The consequences of conviction on that count may potentially lead to punishment over and above what the government's proof actually sustains. This is a danger we have stressed before, albeit in the context of unanimity as to a crime's elements rather than duplicity per se. See Lee, 317 F.3d at 36 (noting that "the unanimity requirement. . . helps to ensure that no defendant will be convicted unless the government has carried its burden of proving guilt beyond a reasonable doubt," and that "leaving jurors free to convict despite disagreements about critical facts will imperil *28 the integrity of the reasonable doubt standard.").
For these reasons, we hold that charges 2, 7, 8, 9, 11, 29 and 30 were duplicitous, and that the failure to provide a specific unanimity instruction was error.

C. If there was error, was it plain?
Nevertheless, despite our concern about the form of the indictment in this case, we cannot lose sight of the fact that these issues were not raised below and so are before us on plain error review. As we have noted on an earlier occasion, the hurdle of plain error "nowhere looms larger than in the context of alleged instructional errors." United States v. Paniagua-Ramos, 251 F.3d 242, 246 (1st Cir.2001).
Although we have concluded that the failure to provide a specific unanimity instruction was error and violated the appellants' right to a unanimous jury verdict, this alone is not sufficient to satisfy the rigors of plain error review. To prevail under plain error requires showing, among other things, that any error of law was plainthat is, that it was "obvious and clear under current law." Smith v. Kmart Corp., 177 F.3d 19, 26 (1st Cir.1999).
We cannot say that the error here met that standard. We note that this court has previously rejected a claim substantially similar to that brought by the appellants, albeit with fairly minimal analysis. See Pagan-Santini, 451 F.3d at 267. Moreover, as we noted in Pagan-Santini, "the law is less clear than it might be as to when juror unanimity is required in the face of alternative paths to a verdict." Id.; see also United States v. Marino, 277 F.3d 11, 32 (1st Cir.2002) (declining to find plain error in trial court's failure to give specific unanimity instruction with respect to charge of conspiracy to murder thirteen individuals on grounds of the "unsettled state of the law.") It appears not to have gotten any clearer since then.
In light of the presence of some, even if not exactly overwhelming, countervailing authority, and because of the lack of doctrinal clarity in this areathe relevant unit of prosecution under § 666(a)(1)(A), the crucial issue underpinning the appellants' claim, appears not to have been hitherto addressed by this circuitwe cannot say with confidence that any error here was plain.
We emphasize, however, that because we hold that the indictment was impermissibly duplicitous, plain error review may prove to be cold comfort for similarly defective charging instruments going forward.

VI. Should Newell have been sentenced under § 450d?
Newell claims that the district court erred in sentencing him pursuant to 18 U.S.C. §§ 666 and 669 rather than 25 U.S.C. § 450d, despite the fact that he was charged with, and convicted of, violating only the former statutes. Section 666 criminalizes the intentional misapplication of funds by an official of an organization receiving over $10,000 per year in federal funds, and carries a maximum sentence of ten years; § 669 criminalizes intentional misapplication of the assets of "health care benefit program," again setting a statutory cap of ten years imprisonment. By contrast, § 450d imposes a maximum sentence of two years for tribal officers who are convicted of misapplying funds received under the Indian Self-Determination and Education Assistance Act. Section 450d is, Newell insists, specifically directed to Indian officials unlike the general purpose §§ 666 and 669 statutes. Newell argues that the rule of lenity, as well as the principle of statutory construction favoring specific statutes over general statutes, require *29 that he be sentenced under § 450d, notwithstanding that one is usually sentenced under the statute that one is accused of violating.
"[Q]uestions of statutory interpretation that bear on sentencing" engender de novo review. United States v. Vidal-Reyes, 562 F.3d 43, 48 (1st Cir.2009).
In support of his position, Newell cites the dissenting opinion in United States v. Largo, 775 F.2d 1099 (10th Cir.1985) (McKay, J., dissenting). In Largo, the majority upheld the defendant's sentence under 18 U.S.C. § 641 for misapplying federal funds, rejecting the argument that the defendant should have been sentenced under § 450d. Id. at 1102. The dissenting judge disagreed, explaining that, because § 450d specifically applied to tribal officers and carried a lighter maximum sentence, remand for resentencing under 25 U.S.C. § 450d was required. Id.
Newell's argument is not persuasive. The statute under which Newell was charged explicitly applies to tribal officers, undermining Newell's contention that Congress intended prosecution of tribal officers to be governed exclusively by 25 U.S.C. § 450d. See 18 U.S.C. § 666(a)(1) (referring specifically to "agent[s] of . . . Indian tribal government."). Moreover, Newell's proposed application of the rule of lenity is questionable. The rule of lenity, which favors narrow construction of ambiguous criminal statutes, is of little import in choosing between the application of overlapping criminal statutes. In any case, absent a discriminatory motive on the part of prosecutors, "what charge to file . . . generally rests entirely in the prosecutor's discretion." United States v. Bucci, 582 F.3d 108, 113 (1st Cir.2009) (internal citations and alterations omitted). Consequently, we discern no error and reject Newell's request for resentencing under 25 U.S.C. § 450d.

VII. Calculation of the restitution order
Parisi objects to the restitution order of approximately $1.6 million that was entered against him. He contends that the restitution order should be remanded to the district court to correct a multitude of alleged errors. We address Parisi's contentions one by one. As is well-established, "[w]e review restitution orders for abuse of discretion and the subsidiary findings of fact for clear error. If the appellant's challenge is based on a legal conclusion, we review that conclusion de novo. Where the defendant has failed to object below . . . we review only for plain error." United States v. Antonakopoulos, 399 F.3d 68, 83-84 (1st Cir.2005) (citation omitted).

A. Who were the victims?
Parisi argues that "to the extent there were any victims, they were the [tribal] programs which did not have use of the funds." The federal agencies to whom Parisi is required to make restitution are not "victims" of his conduct, he claims, because even if "the federal government's funds were not utilized as intended, the federal government turned over the right to possess those funds when it transferred the funds to" the Tribe.
The restitution order is governed by the Mandatory Victim Restitution Act, codified at 18 U.S.C. § 3663. As it happens, the statute includes a definition of "victim": "a person directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered 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." 18 U.S.C. § 3663(a)(2).
*30 We have noted, as Parisi concedes, that governmental entities may, "without dispute," be considered victims under the MVRA. United States v. Janosko, 642 F.3d 40, 41 (1st Cir.2011). What, then, is the basis of Parisi's claim that the agencies were not victims of his conduct? The closest he comes to pressing the point is his assertion, noted above, that the agencies lost any right to possess the relevant funds once they were granted to the Tribe. But this contention misses the point entirely. If the federal agencies were harmed, it was not by losing possession of the fundsthese were, after all, grantsbut rather by not having the funds go to the designated programs.[25] For Parisi to have so much as a shadow of a claim that the federal agencies were not his victims, he would have to show why that kind of frustrated expectation is not a cognizable harm under the MVRA.[26] But he nowhere makes any such allegation. We therefore consider the claim waived, and do not address it.
Parisi spends a good deal of his discussion of restitution claiming that a restitution order would work a "fundamental unfairness." Parisi claims that misuse of federal grant money was standard practice at the Tribe long before he arrived on the scene, and that the tribal council was well aware of this fact. Parisi claims that the tribal council acknowledged, in a May 2004 meeting, both that they were seriously overspending their budget and that federal SAMHSA grant money was being siphoned off to pay their own salaries. In short, Parisi's claim is that the tribal council was entirely aware of and complicit in Newell's financial shenanigans, and that he should not be made to compensate the Tribe for the financial consequences of "decisions of the tribal political leadership, including the governor and tribal council members," particularly when he, as a tribal outsider, had no say in making these decisions.
This is an argument about whether or not what he did ought to be considered a crime, or perhaps whether it is fair to punish him while not punishing the other allegedly complicit parties. It does not appear to be an argument about whether there was error in calculating the restitution order. Parisi had an opportunity to present this argument to a jury of his peers. We will not reopen the matter now.

B. How harmful was it?
Parisi next challenges the inclusion of specific amounts in the restitution order. Parisi disputes the following five amounts: (1) $129,044 relating to the SAMHSA funds at issue in counts three and five; (2) $33,000 spent on a Racino referendum effort, as well as other transfers from the *31 health center's budget over which he had no control; (3) $15,900 of housing authority funds; and (4) a $30,000 DOJ COPS grant.[27]
Before we address these contentions, however, we must first determine whether these claims were preserved. The government claims that Parisi did not properly object to some, and possibly any, of the specified amounts at sentencing. The government claims that Parisi only objected at sentencing to (3), the Racino expenditures, and that it was raised only with respect to the guidelines calculation rather than the size of the restitution order itself. Paragraphs 71-72 of the PSR detailed the use of health center funds to pay for the Racino effort. Parisi objected to paragraph 71 on the ground that he had no authority to initiate or stop the use of the $33,000 for the Racino effort, and he repeated this contention at the sentencing hearing. The government's position appears to be that although Parisi objected to the inclusion of the Racino funds, he did not object to the "amount" imposed.
We do not know what to make of this contention. Parisi's claim was that the Racino funds should not have been included at all, from which it follows that in his view the correct amount was zero. Moreover, the government's contention that "[t]he sentencing transcript reveals only one reference to any of the four" disputed amounts is belied by the record. Parisi's objections to the PSR's inclusion of the $129,044 in SAMHSA funds can be found on pages 8-10 of the sentencing transcript. His objections to the DOJ COPS grant can be found on pages 15-16. The discussion of Parisi's involvement with transfers from the Housing Authority, although more elliptical, can be found on page 8. The objections were preserved.

1. $129,044 of SAMHSA funds
Parisi first contests the inclusion of the $129,044 deriving from the misapplication of SAMHSA funds used to pay ghost employee salaries in the early part of 2004. Parisi argues that he was not the cause of this loss under the standard announced in United States v. Vaknin, 112 F.3d 579, 589 (1st Cir.1997).
In Vaknin, we held that a "modified but for standard of causation is appropriate for restitution under the [Victim and Witness Protection Act]," meaning that "the government must show not only that a particular loss would not have occurred but for the conduct underlying the offense of conviction, but also that the causal nexus between the conduct and the loss is not too attenuated (either factually or temporally)." Id. at 589-90. We cautioned that "what constitutes sufficient causation can only be determined case by case, in a fact-specific probe." Id.[28]
*32 Parisi was acquitted of count three, which alleged the actual misapplication, but was convicted of count five, which alleged filing false statements with HHS relating to the misuse of the SAMHSA funds.[29] Although the timing is not entirely clear, it appears that the funds were disbursed no later than May 2004, i.e., before the falsified 269 forms were filed with HHS. The form therefore could not have been a "but for" cause in causing HHS to disburse the funds. See id. at 589 ("Restitution should not be ordered in respect to a loss which would have occurred regardless of the defendant's conduct."). This sum therefore should not have been included under Vaknin.[30]

2. $33,000 Racino effort and Health Center transfers
Parisi also contests the inclusion of $33,000 used by the tribal government to pay for expenses stemming from an effort to get a referendum question on the November 2007 ballot asking for voter approval of a Racino. Less specifically, he challenges the inclusion of any of the "transfers from the Health Center account used to make PTIT's payroll." Parisi does not provide a specific dollar amount, but the challenge appears to account for over $1 million of the $1.6 million restitution order.
In both cases, the gist of Parisi's argument is that he was not the "cause" of these losses, as the decision to make those illicit transfers was made by Newell and other members of the Tribe's political leadership. Newell, in many cases with the tribal council's express consent, made the decision to transfer funds from federal grants to pay for, among other things, the council members' own salaries. Similarly, the $33,000 check to the Joint Tribal Council to cover the cost of the Racino referendum effort was authorized by Newell and approved by three separate council members. It was delivered to the Joint Tribal Council by Joe Socobasin, the Tribe's lieutenant governor at the time. It does not appear that Parisi had any say in deciding whether to support the Racino effort in the first place, or where the funds to do so would come from. The entirety of Parisi's involvement with this check appears to be that Newell ordered him to have it drawn up, an order that he in turn conveyed to Frances Neptune, the Tribe's IHS bookkeeper. The Tribe's habit of playing fast and loose with federal grant money, Parisi argues, was present "before [Parisi] arrived. . . and continued after he left." Therefore, he contends, he was not a cause of the losses under Vaknin.
The uncontroverted evidence in the record does indeed suggest that Parisi may have been set up by Newell to take the fall for the Tribe's corrupt financial practices. Unfortunately for Parisi, however, it is well established that defendants can be required to pay restitution for the reasonably foreseeable offenses of their co-conspirators. Collins, 209 F.3d at 4. As *33 we noted above, even if Parisi's role was as limited as he suggestscarrying out or transmitting Newell's ordersthat is sufficient to support his conviction for conspiring with Newell to misapply federal funds. Since at some point the financial impropriety must have been glaringly obvious, and since there is no question that Parisi's co-conspirator, Newell, caused the transfers, Parisi's challenge to the inclusion of these amounts must be denied.
Parisi's reliance on United States v. Neal, 36 F.3d 1190, 1200-01 (1st Cir.1994), is misplaced. It is true that we held in Neal that a person who aided others in committing a bank robbery, but did not actually participate in the robbery itself, could not be required on that basis alone to make restitution for the full amount of the loss suffered by the bank. However, as we made clear in Neal, Congress has insisted on a different standard when a defendant has been convicted of a federal crime that "require[s] proof of a scheme, conspiracy, or pattern of criminal conduct." Id. at 1200; see also Collins, 209 F.3d at 3.[31] Unlike the defendant in Neal, Parisi was most definitely convicted of such a crime. Therefore, the reckoning of the losses that may be laid at his doorstep is substantially broader than it otherwise would have been.

3. $15,900 Indian Township Housing Authority
Parisi claims that the district court erred in including $15,900 based on transfers from the Indian Township Housing Authority. The district court, Parisi argues, explicitly conceded that Parisi was not involved in these transfers but went ahead and included them in the restitution order anyway. Our review is for abuse of discretion.
Parisi claims that the district court found that Parisi "had nothing to do" with the transfers from the Housing Authority. It is not clear from the record whether or not the district court made such a finding. The portion of the sentencing transcript on which Parisi relies shows that the parties were disputing another matterParisi's contention that the PSR should reflect that he never transferred money to accounts outside the tribal government's control. The court overruled Parisi's objection, and stated that it "takes into account the parenthetical added to paragraph 26, and with that addition believes the paragraph to be accurate."[32] However, while the referenced parenthetical does include Parisi's insistence that he had nothing to do with the Housing Authority transfers, no actual discussion of that claim is reflected in the sentencing transcript, as the discussion instead was focused on the issue of his responsibility for transferring money to non-tribal accounts.
Also bearing on our analysis here is the fact that many of these transfers from the Housing Authority's funds appear to have been undertaken exclusively by Newell for his own purposese.g., a "donation" for the marriage of "Mr. and Mrs. Tammy Newell," unspecified "loans" in small amounts, compensation to Newell himself for "mileage," and medical assistance to *34 Tribe members whose relationship to Newell and/or Parisi is unexplained. In the absence of an explicit ruling by the district court, we are left uncertain whether the district court viewed these transfers as not within the scope of the (tacit) agreement between Newell and Parisi, but mistakenly did not deduct them from the overall restitution order, or if the court concluded that they were, appearances notwithstanding, indeed part of the overall conspiracy. Particularly in light of the extensive number of transactions involved, and the factual complexity of the case, both possibilities seem equally plausible. Because of the ambiguity in the record, we remand the restitution order to the district court to clarify its disposition of the $15,900 Indian Township Housing Authority transfers.

4. $30,000 DOJ COPS grant
Parisi raises a similar contention in his reply brief as to the inclusion of $30,000 based on the misapplication of a DOJ COPS grant. The district court stated that "[b]oth sides seem to agree that the PSR is inaccurate to the extent it states that Mr. Parisi requested the transfer of those funds. The statement will not be considered by the court." Nevertheless, the restitution order included this amount. Parisi's suggestion is that this was an oversight. The government's somewhat gnostic counter-suggestion is that the district court ruled only that it "would not consider at sentencing" the PSR's claim that Parisi had requested the transfer, but that it nevertheless intended to include the $30,000 in the restitution order.
Once again, it is simply unclear on the record what the district court intended. It is possible that the district court concluded that the $30,000 DOJ COPS transfer was to be excluded from consideration. But we are not in a position to assert as much with any confidence.
However, Parisi only raised this issue in his reply brief. As we have noted, "issues raised for the first time in an appellant's reply brief are generally deemed waived." United States v. Torres, 162 F.3d 6, 11 (1st Cir.1998). Parisi attempts to circumvent this rule by characterizing the DOJ COPS grant issue as merely another instance of the restitution order including "acquitted conduct." But Parisi was not in fact acquitted of this conduct. He was convicted of count 30, which, among other things, alleged misapplication of the COPS grant. The claim is therefore procedurally defaulted.

C. Repayment of misapplied funds
Parisi next argues that the district court failed to consider "amounts that were misapplied but subsequently repaid." As before, our review is for abuse of discretion.
Parisi argues that some of the moneys that were transferred from the federal grants into the Tribe's general accounts were subsequently repaid by the Tribe. Therefore, it was error to base the restitution order on the initial quantity transferred rather than the amount net repayments. Parisi argues that the restitution order "grossly exaggerates" the actual losses, and notes that restitution must be gauged by "actual loss" to the victim, United States v. Galloway, 509 F.3d 1246, 1253 (10th Cir.2007), and that the burden is on the government to establish the amount of the loss. 18 U.S.C. § 3664(e).
Unfortunately, Parisi fails to provide any details about the alleged repayments. He fails to specify to whom the payments were made, who they were made by, when they were made, or how much was repaid. At sentencing, the district court heard from the parties as to whether those Tribe members whose retirement accounts had *35 been affected by the misuse of earmarked money had been compensated, and that the government conceded that "five or six" such individuals had in fact been repaid. Neither party put forward a specific dollar amount that had been repaid.[33]
The MVRA stipulates that "[a]ny dispute as to the proper amount or type of restitution shall be resolved by the court by the preponderance of the evidence." 18 U.S.C. § 3664(e). As it does not appear that Parisi disputed the inclusion of allegedly repaid amounts in the PSR or at sentencing, we do not discern any abuse of discretion on this score.

D. The Excessive Fines clause
Finally, Parisi claims that the imposition of the approximately $1.6 million restitution order is a violation of the Excessive Fines Clause of the Eighth Amendment because (a) the funds were spent on tribal government expenses, (b) Parisi did not personally benefit from the funds in question, (c) he does not have the resources to repay such an amount, and (d) the size of the order will "prevent him from achieving any reasonable livelihood."
We have never held that the Excessive Fines Clause of the Eighth Amendment applies to restitution. The circuits that have considered challenges to restitution orders under the Excessive Fines clause have held that where the restitution order reflects the amount of the victim's loss no constitutional violation has occurred. See United States v. Lessner, 498 F.3d 185, 205-06 (3d Cir.2007); United States v. Newsome, 322 F.3d 328, 342 (4th Cir.2003); United States v. Dubose, 146 F.3d 1141, 1145 (9th Cir.1998) (noting that "[w]here the amount of restitution is geared directly to the amount of the victim's loss caused by the defendant's illegal activity, proportionality is already built in."). This is not surprising, as restitution is inherently proportional, insofar as the point of restitution is to restore the victim to the status quo ante. Restitution is distinct in this regard from forfeiture, as Parisi concedes.
In this case, the amount of restitution ordered was the sum of the moneys that Parisi was found to have misapplied or for which he submitted false claims. Even assuming that restitution orders may be challenged under the Excessive Fines clause, the restitution ordered in this case would not therefore violate Parisi's rights.

VIII. Conclusion
For the reasons given above, we vacate Parisi's conviction on count five, reduce the restitution order entered against him by $129,044, remand for further clarification of whether the Indian Township Housing Authority transfers were meant to be included in the restitution order, and otherwise affirm.
Vacated and Remanded.
NOTES
[*]  Of the Seventh Circuit, sitting by designation.
[1]  There are two Passamaquoddy reservations; this case concerns solely the Indian Township reservation located near Princeton, Maine.
[2]  A tribe receiving BIA funds under a "638 contract" may reallocate funds intended for one program to another program funded by the contract unless the funds have a separate funding code. However, BIA funds cannot be diverted to non-BIA programs.
[3]  The Tribe's General Assistance Office was set up to provide cash assistance and other forms of assistance to needy tribal members. All general assistance had to be approved by the governor.
[4]  The individuals that Newell and Parisi paid through these grants worked for the tribal government, just not for the programs that were funded by the federal grants. In other cases, the "ghost" employees were employed at least part-time with the relevant programs.
[5]  Ronald Smith, the Tribe's outside auditor, testified at trial that interfund transfers were a "necessary part of the business" in light of the complexity of tribal finances, and that he had advised Newell and Parisi that they were consistent with accepted government practices, provided the money was returned and accounted for within "a reasonable time frame." Smith did not specify precisely what such a time frame would be, but suggested "a week" as an example.
[6]  For reference, a summary of the charges brought against Newell and Parisi is attached as an appendix.
[7]  Newell's restitution order was composed of: (1) $305,693.77 to the IHS; (2) $195,895.35 to HHS; (3) $782,693 to the BIA; (4) $45,230.05 to the EPA; (5) $30,000 to the DOJ COPS program; (6) $23,796,96 to the Maine Office of Substance Abuse; (7) $43,367.50 to the Tribe's retirement fund; (8) $215,199.55 to the tribal government; and (9) $100,000 to On Point underwriting.

Parisi's restitution order was identical, except for (4) and (8). The district court found by a preponderance of the evidence that Parisi was not responsible for the losses to the EPA, and deducted amounts tied to "acquitted conduct" from (8), lessening the amount he was required to pay the tribal government to $121,069.55.
[8]  There is some support for the government's interpretation. Prior to trial, Newell presented a motion to dismiss asserting a "privilege based upon the sovereignty and sovereign immunity of the Passamaquoddy Tribe." The motion, which was ultimately denied by the district court, cited the same statutory authority to support the "tribal sovereign immunity" claim as the (allegedly) jurisdictional argument before us on appeal. The sovereign immunity argument presented there appears to have transmogrified into an argument anent subject matter jurisdiction here.
[9]  Section 666(a)(1)(A) reads: "Whoever, if the circumstance described in subsection (b) of this section existsbeing an agent of an organization, or of a State, local, or Indian tribal government, or any agency thereofembezzles, steals, obtains by fraud, or otherwise without authority knowingly converts to the use of any person other than the rightful owner or intentionally misapplies property that is valued at $5000 or more, and is owned by, or is under the care, custody, or control of such organization, government, or agency . . . shall be fined under this title, imprisoned not more than 10 years, or both." 18 U.S.C. § 666(a)(1)(A). The referred to circumstance is "that the organization, government, or agency receives, in any one year period, benefits in excess of $10,000 under a Federal program involving a grant, contract, subsidy, loan, guarantee, insurance, or other form of Federal assistance." Id. § 666(b).
[10]  We do not say that there could never be a challenge to the enforcement of § 666(a)(1)(A) against the Penobscot or Passamaquoddy Tribes. Although conditioned on the receipt of federal funds, § 666(a)(1)(A) does not actually require the misapplied funds to themselves be federal funds. The jurisdictional question would thus be more difficult if the indictment alleged misapplication of settlement fund income, the use or disposition of which is specifically exempted by the Implementing Act. See 30 M.S.R.A. § 6206 ("[T]he use or disposition of settlement fund income shall not be subject to regulation by the State.").

However, Newell has alleged only that "tribal income includes," and that the "statute reaches" settlement fund income, but has not provided any more precise explanation of how counts 1, 2, 29 and 30 do so. What is evident is that these counts contain specific allegations of conspiracy to defraud the United States and the intentional misapplication of the Indian Township Housing Authority's Project Income and NAHASDA accounts, the Tribe's BIA 638 contract, the tribal employees' retirement fund, and a DOJ COPS grant. It is possible that some of these sources (perhaps the Tribe's retirement funds and/or the Housing Authority's Project Income account) were made up of settlement fund income. But we simply cannot say from the record whether this is so. Moreover, because Newell did not raise this issue below, there are no relevant factual findings.
We have never considered whether there might, on some facts, be a conflict between § 666(a)(1)(A) and 30 M.S.R.A. § 6206. In light of the undeveloped factual basis for the claims, we do not decide the issue today.
[11]  The other two Akins factorswhether the practice concerns the Tribe's use of its lands, or natural resources from the landsdo not apply here.
[12]  The governing conspiracy statute is 18 U.S.C. § 371, which reads, in pertinent part, "If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined under this title or imprisoned not more than five years, or both."
[13]  Parisi insists that he was not conspiring with Newell but rather "merely doing what Newell instructed him to do." This misconstrues the issue. The issue is not why Parisi may have agreed to participate in Newell's schemes; it is whether he so agreed. The answer to that question is not affected one way or the other by the observation that Parisi's only reason for being involved was because he was employed by the Tribe.
[14]  Section 1001(a)(2) provides that "[e]xcept as otherwise provided in this section, whoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully . . . (2) makes any materially false, fictitious, or fraudulent statement or representation . . . shall be fined under this title, imprisoned not more than 5 years or . . . or both."
[15]  Because we vacate the conviction, Parisi's additional contention that the 269 form was not "material" because it was incomplete and was not relied upon by agency officials is moot. It is in any case without merit, for the reasons noted in section C, infra.
[16]  "Whoever makes or presents to any person or officer in the civil, military, or naval service of the United States, or to any department or agency thereof, any claim upon or against the United States, or any department or agency thereof, knowing such claim to be false, fictitious, or fraudulent, shall be imprisoned not more than five years and shall be subject to a fine in the amount provided in this title." 18 U.S.C. § 287.
[17]  Perhaps one might wonder whether this understanding of materialitytaken from the context of § 1001is appropriate in the context of § 287. Parisi, however, is in no position to raise this argument. Parisi's argument for reading materiality into § 287 in the first place rests on the putative statutory history of §§ 287 and 1001. He argues that § 1001 includes an explicit reference to materiality because it was designed to address false statements, which, unlike the false claims penalized in § 287, was not a common law term of art that already implicitly incorporated a materiality requirement. Therefore, § 287 does not include a reference to materiality simply becauseaccording to Parisidoing so would have been otiose. We express no view on the veracity of this account of the distinction between §§ 287 and 1001, but note that if Parisi is correct, then it stands to reason that materiality under § 1001 ought to be identical to that under § 287, as the former (allegedly) only makes explicit what is anyway implicit in the latter.
[18]  The false claims at issue in counts 12-15 were requests for reimbursement from SAMHSA for the salaries of the same three tribal council members that were the subject of counts 3 and 5. None of these council members worked for the Wonahkik program. Although it is plausible that Parisi did not know of the fraudulent nature of these claims with respect to the initial 269 formfiled shortly after he began working at the Tribethese forms were filed more than a year after he was hired. Parisi does not contend that he did not know, at this point, that these individuals did not work for Wonahkik and so were not eligible to have their salaries paid by SAMHSA.
[19]  Our conclusion here means that there is no need to dwell on Parisi's complaint (which Newell joins) that the district court erred in failing to instruct the jury on materiality with respect to counts 12-15 (the counts alleging violations of § 287). Even assuming that materiality is an element under § 287, the failure to instruct the jury on materiality is subject to harmless error review. See Neder v. United States, 527 U.S. 1, 9, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) ("Unlike such defects as the complete deprivation of counsel or trial before a biased judge, an instruction that omits an element of the offense does not necessarily render a criminal trial fundamentally unfair or an unreliable vehicle for determining guilt or innocence."). Harmless error review requires ascertaining "whether it appears beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained." Id. at 15, 119 S.Ct. 1827 (internal quotation marks and citation omitted). Our conclusion entails that even if the district court erred in not giving the requested materiality instructionand we certainly do not say it didthat error was harmless as the evidence of materiality was more than sufficient to support the convictions under this standard.
[20]  The other material statute in the challenged counts is § 669. Oddly, however, the parties focus their discussion exclusively on § 666(a)(1)(A). Our analysis, accordingly, is also focused exclusively on § 666(a)(1)(A).
[21]  To conclude otherwise would be to conflate two distinct senses of "alternate means of committing a crime." The distinction is easily illustrated. Suppose, for instance, that there is some doubt as to whether A robbed B with a knife or a pistol. The government may obtain a conviction for armed robbery even if some of the jurors believe A used a knife and others believe he used a gun. But one thing the government certainly could not do is to charge A with two armed robberiesonce with the knife, and once with the gun. The appellants' complaint in this case raises the latter concern, but the government's response addresses the former.

Indeed, were the facts sufficient to support two distinct armed robberiesif, say, A robbed B with a knife and then, feeling peckish, returned at a later point and robbed B again with a pistolthe jury would be required to unanimously agree which of the crimes the government had proven. The point of specific unanimity instructions is, presumably, to preserve this right to a unanimous verdict regardless of whether the government decides to charge the two armed robberies in separate counts or to instead fold them into a single duplicitous one.
[22]  Schad was decided by a plurality. Hence, Justice Scalia's vote was necessary to the outcome.
[23]  We have not always needed to engage in extended analysis of the allowable unit of prosecution under plain error. For instance, in United States v. Leahy, 473 F.3d 401, 409-10 (1st Cir.2007), we were able to sidestep analysis of this thorny question because First Circuit precedent had already established the unit of prosecution under the relevant statute. This is not the case here; the unit of prosecution under § 666(a)(1)(A) appears not to have been previously considered by this court.
[24]  Focus on the transaction as the unit of prosecution, at least when Congress has left the issue open, is consistent with how we have treated claims of multiplicity in an indictment. Multiplicity is the converse of duplicity: it alleges that the government seeks multiple punishments for the same offense via an impermissibly repetitive indictment. In addressing multiplicity challenges, we have noted that "an inquiring court must determine whether the facts undergirding each count can be treated as a distinct unit of prosecution." United States v. Pires, 642 F.3d 1, 15 (1st Cir.2011). In applying this test, we focus on whether there is evidence that might establish that the conduct in question constitutes "separate and distinct transactions." Id.
[25]  The legislative history of § 666 makes this point clear, as § 666 was designed to cover the situation in which "even though title to the monies may have passed, the Federal Government clearly retains a strong interest in assuring the integrity of such program funds." Cicco, 938 F.2d at 445 (quoting S.Rep. No. 225, at 369 (1983), reprinted in 1984 U.S.C.C.A.N. 3182, 3510).
[26]  This is consistent with United States v. Cornier-Ortiz, 361 F.3d 29, 41-42 (1st Cir. 2004), in which we vacated a restitution order requiring the defendant, who had been convicted under § 666(a)(1)(A), to compensate HUD for intentionally misapplied funds. There, we emphasized that even though the defendant had intentionally misapplied the funds, the work that the funds were meant to pay for had actually been completed, a fact pointed out by the government's own witness. Id. at 42. In light of the lack of evidence as to any actual loss, ordering restitution under these circumstances would, we found, "be an unfair windfall to HUD." Id. In this case, however, although the misapplied funds were arguably used for the benefit of the Tribe, they were used in contravention of their specified purposes.
[27]  In his opening brief, Parisi contested the inclusion of $229,000 from count eleven, claiming that he had been acquitted on that count. The government pointed out that Parisi was in fact convicted on count eleven. Parisi conceded the point in his reply brief, but then substituted a challenge to the $30,000 COPS grant instead.
[28]  Vaknin interpreted the predecessor to the MVRA, the Victim and Witness Protection Act ("VWPA"). However, we have noted that "the causation language of the MVRA is the same as that in the VWPA, making it appropriate for us to turn to Vaknin for guidance" in interpreting the MVRA. United States v. Cutter, 313 F.3d 1, 7 (1st Cir.2002). There is a further wrinkle, however, insofar as the VWPA was amended after Vaknin to clarify that restitution may be ordered for harms caused not just by a defendant personally, but also by his or her co-conspirators as well, at least so long as those harms were "reasonably foreseeable." See United States v. Collins, 209 F.3d 1, 4 (1st Cir. 1999). Similar language is contained in the MVRA. See 18 U.S.C. § 3663(a)(2). Nevertheless, even if the eligible sources of harm are more numerous now than they were under Vaknin, this is a distinct issue from what it takes to count as having caused the harm, on which Vaknin remains authoritative.
[29]  As noted above, we vacate Parisi's conviction on this count on grounds of insufficient evidence that he knew the forms to be false.
[30]  To be clear, we do not base our conclusion here on our holding that the evidence was insufficient to convict Parisi for knowingly making false statements to HHS. See United States v. Watts, 519 U.S. 148, 156, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997) (noting, in a pre-Booker Guidelines case, that "application of the preponderance standard at sentencing generally satisfies due process.") Our conclusion is based on First Circuit precedent as to which harms are compensable under the MVRA.
[31]  The operative statutory language of the VWPA, at issue in Neal and Collins, is identical to that of the MVRA, applicable here. Compare Neal, 36 F.3d at 1200 (discussing VWPA), and Collins, 209 F.3d at 2-3 (same), with 18 U.S.C. § 3663(a)(2) (MVRA).
[32]  The parenthetical reads, "Parisi advised that he never transferred any money from a federally-funded account to an account outside the control of the [Tribe]. He only transferred federal funds between [Tribe]-controlled accounts, and always at the Governor's direction. Parisi had nothing to do with Housing Authority transfers."
[33]  Count 30 of the indictment charged Newell and Parisi of misapplying $45,824 from the Tribe's retirement fund; the judgment entered against Parisi ordered restitution in the amount of $43,367.50.
