
    UNITED STATES, Appellee, v. Jamie DWYER, Defendant, Appellant.
    No. 05-2051.
    United States Court of Appeals, First Circuit.
    Aug. 24, 2007.
    
      John S. Ferrara with whom Dalsey, Ferrara & Albano was on brief, for appellant.
    Yijay Shanker, Attorney, Criminal Division, with whom Michael J. Sullivan, United States Attorney, and William M. Welch, II, Assistant U.S. Attorney, United States Department of Justice, were on brief, for appellee.
    Before LYNCH, Circuit Judge, CAMPBELL, Senior Circuit Judge, and LIPEZ, Circuit Judge.
   CAMPBELL, Senior Circuit Judge.

Following a jury trial in the district court, Jamie Dwyer appeals from her convictions for conspiracy to commit federal program fraud, federal program fraud itself, conspiracy to obstruct justice, obstruction of justice, and making false statements. Dwyer argues (1) there was insufficient evidence for a jury to convict her; (2) her prosecution for conspiracy to commit federal program fraud was barred by the “bona fide wages” exclusion of 18 U.S.C. § 666(c); (3) the district court’s instructions regarding two of the counts impermissibly amended the indictment; and (4) the cumulative effect of the court’s allegedly mistaken denial of pretrial motions, erroneous evidentiary rulings, improper jury instructions, and the improper prosecutorial argument created a substantial risk of the miscarriage of justice. We affirm the convictions.

Background

On September 2, 2004, a federal grand jury returned a nineteen-count superseding indictment against Dwyer and co-defendants Gerald Phillips, Giuseppe Polimeni, and Luisa Cardaropoli. Eleven of the counts involved Dwyer, who was charged with the following crimes: conspiracy to commit wire fraud and federal program fraud (1); two counts of wire fraud (2, 4); four counts of federal program fraud (3, 7, 8, and 9); conspiracy to obstruct justice (10); two counts of obstruction of justice (11 and 15); and making false statements (16). The district court denied Dwyer’s motions to dismiss the indictment and to sever trial of the charges against her from those against her co-defendants. On October 1, 2004, we denied her interlocutory appeal from the denial of her motion to dismiss. A jury trial of the four defendants began on January 18, 2005. On February 28, 2005, the jury found Dwyer guilty of Counts 1, 2, 4, 7, 9, 10, 15, and 16 and acquitted her on Counts 3, 8, and 11. On June 8, 2005, 376 F.Supp.2d 6, the district court granted Dwyer’s motion for judgment of acquittal on the two wire fraud counts (Counts 2 and 4) on the ground that there was no interstate communication as required under the wire fraud statute. Dwyer accordingly stands convicted on six of the counts: 1, 7, 9, 10, 15, and 16. The district court sentenced her to concurrent three-year terms of probation on each count of conviction and further ordered her to pay a fine of $5,000 and $12,300 restitution to the city of Springfield, Massachusetts. This appeal followed.

Facts

The evidence at trial was as follows. The Massachusetts Career Development Institute (“MCDI”) is a public department of the City of Springfield. It is a skills-training center for citizens on welfare or trying to get off welfare. MCDI has a private, incorporated, not-for-profit affiliate known as MCDI, Inc. MCDI, Inc. was formed in part to use its tax-exempt status in applying for grants to fund MCDI’s programs. MCDI and MCDI, Inc. received at least eighty percent of their funds from state and federal grants. Phillips became the executive director of MCDI in 1997 and also served as police commissioner of Springfield. Polimeni was president of MCDI, Inc. MCDI and MCDI, Inc. were technically separate entities and maintained separate accounting books. In practice, however, Phillips ran both MCDI and MCDI, Inc., and Polimeni was Phillips’ closest aide in both entities. Polimeni was in charge of day-to-day operations, including payroll, at MCDI and MCDI, Inc. At times, more than 200 employees worked for the two entities.

MCDI Baking Company (“MCDI Baking”) was part of MCDI, Inc. and was run by Polimeni. MCDI Baking supplied hot breakfasts, lunches, and muffins to Springfield public schools. The Springfield School Department paid for MCDI Baking’s ingredients and labor. MCDI Baking operated out of three locations: a kitchen in MCDI’s main building, a commissary where the school department items were produced, and a warehouse. It made its own revenues through payments from the school department, money from catering jobs, and daily cash receipts from the main building kitchen where MCDI employees bought meals.

Dwyer was an administrative assistant at MCDI who reported to Phillips and Polimeni. She joined MCDI in 1982 and assisted with MCDI Baking’s personnel and financial business, including payroll, from its creation in 1992 through April 2001. Dwyer collected MCDI Baking employee timesheets; checked the calculations on them; totaled the hours; created a weekly payroll spreadsheet; faxed the information to Checkwriters (the check-writing company for MCDI and MCDI, Inc.); and distributed MCDI Baking employee paychecks. Dwyer also wrote checks (but she could not sign them), deposited checks, and balanced MCDI Baking’s checkbook. Thomas Grimes, the fiscal officer of MCDI, testified that Dwyer had no role in policy-making decisions for MCDI, no authority to hire or fire employees, and no check-signing authority. She never signed a check that issued from MCDI Baking.

Dwyer had some oversight of MCDI Baking’s muffin-making program. She took orders and calculated how many muffins had to be produced and how much labor would be needed. Every month, Dwyer compiled and sent to the school department the bills for MCDI’s production of the hot meals and muffins.

The timesheets at MCDI Baking had spaces for “time in,” “time out,” total hours, employee signature, supervisor signature, and authorizing signature. Each timesheet spanned one month, with a row for each week. Once a week, Dwyer went to the kitchen to pick up employees’ time-sheets. She checked the math totals for accuracy and entered the data onto a spreadsheet, and then generated a report for Checkwriters. If there was a discrepancy on the timesheet, Dwyer told the employee.

On August 11, 1998, Phillips sent a memo to the MCDI staff stating that when employees completed timesheets, they were representing that they had worked the stated hours, and that if they had not worked the hours claimed, they were subject to termination. On February 1, 2000, Phillips sent another memo to MCDI employees, noting that new payroll time-sheets were being implemented, explaining how to complete them, stating that they be submitted every Friday, and warning that non-submission would result in reduced pay. The memo also included a sample timesheet, which carried a warning against “perjury” and required the signatures of the employee and the employee’s supervisor. The memo had been prompted by an audit company’s finding that many time-sheets lacked employees’ and supervisor’s signatures.

In an April 27, 2000 memo, Phillips again advised MCDI staff that “filling out your timesheets properly is a very serious matter” (emphasis in original). On February 27, 2001, Phillips sent out a memo reiterating that “all timesheets MUST be completed and turned in by Friday,” that “[e]ach staff member is responsible for his or her own timesheets,” and that failure to turn in a timesheet would prevent the employee from getting paid. This memo had also been prompted by an auditor’s observation that timesheets were missing necessary signatures.

In 2000, the FBI was investigating allegations of an illegal gambling operation in Springfield. The investigation led to the arrest of several MCDI employees and also brought to light significant discrepancies between the timesheets and payroll information of several MCDI employees. Two of these employees relate to Dwyer’s present appeal: Gretchen Ortiz and Todd Illingsworth.

i. Gretchen Ortiz

Gretchen Ortiz was a student and then an employee at MCDI. In early 2000, Ortiz was evicted from her apartment. Polimeni told Dwyer via a March 30, 2000 memo to advance Ortiz $500 pay. The next day, as MCDI Baking’s check register showed, Dwyer wrote and Polimeni signed a $500 check to Ortiz as advance pay.

Ortiz was then summoned to an MCDI office, where Phillips presented her the $500 check. Phillips then took Ortiz to an apartment complex his brother owned. Ortiz gave the check to Phillips’s brother and in exchange got an apartment on the second floor of the building. She did not sign a lease, and she never wrote a rent check; Phillips paid her rent and utility bills. Ortiz and Phillips became involved in a sexual relationship. Phillips visited Ortiz at the apartment once or twice a day. Phillips also often summoned Ortiz from class or work to meet him at his office. Grimes and Dwyer, both of whom had daily contact with Phillips, testified that they were unaware of his relationship with Ortiz. Dwyer kept track of the loan to Ortiz. Initially, Dwyer caused three hours’ pay, or $24, to be deducted from Ortiz’s weekly paycheck to help repay the loan. In May 2000, however, Polimeni told Dwyer to stop deducting Ortiz’s pay. Dwyer made handwritten notes on Ortiz’s payroll documents showing that a balance of $403 was left on the loan at that time. Ortiz never repaid the remainder of the $500 loan from MCDI Baking, nor was she asked to do so.

Ortiz was first designated by MCDI Baking as a muffin-wrapper and then as a janitor. In about July 2000, Phillips, via Polimeni, told Dwyer to pay Ortiz for thirty-five hours of work per week until further notice. In accordance with this instruction, Dwyer regularly issued payroll checks to Ortiz paying her for thirty-five hours of work per week, even for weeks when Dwyer knew that Ortiz had worked fewer than thirty-five hours and even when Ortiz had either not submitted any timesheet or had submitted an incomplete one. Dwyer never told MCDI’s fiscal officers or outside auditors about Phillips’ instruction to her to pay Ortiz weekly for thirty-five hours. The payroll records reflecting payment to Ortiz for thirty-five hours of work per week were reviewed weekly by Grimes and Phillips. Grimes never questioned Dwyer about Ortiz’s hours. There was evidence that Ortiz did not work the thirty-five weekly hours for which she was paid. She was supposed to work until 5:30 p.m. each day, but in her trial testimony she recalled only one day that she actually did so. She further testified that when she was doing janitorial work, she took “about two, three hours” a day to complete it. The welfare department required that she work approximately nineteen hours a week, and Ortiz testified that though MCDI regularly told the welfare department that she had worked those hours, she did not always do so. Once or twice a week, Phillips would ask Ortiz to leave work early. On those occasions, Phillips would take Ortiz to a lake, the woods, and other places. Other employees noticed that Ortiz was being paid despite not being at work, and that she worked only occasionally and for a few months total. Phillips occasionally told Ortiz not to worry about her failure to work her required hours; he said he would take care of it.

Dwyer, the payroll clerk for MCDI Baking, picked up Ortiz’s timesheets from the kitchen and reviewed them. Starting in June 2000, Ortiz’s timesheets showed significant deficiencies. They lacked the required signatures and the “in” and “out” times. Payroll summary sheets showed that Ortiz was nonetheless consistently paid for thirty-five hours of work. For the week ending June 30, 2000, Ortiz worked only five hours. She received through Checkwriters a check for that number of hours, but she also received another check, for the same week, for thirty hours of work. The check was handwritten by Dwyer and signed by Polimeni.

By mid-July 2000, Ortiz was working few hours or not at all, but she was still receiving thirty-five hours’ pay each week. For the week ending July 7, 2000, Ortiz’s timesheet reflected that she had worked zero hours, but she was paid for thirty-five hours. That week included two days off for Independence Day, but Ortiz was paid as though she had worked every day of the week, reinforcing the inference that her weekly payments were not based on reality. Ortiz also received five days’ pay each week for the weeks in which Labor Day, Columbus Day, and a two-and-a-half-day Thanksgiving holiday occurred. Dwyer entered thirty-five hours in the total hours section of those timesheets.

On Ortiz’s August 2000 timesheet, the rows for two weeks had no hours listed, the rows for the other two weeks showed ten hours of work per week, and Ortiz did not sign the timesheet. Ortiz was nevertheless paid for thirty-five hours every week that month. In September, October, and November, Ortiz’s timesheets had no time-in/time-out documentation; they showed only totals of thirty-five hours each week, and Ortiz was paid for thirty-five hours per week.

Airline boarding passes showed that Ortiz went to Puerto Rico on November 20, 2000, but she received a full week’s pay for the week ending November 24. Dwyer received a complaint from another MCDI employee that Ortiz was paid despite having gone on vacation. In addition, though Ortiz was terminated December 1, 2000, a form in Ortiz’s personnel folder, completed by Dwyer, and a note in the folder in Dwyer’s handwriting indicated that Ortiz was nonetheless paid for the week ending December 8, 2000. Ortiz’s file contained a December timesheet for the weeks ending December 1 and 8, with no times or signatures but totals of thirty-five hours per week. For the week ending December 8, 2000, the timesheet initially recorded that Ortiz worked zero hours, but a “35” was written over the “0.” Ortiz’s check for the week ending December 8, dated December 14, was handwritten by Dwyer and signed by Polimeni. No taxes were withheld.

The entries on Ortiz’s timesheets for April, May, June, and August-December 2000 were all in Dwyer’s handwriting. Dwyer’s payroll summary sheets show that from August 25, 2000, forward, Ortiz did not submit any timesheets but was paid for thirty-five hours per week “per Mr. Phillips.” Dwyer testified that she added the “per Mr. Phillips” notation “in case Grimes inquired about me or there was an audit and I can refer back to them to refresh my memory.”

Unlike other employees, Ortiz was handed her weekly paycheck by either Phillips or Polimeni. Dwyer was aware that Ortiz’s paycheck was missing each week from the group of paychecks she received for distribution. Although Ortiz originally cashed many of her paychecks, beginning in June 2000, the endorsements on the backs of her checks were forged. Phillips and Polimeni cashed Ortiz’s checks. Ortiz never approached MCDI saying she had not received her pay. Phillips was paying Ortiz’s personal bills, including rent and utilities, through November 2000. The wages paid to Ortiz from March 2000 through December 14, 2000, totaled $7,700. Of that total, $5,300 was paid from the beginning of July through December 14, 2000, during which period, the government asserts, Ortiz worked close to zero hours.

ii. Todd Illingsworth

Todd Illingsworth was engaged to and then married to Polimeni’s daughter. Illingsworth worked at MODI from July 1992 through October 1998, at which time he left. He returned in May 1999. When Illingsworth returned to MODI in 1999, he began working at the commissary for eight dollars an hour, and, initially, he showed up to work regularly. After four or five months, however, his attendance began to diminish until he stopped showing up almost entirely. Another employee working at the commissary from late 1999-2001 saw Illingsworth only a “handful” of times. Illingsworth’s supervisor, Dennis Wilson, called Polimeni to report the absenteeism; Polimeni told Wilson not to worry because, he said, Illingsworth was using accrued compensatory time, or “comp time.” After Wilson questioned Illingsworth’s attendance, Illingsworth’s timesheets began to be kept in the MODI main building rather than at the commissary, and Wilson stopped receiving Illingsworth’s time-sheets. Previously, following normal practice, Wilson would enter the “time in” and “time out” and “total hours” figures on Illingsworth’s timesheets and would have Illingsworth sign them at the end of the week. Wilson would then take the time-sheets to Dwyer. Now Wilson had to go to the main building, where Dwyer worked, in order to complete Illingsworth’s monthly timesheets, a procedure not utilized for any other employee. Wilson received no explanation for this separate procedure. Wilson was told by Dwyer or Polimeni to fill out Illingsworth’s time-sheets which already contained weekly hour totals marked on them. Wilson would simply add daily hours so that they added up to these weekly hour totals.

In September 1999, Illingsworth’s time-sheets began to show significant deficiencies. His timesheets for September-December 1999 showed alterations to several of the time entries. On some of Illingsworth’s timesheets, the full “total hours” row was covered with correction fluid and new numbers were inserted. The handwriting in the “total hours” column of Illingsworth’s timesheets was Dwyer’s. In addition, Polimeni and Phillips, who were not Illingsworth’s immediate supervisors, nevertheless signed many of his time-sheets, in contravention of the process laid out in Phillips’ own memos. Dennis Wilson, who was his supervisor, did not sign any of his timesheets in 2000. From May 1999 through July 2000, Illingsworth was paid a total of $12,800. $5,600 of that was for time supposedly worked between March and July, 2000.

Illingsworth was in a car accident on January 18, 2000, and doctors told him not to work for three days. Timesheets for January 2000, however, show that Illingsworth was paid for full days of work on three days after January 18. According to disability forms signed by Polimeni, 111-ingsworth was unable to work until February 28. Illingsworth never showed up for work at the commissary after his accident on January 18, but he continued to be paid.

iii. FBI Investigation

The FBI first approached Dwyer at her home on March 6, 2002. Relying on an MCDI memorandum instructing employees to refer to the administration any agencies that contacted them, she told the visiting agents she could not speak to them without first consulting her supervisors. That night, Dwyer spoke to Polimeni, and the next morning, she spoke to Phillips. The FBI questioned Dwyer about Ortiz at MCDI on March 7, 2002. Dwyer told the FBI she assumed Ortiz had worked all the hours for which she had been paid, but that she could not verify that. She did not tell the FBI that she had been given a standing instruction to pay Ortiz for thirty-five hours per week, that she regularly filled in the hours on Ortiz’s timesheets, or that Ortiz was paid even after she ceased to be employed at MCDI. Dwyer also told the FBI the only preferential treatment Ortiz had received was the chance to work more hours than other employees. She did not tell the FBI that Ortiz had received a pay advance she did not repay, even though the FBI specifically asked her about pay advances and she identified several employees who received them.

The government sought evidence from MCDI related to its investigation of no-show employees through grand jury subpoenas, the first of which was issued on October 23, 2001; a consensual search; and a warrant-authorized search. Customarily, Grimes testified, when a subpoena arrived at MCDI, he would inform essential employees affected by the data collection, including Dwyer, and would assign individuals, including Dwyer, the responsibility of retrieving documents, stressing the importance of producing all documents. Dwyer and another individual, Karen Dean, were responsible for gathering documents relating to Ortiz. Dwyer, however, did not produce a copy of the memo from Polimeni about the $500 advance for Ortiz, even though the memo was in her files and the government had subpoenaed all documents “relating to things received, including, but not limited to, compensation for work performed, compensatory time, and loans received and/or forgiven,” with respect to Ortiz, among other people. Dwyer asserts that the memo was not purposely withheld and that there is no evidence that Dwyer was aware of a subpoena commanding its production. A copy of that memo, which the government found during a search of MCDI, had a copy of the check attached and contained Dwyer’s handwriting and notations indicating that the loan was for housing and had not yet been repaid.

After the government issued its first subpoena, Grimes walked into the office of Anne Scala and saw Polimeni standing behind Scala as she compared Illingsworth’s timesheets to payroll records and covered the hour entries on the timesheets with correction fluid. The covered hour entries were subsequently written over with new entries, in Dwyer’s handwriting.

The FBI conducted a warranted search at MCDI on May 21, 2003. Agents discovered a locked vault, in which they found payroll summary sheets for Ortiz that differed from the sheets produced in response to the grand jury subpoenas. The payroll documents were held in two boxes labeled “Jamie’s Office.” The documents were in manila folders along with personal correspondence in Dwyer’s name, and in-eluded handwritten notes and post-it notes addressed to Dwyer.

Similarly, payroll documents related to Illingsworth found at MODI differed from those produced by MODI in response to grand jury subpoenas. The documents seized from MODI were again in the vault in a box labeled “Jamie’s Office.” The timesheets submitted in response to the subpoenas showed more hours than the timesheets for the same weeks found in the vault. The original timesheets from May 1999 through January 20, 2000 consistently showed total hours that had been concealed by correction fluid and then altered.

In May 2000, shortly after Ortiz was put on MODI Baking’s payroll and Dwyer was asked to advance Ortiz $500 in pay, Phillips asked Grimes to prepare a detailed salary history for Dwyer from 1985 through June 1999. In a memo dated May 2, 2000, Phillips then instructed Scala to increase Dwyer’s salary by fifty dollars, to $631 a week. On June 13, 2001, Phillips again raised Dwyer’s weekly salary, by $136, to $767 per week. This memo preceded by a few months the first grand jury subpoena in the case. In July 2002, a few months after Dwyer was interviewed by the FBI, Phillips again raised her salary, to $789 per week. In just over two years, Dwyer’s salary increased by $289 per week, or approximately fifty percent, while MCDI, Inc. and MCDI Baking were losing money. Dwyer’s personnel folder documented outstanding performance evaluations throughout her time at MCDI. Grimes testified that Dwyer’s pay increases were well-deserved.

Dwyer testified in her own defense. On direct examination, she stated that she did not have any supervisory or scheduling responsibilities; that she issued Ortiz the pay advance in good faith, according to Polimeni’s instructions; and that she entered or changed times on Ortiz’s time-sheets in good faith to correct errors or reflect later-obtained information that Ortiz had worked additional hours. She conceded she had been told to pay Ortiz for thirty-five hours per week and that Ortiz eventually stopped submitting timesheets, but she stated her continued payments to Ortiz were in good faith. She testified she made notations on Ortiz’s payroll documents in case Grimes or outside auditors had questions about Ortiz’s pay. Dwyer said she told the FBI at her interview that she was unable to verify Ortiz’s hours and that she had received a complaint that Ortiz had been paid while she was in Puerto Rico. She said the FBI did not ask any follow-up questions on this point. Dwyer testified she answered all questions at the FBI interview truthfully and to the best of her recollection.

On cross-examination, Dwyer asserted it was her good-faith belief that Ortiz had worked on holidays — including July 4, Labor Day, and Thanksgiving — when MCDI was closed. She again admitted that in July, 2000, Polimeni had told her to pay Ortiz for thirty-five hours per week until further notice, and that, eventually, she was issuing Ortiz payroll checks for thirty-five hours per week without knowing whether Ortiz had worked or not.

Dwyer originally claimed she believed Ortiz had worked thirty-five hours the week ending December 8, 2000, but then she admitted writing a note in Ortiz’s folder indicating that Ortiz was terminated on December 1, 2000. Dwyer said that when she arrived at work on payday, the employees’ payroll checks would be in a mailbox outside her office, but that Ortiz’s check had always been taken out by that point. She acknowledged that, even though the FBI had asked her about payroll advances, she did not mention the payroll advance to Ortiz.

The defense argued that Illingsworth had been paid for hours he did not work because, during his employment by MCDI ending October 1998, he had built up compensatory time (time accrued by an employee which can be credited as paid time off). About a year after the government’s second subpoena to MCDI on July 11, 2002, requesting, inter alia, all records relating to compensatory time accrued, earned, or received by Illingsworth, MCDI produced a letter from Illingsworth to Phillips dated November 24,1998, a month after he had left MCDI. Illingsworth claimed in the letter he had accumulated 232 hours of compensatory time at $18/ hour through extra overtime hours he had spent painting the MCDI building. He sought payment for those hours. Attached to the letter were several sheets of notebook paper with handwritten requests to use the compensatory time. The defendants argued that Phillips refused Illingsworth’s request to be paid for compensatory time, so Illingsworth returned to MCDI in a part-time capacity. He then supposedly used the compensatory time he had accumulated in his earlier stint at MCDI. Dwyer testified at trial that it was her understanding that Illingsworth would be permitted to recoup the compensatory time he was owed.

Grimes, however, testified that MCDI’s unwritten policy was that when an employee left MCDI, he lost built-up compensatory time and could not thereafter be paid for it. Grimes did not know that Illingsworth was being paid for compensatory time and learned of that claim only after the government issued subpoenas for Illingsworth’s records. He did not know any other MCDI employee who had left MCDI and then had compensatory time restored. MCDI had no written policy regarding compensatory time, and MCDI’s time-sheets and leave forms do not mention it. FBI Special Agent Wittrock testified that, during his investigation, he became aware of no other employees who had received payment for compensatory time.

Agent Wittrock testified that Illingsworth’s November 24, 1998 letter was unusual because Wittrock had not seen any other requests for payment for compensatory time in the documents turned over during the investigation. Unlike other requests for leave, Illingsworth’s handwritten notes requesting compensation for time off had not been attached to his related timesheets. Further, while some of Illingsworth’s timesheets contained notations about compensatory time, the handwritten notes from Illingsworth did not match the timesheets. Wilson, Illingsworth’s direct supervisor, testified he never saw the handwritten individual requests by Illingsworth for application of compensatory time. Additionally, the FBI knew from its gambling investigation that Illingsworth had been at his home making phone calls on many of the occasions he said he was working and subsequently attributed his earnings to the use of compensatory time.

Dwyer testified that she thought Illingsworth had earned compensatory time for painting the MCDI building outside of regular work hours. After Illingsworth left MCDI, she said, he was entitled to be paid for his accrued compensatory time. To this end, she had helped Illingsworth write the 1998 letter to Phillips requesting payment. Dwyer denied telling Wilson to enter times on Illingsworth’s timesheets but conceded she “might have” changed the totals on his timesheets. She denied changing payroll spreadsheets.

On cross-examination, Dwyer admitted she had “corrected” Ulingsworth’s time-sheets “[t]o an extent,” so that they corresponded with his paychecks. She also testified to writing in the hours on top of correction fluid on “one or two” of Illingsworth’s timesheets. But she said she did this before the issuance of a grand jury subpoena, and that she had never altered documents “[a]fter a grand jury subpoena had been issued.”

Discussion

Dwyer argues there was insufficient evidence to support her convictions for conspiring to commit federal program fraud, committing such fraud, making false statements, obstructing justice, and conspiring to obstruct justice. She asserts there was insufficient evidence to support a finding that payments to Ulingsworth were not “bona fide wages” under 18 U.S.C. § 666(c). Dwyer additionally argues that the indictment was constructively amended by the court’s jury instructions and that the court made cumulatively prejudicial errors that resulted in the denial of due process. Each of Dwyer’s contentions fails. We address them in turn.

I. Sufficiency of the Evidence

a. Standard of Review

Dwyer moved for a judgment of acquittal at the close of the evidence, preserving her claim for review. See United States v. Van Horn, 277 F.3d 48, 54 (1st Cir.2002). We review the denial of a motion for acquittal de novo. United States v. Thompson, 449 F.3d 267, 275 (1st Cir.2006). In evaluating sufficiency, we view the evidence and credibility determinations in the light most favorable to the verdict and inquire whether a reasonable factfinder could have found the defendant guilty beyond a reasonable doubt. Id. We “need not believe that no verdict other than a guilty verdict could sensibly be reached, but must only satisfy [ourselves] that the guilty verdict finds support in a plausible rendition of the record.” United States v. Hatch, 434 F.3d 1, 4 (1st Cir.2006) (internal quotation marks omitted). The jury is free to choose among reasonable constructions of the evidence. See United States v. Hughes, 211 F.3d 676, 681 (1st Cir.2000). An insufficiency claim presents “daunting hurdles.” Hatch, 434 F.3d at 4 (internal quotation marks omitted).

b. Conspiracy to Commit and Commission of Program Fraud

i. Conspiracy to Commit Program Fraud

In order to prove the conspiracy, the government had to demonstrate an agreement to commit program fraud, Dwyer’s knowledge of and voluntary participation in the agreement, and an overt act in furtherance of the agreement. United States v. Ruiz, 105 F.3d 1492, 1499 (1st Cir.1997). The agreement need not be express; a tacit understanding may suffice. Each conspirator need not know all of the details of the conspiracy or participate in every act in furtherance of it. United States v. Perez-Gonzalez, 445 F.3d 39, 49 (1st Cir.2006). But “mere association” with conspirators or “mere presence” cannot alone establish knowing participation, United States v. Nelson-Rodriguez, 319 F.3d 12, 28 (1st Cir.2003) (internal quotation marks omitted); the defendant must be found to have shared her co-conspirators’ intent to commit the substantive offense. United States v. Llinas, 373 F.3d 26, 30 (1st Cir.2004).

From the evidence introduced at trial, the jury could reasonably have found that Dwyer had voluntarily joined in an agreement with Phillips and Polimeni to pay Ortiz from MCDI, Inc.’s payroll for hours she had not worked. Dwyer stopped deducting pay from Ortiz to repay an initial $500 loan made to Ortiz at Phillips’ and Polimeni’s request. Upon instructions from Phillips and Polimeni, she took steps to pay Ortiz regularly for thirty-five hours of work per week while knowing that Ortiz was not working those hours for MCDI Baking. In furtherance of the conspiracy, Dwyer ordered or prepared the checks and timesheets needed for the overpayments to Ortiz. Dwyer acknowledged in her testimony that she knew that Ortiz was not working the hours listed on her timesheets.

In respect to Illingsworth, Dwyer kept and filled in entries on Illingsworth’s time-sheets, and she instructed and observed Wilson complete them by writing in hours that added up to pre-entered totals. There was ample evidence from which the jury could determine that Dwyer knew Illingsworth was not working during all the hours for which he was paid.

The government argued at trial that Dwyer’s participation in the overpayments to both people was knowing and voluntary, noting that she knew the payments were excessive for the hours actually being worked at the time and disregarded MCDI’s prescribed procedures about the proper way to complete timesheets. The government pointed out that Dwyer’s own pay-raises dovetailed suspiciously with the times of her improper actions. While Dwyer denied any connection, the jury could plausibly have inferred from the timing and unusually high amounts of the raises that Phillips and Polimeni were rewarding her for her cooperation. See United States v. Gomez-Pabon, 911 F.2d 847, 853 (1st Cir.1990) (“[PJroof [of membership in a conspiracy] may consist of circumstantial evidence, including inferences from surrounding circumstances, such as acts committed by the defendant that furthered the conspiracy’s purposes.”).

Dwyer says her involvement with the program fraud was “reluctant acquiescence” rather than “voluntary participation” and claims that her “dedication and character” are inconsistent with a finding that her actions, done at Phillips’ and Polimeni’s behest, reflected any criminal intent. She argues that she simply failed to appreciate that it was wrongful to do what her bosses told her to do, hence lacked the intent to conspire to commit program fraud.

The evidence indicated, however, that she was well aware that Ortiz and Illingsworth were being paid from MCDI’s funds for improperly documented work that the two individuals never performed, and that her own activities directly furthered those irregularities. She and those she was assisting were employees of a firm that was part of a public department of the City of Springfield. In those circumstances, the jury could have inferred that she did not believe that Polimeni and Phillips could properly direct and authorize her to pay out MCDI funds to the two non-performing public employees. It is true she may have been in part influenced by the fear that if she did not go along with her supervisors’ directions, they would retaliate against her; but there was no evidence of threats, and a general concern of this kind would fall short of precluding a finding of conspiracy. Dwyer does not argue otherwise. See, e.g., United States v. Freeman, 208 F.3d 332, 342 (1st Cir.2000) (a generalized fear of harm is no defense to a conspiracy charge; evidence precluding inference of an agreement would have to show that the duress to which defendant was subject was “enough to overbear [her] will and make [her] participation in the conspiracy involuntary”).

The jury heard all the evidence, including Dwyer’s testimony, and could reasonably decide that she had knowingly and voluntarily participated and that her denial of doing so was lacking in credibility. See United States v. Maldonado-Garcia, 446 F.3d 227, 231 (1st Cir.2006) (on sufficiency review, we “may neither evaluate the credibility of the witnesses nor weigh the relative merit of theories of innocence postulated by the defendant”). There was sufficient evidence to support the jury’s verdict on the conspiracy charge.

ii. Program Fraud

Commission of program fraud in violation of 18 U.S.C. § 666(a)(1)(A) may be shown by establishing, inter alia, that a state government employee knowingly converted to the use of any person other than the rightful owner, property worth $5,000 or more belonging to the state, if the defendant’s employing agency receives at least $10,000 in federal funds within a calendar year. 18 U.S.C. § 666; see United States v. Cruzado-Laureano, 404 F.3d 470, 483-84 (1st Cir.), cert. denied, 546 U.S. 1009, 126 S.Ct. 639, 163 L.Ed.2d 517 (2005). Dwyer does not dispute that she was a state government employee and that MCDI received annually more than $10,000 in federal funds. She challenges only the finding of a knowing conversion of $5,000 or more.

In the case of Ortiz, the uncontroverted evidence was that she was paid $7,700 from March 2000 through December 14, 2000, of which $5,300 was paid from July through December 14, 2000. The evidence showed that from at least June 2000 through December 14, 2000, Ortiz was working either no or, at most, very few hours per week. The evidence also showed overpayments on occasions prior to June. We think the evidence overall permitted the jury to conclude reasonably that at least $5,000 of the $7,700 paid to Ortiz was fraudulently converted by Dwyer to Ortiz’s use.

Ortiz received, in March 2000, a $500 loan, of which she repaid only ninety-three dollars. Ortiz’s timesheets (which were in Dwyer’s handwriting for the months of April, May, June, September, October, November, and December, 2000) contained substantial, repeated deficiencies. Grimes testified that Ortiz should not have been getting paid based on the poor state of her timesheets. Despite the fact that her timesheets lacked required signatures and the “in” and “out” times, Ortiz was regularly paid for thirty-five hours of work per week. The evidence is clear that she recorded no hours of work the week ending July 7 as well as the week ending November 24 when she was vacationing in Puerto Rico. Ortiz was paid for the week of work following her termination on December 1, 2000. Ortiz’s August 2000 timesheet had no hours listed for two weeks, and only ten hours each week for the other two weeks. Nevertheless, she was still paid for thirty-five hours of work each week. In September, October, and November, Ortiz’s timesheets contained no time-in/ time-out documentation, showing only the totals of thirty-five hours each week. Additionally, Ortiz cashed her paychecks only until June, 2000, at which point the signatures on the back of her checks were forged, with Phillips and Polimeni cashing the checks. In light of all the other evidence of default, the fact that Ortiz did not fill out her timesheets, pick up her checks, or complain when Phillips or Polimeni cashed her checks, supported a reasonable inference by the jury that she was not working to any extent at this time.

Ortiz’s own testimony, indeed, tended to reinforce such an inference. She said she remembered only one occasion on which she worked until 5:30, the prescribed quitting hour. She further testified that when she was doing janitorial work, she took “about two, three hours” a day to complete it. The welfare department required that she work approximately nineteen hours a week, and Ortiz conceded that though MCDI regularly told the welfare department that she had worked those hours, she did not always do so. Moreover, Ortiz responded that she “didn’t know” when asked if she was “certain” she was still working at MCDI after she moved to Forest Street, a move made on August 1, 2000.

Dwyer insists there was no clear evidence Ortiz was overpaid by as much as $5,000 since Ortiz’s own testimony lacked any certitude as to the period or periods of time she had worked. There are no absolute records to verify the precise number of hours actually worked. But given the total payment to her of $7,700 and, in particular, the $5,300 paid during the July-December period when the evidence of her almost total absence from work was quite strong, we believe there was sufficient evidence from which the jury could reasonably infer that she was overpaid by at least $5,000. The government did not have to establish with absolute mathematical precision the number of hours Ortiz did or did not work so long as it presented evidence from which it could reasonably be inferred that she did not work sufficient hours to warrant her being paid $5,000 during the period in question. We think the evidence was sufficient to allow such an inference to be drawn. We believe a reasonable jury could have inferred that Ortiz did not perform sufficient work to justify being paid at least $5,000 of the pay she received.

Regarding Illingsworth, it was established that he was paid $7,200 in wages from May 1999 through January 2000 and $5,600 from March through July 2000, for a total of $12,800. However, beginning September 3, 1999, Illingsworth’s time-sheets became significantly deficient and around that same time, Illingsworth began missing time at work until he stopped coming altogether. He never returned to the commissary after January 18, 2000. The government thus argues that the record entitled the jury to conclude that Illingsworth was paid at least $5,000 in wages he did not earn.

The defense responds that Illingsworth was entitled to offset compensatory time from unpaid overtime work he allegedly had earlier performed for MCDI prior to his leaving it in October, 1998. Beginning in December 1997, it is asserted, Illingsworth painted the inside of the MCDI building during overtime hours. He says he was not then paid, and was, therefore, entitled to be credited with compensatory time, meaning he was entitled to take equivalent time off after he was rehired by MCDI and be paid for it. In its opening argument, the government conceded that Illingsworth seemed to have earned about 240 hours of compensatory time at $18/ hour but asserted that Illingsworth had forfeited the right to receive that income when he left his employment at MCDI in October, 1998. The MCDI Employee Policy Manual says nothing about the subject of compensatory time, and the defense acknowledges that Phillips, MCDI’s executive director, rejected Illingsworth’s request in his November 24,1998 letter to be paid for the alleged overtime painting hours. Over Dwyer’s objection, the government elicited testimony from Grimes that there was an unwritten policy at MCDI that someone who left employment at MCDI lost all accrued comp time. The government cites Grimes’ testimony in contending that the payments made to Illingsworth after leaving and being rehired by MCDI could not be justified on the basis of comp time allegedly earned during his prior employment by MCDI. The government analogizes the loss of the comp time to the loss of accrued sick leave or vacation upon leaving a particular job. The government also points out that the comp time argument was assembled only after the FBI investigation began and that Illingsworth’s supervisor, Wilson, did not see any requests for compensatory time from Illingsworth when he was supposedly-working for Wilson. The defense points to no actual agreement with MCDI whereby Illingsworth was permitted to apply comp time to the wages earned after his rehire. By creating what was essentially a false paper trail of time when Illingsworth was alleged to be working but in fact was not, Illingsworth, with the assistance of Dwyer and Illingsworth’s father-in-law, Polimeni, simply undertook to pass along to the City of Springfield the costs of work supposedly done a year and a half prior.

Given Grimes’ testimony that compensatory time could not be credited after leaving MCDI; the absence of any evidence that MCDI, in any formal or regular way, credited Illingsworth with compensatory time; the lack of proper and meaningful contemporaneous records, including time-sheets, establishing that Illingsworth’s pay for work not done was being given for compensatory time; and the further evidence indicating that the compensatory time argument was concocted after the investigation had begun, we believe the jury could have reasonably concluded that it was improper to compensate him for work he never performed in 1999 and thereafter.

Dwyer responds that while a Massachusetts statute, Mass. Gen. Laws ch. 149, § 148, prohibits “comp time” as such, it does require that an employee be paid for all wages earned. That statute states, in part:

Every person having employees in his service shall pay weekly or biweekly each such employee the wages earned by him to within six days of the termination of, the pay period during which the wages were earned if employed for five or six days in a calendar week, or to within seven days of the termination of the pay period during which the wages were earned if such employee is employed seven days in a calendar week.
[A]ny employee leaving his employment shall be paid in full on the following regular pay day, and, in the absence of a regular pay day, on the following Saturday ... and every county and city shall so pay every employee engaged in its business the wages or salary earned by him____ The word “wages” shall include any holiday or vacation payments due an employee under an oral or written agreement.... No person shall by a special contract with an employee or by any other means exempt himself from this section....

Id. Thus, Dwyer argues, MCDI could not lawfully refuse to pay Illingsworth for the compensatory time he was owed, hence there was no fraud in paying him later even if such payment was made informally under the guise of paying him for work he in fact never performed.

However, the very compensatory time policy which Dwyer argues entitled Illingsworth to be paid long after the fact would itself appear, if anything, to violate the plain language of the statute. According to the statute, Illingsworth was to be paid promptly after he performed the painting work in 1998; he was not so paid. Indeed, Phillips apparently refused his request to be paid. Instead, Illingsworth now claims he was paid later pursuant to timesheets which reflected a fictional account of work he did not perform at the times they said he did. The evidence of a policy that compensatory time was forfeited after departure from the company, coupled with Illingsworth’s failure to secure any form of official authorization from his employer to carry forward and use compensatory time in the manner now claimed — as well as the surreptitious manner in which his father-in-law Polimeni and Dwyer went about paying him after his supervisor noted that he was not, in fact, working at the times he was supposed to work — could have prompted a reasonable jury to conclude Illingsworth was not entitled to it, and that he was, at best, using an extra-legal avenue to secure what he now feels he was owed.

Dwyer’s own testimony about her belief that Illingsworth deserved his compensatory time and her role in helping Illingsworth request payment for the time in November, 1998, along with her subsequent participation in the altering of the timesheets, could also be found to indicate a desire on her part to make payments to Illingsworth even though she was aware that such belated reallocation of funds could not properly and legally be effected.

Dwyer testified that she believed Illingsworth had earned comp time for painting the interior of the building and that he wanted to be paid for that time. She testified that she assisted him in drafting the letter requesting comp time after he had left MODI. She admitted to the possibility of her having changed some of the “in” and “out” times on Illingsworth’s timesheets so that they would more correctly reflect what he had been paid, but not the hours he actually worked. Illingsworth’s immediate supervisor, Wilson, never signed any of the timesheets for his employee during 2000, thus deviating from the established MCDI policy. In 2000, Illingsworth was found at home gambling on days when the timesheets show he was supposedly working. Given Dwyer’s role in adjusting the timesheets to put them in line with the payroll sheets after the fact, her veracity could reasonably have been doubted by the jury on the issue of her good faith belief that Illingsworth was properly entitled to the belated payment. If he was, why was it necessary to participate in the creation of a false paper trial of time worked after the fact?

The jury could have reasonably concluded that Illingsworth’s failure to return to work, the lack of a formal record of his comp time, the evidence of MCDI’s non-accrual policy, and the lack of any demonstrated formal relationship between the later overpayments and the earlier absence of compensation, all indicated that he was not receiving legitimate comp wages and thus that Dwyer had participated in converting to Illingsworth more than $5,000 as required to prove program fraud under the statute.

iii. Bona Fide Wages Exception

Section 666(c) by its terms “does not apply to bona fide salary, wages, fees, or other compensation paid, or expenses paid or reimbursed, in the usual course of business.” 18 U.S.C. § 666(c); see United States v. Cornier-Ortiz, 361 F.3d 29, 33 (1st Cir.2004). Dwyer contends that her convictions for conspiring to commit program fraud and committing program fraud are barred by this exception as related to Illingsworth.

Whether wages were bona fide is a question of fact for the jury. See Cornier-Ortiz, 361 F.3d at 36. Here, the district court instructed the jury on the exception, and there was more than sufficient evidence to support the jury’s conclusion that the payments to Illingsworth were not bona fide wages. As noted, Illingsworth was engaged to and later married Polimeni’s daughter. The evidence taken in the light most favorable to the government showed he was paid repeatedly for weeks he did not work. Illingsworth was paid on days when he was out due to injury, and he continued to be paid after he stopped working. A reasonable jury could find that the payments to Illingsworth were not made in the usual course of business and thus were not bona fide. Cornier-Ortiz, 361 F.3d at 36 (payments not bona fide “if they were intentionally misapplied, as they were here via sham contracts that skirted conflict of interest rules and allowed [a corporation] to receive preferential treatment and other benefits”); United States v. Grubb, 11 F.3d 426, 431, 434 (4th Cir.1993) (bona fide wages exception inapplicable where employee “performed little work for the Sheriffs office” and did not “perform functions for the Sheriffs office on a regular basis”); cf. United States v. Mills, 140 F.3d 630, 633 (6th Cir.1998) (bona fide wages exception applicable because there was no allegation that employees “did not responsibly fulfill the duties associated with their employment”). We would add that to the extent the payments were, as was argued, not intended as wages for work actually performed but reflected some kind of informal and unauthorized compensatory time reimbursement, they were also not bona fide wages. The jury could reasonably find that the bona fide wages exception does not come into play.

c. False Statements, Obstruction of Justice, and Conspiracy to Obstruct Justice

Count Ten charged Dwyer with conspiring with Phillips, Polimeni, and Cardaropoli to obstruct and impede the government’s investigation of MCDI in violation of 18 U.S.C. § 1503(a), which provides:

Whoever corruptly, or by threats or force, or by any threatening letter or communication, endeavors to influence, intimidate, or impede any grand or pet-it juror, or officer in or of any court of the United States, or officer who may be serving at any examination or other proceeding before any United States magistrate judge or other committing magistrate, in the discharge of his duty, or injures any such grand or petit juror in his person or property on account of any verdict or indictment assented to by him, or on account of his being or having been such a juror, or injures any such officers, magistrate judge, or other committing magistrate in his person or property on account of his performance of his official duties, or corruptly or by threats or force, or by any threatening letter or communication, influences, obstructs, or impedes, or endeavors to influence, obstruct or impede, the due administration of justice, shall be punished....

The overt acts alleged in Count Ten included the backdating and alteration of Illingsworth’s timesheets; Polimeni’s allegedly making a false statement to a special agent of the FBI on January 15, 2002; Dwyer’s allegedly making false statements to the FBI on March 7, 2002; Cardaropoli’s allegedly making false statements to the FBI in February, 2003; and Phillips’ threatening Densing Abraham, a seventeen-year-old MCDI employee and potential grand jury witness, on March 11, 2003. The jury found Dwyer not guilty of conspiring with Polimeni to alter Illingsworth’s timesheets. Cardaropoli was found not guilty of lying to the FBI, and Dwyer was found not guilty of program fraud arising from the wages paid to Cardaropoli. Phillips was found not guilty of threatening Abraham. Accordingly, after eliminating the overt acts related to these counts, it can be assumed that Dwyer was found guilty of conspiracy to obstruct justice in Count 10 on the basis of the statements she gave to the FBI on March 7, 2002. Dwyer was charged in Count 15 with obstruction of justice based on those statements, violating 18 U.S.C. § 1503, and in Count 16 with making false statements. We assess the sufficiency of the evidence for these three counts in concert, as they are all based on the underlying claim of false statement.

“In order to convict a defendant of making a false statement under 18 U.S.C. § 1001, the prosecution must prove that the defendant, in a matter within the jurisdiction of the United States government, knowingly made a material statement to the government which was false.” United States v. Sebaggala, 256 F.3d 59, 63 (1st Cir.2001); see United States v. Duclos, 214 F.3d 27, 33 (1st Cir.2000).

The government argues that Dwyer knowingly and willfully made material false statements to the FBI when speaking to Agents Clifford Hedges and Susan Kossler on March 7, 2002. She told the FBI she assumed Ortiz had worked all of the hours she was paid for, but that she could not verify that Ortiz had done so. Dwyer had, however, been given a standing instruction to pay Ortiz for thirty-five hours per week; she routinely filled in the hours on Ortiz’s timesheets, noted on the payroll summary that Ortiz had worked zero hours but was being paid for thirty-five “per Mr. Phillips,” and wrote a check to Ortiz after she knew Ortiz had been terminated. She did not explain this situation to the FBI. Dwyer also told the FBI that the only preferential treatment Ortiz had received was the opportunity to work more hours than other employees. Dwyer knew, however, that Ortiz had received a payroll advance which she did not repay. Asked about payroll advances, Dwyer identified several other employees who had received them but did not mention Ortiz. The government argues that this was more than enough evidence to support the jury’s finding that Dwyer knowingly made false statements. See Hatch, 434 F.3d at 6 (“The determination as to [the defendant’s] state of mind — his belief in the untruthfulness of his statement — is one which the jury is best equipped to perform.”); United States v. Singh, 222 F.3d 6, 10 (1st Cir.2000).

Dwyer argues in response that the FBI agents did not ask any follow-up questions and did not seek more complete answers than the ones she gave. She also points out that the interview was not recorded and that no written statement was taken. Kossler testified that she did not inform Dwyer what the FBI was investigating beyond telling her that it was about MCDI and her role there. Kossler additionally testified that Dwyer volunteered that someone had once complained to her that Ortiz had been paid for a week when she was not even working, when she had been in Puerto Rico. The agent did not ask any follow-up questions on that point.

Dwyer herself also testified about the March 7 interview. She said that she had answered all questions truthfully and did not believe she was a focus of the investigation. But Dwyer did not contest that she stated that she assumed Ortiz’s hours were correct when in fact she knew of a standing order to pay her for thirty-five hours regardless of whether she worked zero hours. She also stated that she did not know of any preferential treatment when she knew Ortiz had not been required to repay a loan. She thus made affirmative false statements and did not just omit or fail to volunteer information when the FBI did not ask follow-up questions.

Further, those false statements were material. “The test of materiality is whether the false statement in question had a natural tendency to influence, or was capable of influencing, a governmental function,” Sebaggala, 256 F.3d at 65 (citation omitted). “[I]f a statement could have provoked governmental action, it is material regardless of whether the agency actually relied upon it.” Id. Dwyer’s statements were about issues at the center of the investigation. If she had been truthful about Ortiz’s standing thirty-five-hour-per-week pay schedule and the preferential treatment she received, the investigation could have been significantly shortened. We hold, therefore, that there was sufficient evidence to support Dwyer’s conviction for making false statements.

There is likewise sufficient evidence supporting Dwyer’s convictions for obstruction of justice and conspiracy to obstruct justice. In order to demonstrate obstruction of justice in violation of 18 U.S.C. § 1503, the government had to prove that Dwyer corruptly influenced, obstructed, impeded, or endeavored to influence, obstruct or impede, the due administration of justice. The government had to show that there was a pending judicial proceeding; that Dwyer had notice of the proceeding; and that she acted corruptly with the intent to influence or obstruct, or endeavored to influence or obstruct, the proceeding. See United States v. Frankhauser, 80 F.3d 641, 650-51 (1st Cir.1996).

“It is well-established that a grand jury investigation constitutes a pending judicial proceeding for purposes of § 1508.” United States v. Macari, 453 F.3d 926, 936 (7th Cir.2006). The grand jury proceeding here was underway before the government interviewed Dwyer on March 7, 2002. Grimes testified that when a grand jury subpoena came in, the group of employees, including specifically Dwyer, responsible for gathering documents responsive to it would be told of, and would know about, the existence of the subpoena. Before her interview with the FBI, Dwyer spoke with Phillips and Polimeni, both of whom, Grimes testified, would also have been aware of the existence of a grand jury subpoena. A reasonable jury could have concluded from the testimony that Dwyer had notice of the October 23, 2001 subpoena, was aware that it had been issued by a grand jury, and was further aware from the nature of the materials she was directed to gather that the grand jury’s investigation pertained to the payment of employees at MODI. The jury could also conclude that she would have known from the character of the questions the FBI subsequently put to her in her interview that matters relevant to the grand jury’s investigation were the subject of the FBI’s inquiry. Additionally, evidence that Dwyer made false statements to the FBI agents supported the jury’s conclusion that she intended to influence or obstruct the grand jury proceeding.

Dwyer argues that the government didn’t prove she knew her statements would be submitted to a grand jury. See United States v. Aguilar, 515 U.S. 593, 598-600, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995) (requiring a “nexus” between the defendant’s act and the judicial proceeding; i.e., “the act must have a relationship in time, causation, or logic with the judicial proceedings”). As we have said, however, the evidence was sufficient for a jury to infer therefrom that she was aware her statements would go to the grand jury.

In Aguilar, the government had failed to show that the FBI agents were acting as an arm of the grand jury or that it had even sought their testimony, so that the mere “uttering [of] false statements to an investigating agent ... who might or might not testify before a grand jury” was insufficient to establish a violation of Section 1503. 515 U.S. at 600, 115 S.Ct. 2357. In order to show that an FBI investigation constitutes a “judicial proceeding” for purposes of § 1503, the government must establish that the FBI was acting as “an arm of the grand jury.” Macari, 453 F.3d at 937. It must show that the agents were “integrally involved” in the grand jury investigation and that the investigation was undertaken “with the intention of presenting evidence before [the] grand jury.” Id. (internal quotation marks omitted).

Here, the government showed that the FBI was working as an arm of the grand jury by collecting evidence that was eventually presented to the grand jury. Agent Kossler testified that the grand jury investigation was underway by early 2002, and the FBI was gathering information, conducting interviews, and reviewing documents. The agents were not conducting “some ancillary proceeding, such as an investigation independent of the court’s or grand jury’s authority,” Aguilar, 515 U.S. at 599, 115 S.Ct. 2357. A reasonable jury could infer, moreover, that Dwyer knew her statements would be submitted to the grand jury, as she was aware of the grand jury subpoena and related investigation, had spoken to Phillips and Polimeni before her interview with the FBI, and had answered questions on topics related to documents sought in the October 23, 2001 subpoena. There was sufficient evidence of a nexus between Dwyer’s false statements and the grand jury proceeding.

There was also sufficient evidence for a reasonable jury to find that Dwyer was guilty of conspiracy to obstruct justice. The evidence supported the jury’s inference of a knowing and voluntary agreement: Dwyer had spoken "with Phillips and Polimeni before making the false statements about Ortiz. She also received a pay raise soon after. There was an overt act: the making of the false statements in interference with a pending grand jury proceeding. Ruiz, 105 F.3d at 1499. The circumstantial evidence more than supported a conclusion that Dwyer was part of a conspiracy to obstruct justice. See Gomez-Pabon, 911 F.2d at 853.

II. Constructive Amendment

Dwyer argues for the first time on appeal that jury instructions on the federal program fraud count relating to Ortiz (Count 9) and the false statement count (Count 16) constructively amended the indictment.

Had an objection of constructive amendment been made at trial, this court would determine de novo whether the indictment was constructively amended. United States v. Kelly, 722 F.2d 873, 876 (1st Cir.1983) (the question is whether the defendant “has made a convincing showing that the alleged alteration in the indictment did in fact change the elements of the offense charged and whether he was convicted of a crime not charged in the grand jury indictment”). Here, however, the constructive amendment claim was not preserved by timely objection made in the district court; our review, therefore, is for plain error only. United States v. DeCicco, 439 F.3d 36, 44-45 (1st Cir.2006).

“An amendment of the indictment occurs when the charging terms of the indictment are altered, either literally or in effect, by the prosecutor or the court after the grand jury has returned the indictment.” United States v. Cianci, 378 F.3d 71, 93 (1st Cir.2004); see United States v. Dubon-Otero, 292 F.3d 1, 4 (1st Cir.2002).

a. Constructive Amendment of Count 9

Count 9 charged the defendants with committing federal program fraud by submitting to the Springfield School Department monthly invoices that reflected the labor costs for Ortiz when Ortiz had not worked. The court instructed the jury that the defendants were charged with converting or aiding and abetting the theft of funds under the control of MCDI and/or the City of Springfield. That instruction was correct. “A primary objective of the rule against constructive amendment of indictments is to ensure defendants have notice of the charges they must defend against.” Dubon-Otero, 292 F.3d at 5.

Dwyer argues that there was no evidence of submission of “monthly invoices to the Springfield School Department that falsely included the labor costs of Gretchen Ortiz.” She claims the school department would pay only for the labor of Baking Company employees who worked at the commissary or warehouse. MODI would bill the School Department periodically for that labor. Only the labor for those workers involved in pizza and cookie production, she says, was billed to the Springfield School Department, and Ortiz worked in MCDI’s main building wrapping muffins. Thus, Dwyer claims, Ortiz’s labor costs were never billed to the Springfield School Department. The record does not support Dwyer’s characterization of the payment of labor. She cites the testimony of Thomas Mazza, the assistant finance manager of the Springfield School Department, for the proposition that Ortiz’s labor costs were never billed to that department. But Mazza, answering a series of questions about the cost of the muffins billed to the department, said the following:

Q: With respect to the hot lunches and the muffins program, how was the billing done? How did you pay for it? What was the structure in terms of the way you would bill for those services?
A: Hot lunch or hot breakfast?
Q: Excuse me, hot lunches and muffins, the one that was done at 140 Wilbraham Road [MCDI’s main facility].
A: We were billed on a per item cost. There was a set cost for each per unit that was produced in a given month and we were billed.
Q: So each muffin would have a particular cost associated with it?
A: Yes.
Q: And the same with each lunch?
A: Hot breakfast.
Q: Hot breakfast. I want to keep calling it lunch. So with respect to what went into making up that unit cost, what were the ingredients, so to speak, of the unit cost for the muffins for the hot breakfast?
A: I believe it was the labor that MCDI incurred to produce them, the production (emphasis supplied).

Dwyer had sufficient notice of the charges. Here, as in Cianci, “[n]o intimations by the court recast the ‘essential’ elements” of the crime charged. 378 F.3d at 94.

b. Constructive Amendment of Count 16

Dwyer also argues that the district court impermissibly broadened Count 16, which alleged a false, fraudulent, and fictitious material statement in violation of 18 U.S.C. § 1001, by instructing the jury it could find the defendants guilty if they made a material false statement or concealed or covered up a material fact by trick, scheme, or device. She claims that the reference to “trick, scheme, or device” unlawfully amended the indictment. The instruction stated in part:

The first element the government must prove beyond a reasonable doubt is that the defendant intentionally made a material false statement or intentionally concealed or covered up a material fact. These words almost define themselves.
To falsify means to make an untrue statement which is untrue at the time made is known to be untrue at the time made. However a statement that is literally true can constitute a false statement if the defendants, through a scheme, trick or device, are actively trying to mislead the government.
To satisfy this first element, the government must prove beyond a reasonable doubt that the fact allegedly falsified or covered up was material. A statement is material if it has a natural tendency to influence or to be capable of influencing the decision of the decisionmaker to which it was addressed, regardless of whether the agent actually relied on it.
I will now enumerate the specific charges of false statement:
Count 16: Ms. Dwyer is charged with falsely stating to a special agent of the Federal Bureau of Investigation on March 27, 2000 that she assumed that Gretchen Ortiz worked her full shift but could not verify the actual number of hours worked by Ms. Ortiz, and that the only preferential treatment received by Ms. Ortiz from the administration about which Ms. Dwyer had knowledge was that she had heard other employees complain that Ms. Ortiz got to work more hours than other employees.

In her brief, Dwyer cites a truncated version of the instruction, implying that the court failed to address the specific charge of false statement against her and thus unlawfully amended the indictment with its reference to a statement which through a “scheme, trick, or device” actively attempts to mislead the government. The court’s instruction on the specific charge pertaining to Dwyer “was taken largely from the indictment,” Cianci, 378 F.3d at 94, and did not amend it. The court made clear in its instructions that Dwyer was accused of specific false statements, which the jury could then judge if she made.

Dwyer’s constructive amendment claims fail, therefore, whether judged de novo or under a plain error standard.

III. Cumulative Errors

Finally, building on her sufficiency argument, Dwyer claims that a number of other errors by the district court cumulatively created a substantial risk of the miscarriage of justice. We deal with these arguments below seriatim, finding that there was no error as to any of them, hence no prejudice, cumulative or otherwise. See United States v. Barrow, 448 F.3d 37, 44 (1st Cir.), cert. denied, — U.S. -, 127 S.Ct. 176, 166 L.Ed.2d 124 (2006).

a. Motion to Sever

Dwyer argues that evidence of Phillips’s sexual relationships with MCDI employees entitled her to have her trial severed from his. We review the district court’s denial of a motion to sever for abuse of discretion. United States v. Casas, 425 F.3d 23, 36 (1st Cir.2005), cert. denied, 547 U.S. 1061, 126 S.Ct. 1670, 164 L.Ed.2d 409 (2006). “To demonstrate abuse of discretion, defendants must show that joinder deprived them of a fair trial, resulting in a miscarriage of justice.” United States v. Soto-Beniquez, 356 F.3d 1, 29 (1st Cir.2004). “[T]he burden is on the party who challenges the refusal to sever to make a convincing showing of prejudice as a prerequisite to gaining a new trial.” United States v. Vega Molina, 407 F.3d 511, 531 (1st Cir.), cert. denied, 546 U.S. 919, 126 S.Ct. 296, 163 L.Ed.2d 258 (2005).

“Because the general rule is that those indicted together are tried together to prevent inconsistent verdicts and to conserve judicial and prosecutorial resources, severance is particularly difficult to obtain where, as here, multiple defendants share a single indictment.” Soto-Beniquez, 356 F.3d at 29. This is especially true in conspiracy cases, where “severance will rarely, if ever, be required.” United States v. Flores-Rivera, 56 F.3d 319, 325 (1st Cir.1995) (internal quotation marks and citations omitted).

There was no abuse of discretion in the denial of severance here. Dwyer has not made a convincing showing that the jury was unable to separate the evidence against Phillips from that against her. The district court repeatedly instructed the jury that the evidence about Phillips was not relevant to the other defendants. See United States v. DeLuca, 137 F.3d 24, 37 (1st Cir.1998) (“[T]he district court took prudent precautions against judicial spillover by repeatedly instructing the jury that it must consider the evidence against each individual defendant in relation to each count.”). We “presume that jurors will follow clear instructions to disregard evidence unless there is an overwhelming probability that the jury will be unable to follow the court’s instructions, and a strong likelihood that the effect of the evidence will be devastating to the defendant.” United States v. Portela, 167 F.3d 687, 701 (1st Cir.1999) (internal quotation marks and citation omitted). “[A] measure of evidentiary spillover is a foreseeable concomitant of virtually every joint trial, yet seldom indicates undue prejudice.” DeLuca, 137 F.3d at 36. Here, especially where the court took particular care to emphasize the need to differentiate the evidence for each defendant, it did not abuse its discretion in denying a motion to sever.

b. Evidentiary Rulings

Dwyer argues that, in any event, the evidence of Phillips’s sexual relationships should have been excluded as unfairly prejudicial to her. We review evidentiary decisions for abuse of discretion. United States v. Flemmi, 402 F.3d 79, 86 (1st Cir.2005). “[District courts enjoy wide latitude in passing upon the relevancy of evidence.” United States v. Maldonado-Garcia, 446 F.3d 227, 231-32 (1st Cir.2006). “As to prejudice, ‘[t]rial judges enjoy wide latitude in making Rule 403 rulings and are only overturned after a showing of egregious error.’ ” United States v. Perez-Gonzalez, 445 F.3d 39, 47 (1st Cir.2006) (quoting United States v. Kornegay, 410 F.3d 89, 96 (1st Cir.2005)). We find nothing unreasonable in the court’s allowance of the evidence against Phillips. The district court gave several warning instructions about use of the Phillips evidence. See United States v. Richardson, 421 F.3d 17, 41 (1st Cir.2005), cert. denied, — U.S. -, 126 S.Ct. 2319, 164 L.Ed.2d 838 (2006).

Dwyer also challenges briefly and in the most general terms a range of additional . evidentiary admissions as highly prejudicial but does not develop any argument as to why any was improperly admitted. “Virtually all evidence is prejudicial — if the truth be told, that is almost always why the proponent seeks to introduce it — but it is only unfair prejudice against which the law protects.” United States v. Pitrone, 115 F.3d 1, 8 (1st Cir.1997). Dwyer makes no specific argument as to how the evidence “invite[d] the jury to render a verdict on an improper emotional basis.” ' United States v. Varoudakis, 233 F.3d 113, 122 (1st Cir.2000).

c. “Following Orders” Jury Instruction

Dwyer takes issue with the court’s instruction to the jury that “if you find that the evidence established beyond a reasonable doubt that the defendant willfully and knowingly participated in the scheme to defraud, it is not a defense to the crime of wire fraud for a defendant to claim that he or she was following orders.” This instruction pertained only to the wire fraud counts, which the court dismissed. Dwyer argues that since the wire fraud counts were only dismissed by the court on her motion under Fed.R.Crim.P. 29(c), after the jury returned its verdicts, it is unlikely that the jury understood that the following orders instruction pertained only to the wire fraud counts. The instruction, however, clearly referred to the wire fraud counts, and the jury demonstrated its ability to distinguish among counts by acquitting on some and convicting on others. See United States v. Freeman, 208 F.3d 332, 345-46 (1st Cir.2000).

d. Prosecutor’s Statements in Closing Argument

Dwyer argues that the government improperly equated “intent” with “knowledge” in its rebuttal closing argument. The government said:

I want to talk about intent because it’s something that has been mentioned both by Mr. Hoose and some of the other lawyers during their closing arguments and the judge will tell you what intent is. You’ll be able to learn from the instruction that intent is not someone waking up in the morning and saying, “today I am going to defraud the City of Springfield.” Intent is not like that. Intent is simply knowing the consequences of your actions. Knowing that when a payroll check is being issued and someone is not performing work for that payroll check, that the City of Springfield, MCDI is losing money as a result. That, in essence is intent, knowing the consequences of what flows from your actions.

At the conclusion of the rebuttal, the court reminded the jury that the closing arguments of counsel are not evidence. The defendant objected to a couple of points, including the intent definition, at the end of the rebuttal summation, saying, “I want to object to Mr. Welch’s suggestion or his definition of intent. I realize the Court was giving a curative instruction, but I want to note these objections and ask the Court to specifically instruct the jury to disregard those things.” The court responded:

All right. Well, I don’t think it’s necessary for me to do the latter [i.e., give specific instruction]. And my remarks at the end of the closing were not intended to cure anything specifically related to Mr. Welch’s rebuttal. I hope that wasn’t interpreted that way. It just seemed to me to be a good time at the end, sometimes I do it at the beginning and perhaps it would have been better if I had done it at the beginning but it was simply intended as a general admonition....
The issue of the instructions, several of you have referred to what you thought I would say in my instructions, and I’ll be saying right in the very first page or two of my instructions that anything counsel may say about the instructions that is inconsistent with my instructions is to be disregarded. So that will be right at the beginning of the instructions so in a sense you -will get that instruction.

The next day, the court gave the jury instructions which included the following:

Counsel have quite properly referred to some of the governing rules of law in their arguments. If, however, any difference appears to you between the law as stated by counsel and that stated by the Court in these instructions, you of course are to be governed by these instructions ....
In weighing the evidence on the conspiracy charge you must find beyond a reasonable doubt that the defendants intentionally joined the conspiracy before you may find them guilty on that charge. In fact, the law requires that the government prove two types of knowing intent beyond a reasonable doubt before a defendant can be said to have willfully joined the conspiracy.

The court went on for several more paragraphs on the meaning of intent.

Where there is prosecutorial argument with contemporaneous objections, we review de novo whether the comment was improper and review for abuse of discretion whether the misconduct, if any, warrants a new trial. United States v. Lewis, 40 F.3d 1325, 1337-38 (1st Cir.1994). To be held responsible for participation in a criminal conspiracy, a defendant must be shown to have entered knowingly, willfully and intentionally into an agreement with the specific intent that the conspiracy’s criminal purposes be accomplished. United States v. O’Campo, 973 F.2d 1015, 1020 (1st Cir.1992). The prosecutor’s argument suggested to the jury that if they concluded that Dwyer’s notations on the payroll spreadsheets proved knowledge, then intent could be presumed. The prosecutor should not have characterized intent and knowledge as essentially interchangeable, but we find no abuse of discretion in the court’s handling of the summation. The court repeatedly emphasized the definition of intent during instructions the following day and emphasized further that the court’s characterization of the law was the one to follow. The jury is presumed to have followed the court’s instructions and the definition it gave of intent. See Soto-Beniquez, 356 F.3d at 43 (curative instruction and correct instruction on point of law prevented any prejudice to defendant from prosecutor’s misstatement of law in closing argument).

Affirmed. 
      
      . Defendant states in her appellate brief that "Count One also alleged conspiracy to commit wire fraud, but the Trial Court determined that there was no interstate communication as required by 18 U.S.C. § 1343, and dismissed all wire fraud counts. Implicitly, the Court’s ruling narrowed Count One to the Program Fraud allegations.” The government did not disagree with this statement, and, without ruling on the matter, we shall assume that the conspiracy conviction as it now stands is for program fraud only.
     
      
      . Dwyer notes that she was acquitted of the charge of purposefully altering Illingsworth’s timesheets to obstruct the grand jury investigation. After Illingsworth was arrested in 2000 for gambling, Dwyer testified, Anne Sea-la, the payroll and accounts receivable clerk, spoke to Dwyer about reconciling his time-sheets to reflect comp time he had been paid which had not been entered on his time-sheets. Dwyer testified that in response to Scala's inquiry, she may have entered the totals on the Illingsworth timesheets to reflect the amounts he had been paid but did not change any of the "time in” or "time out” entries. Dwyer’s handwriting is not found on any of the latter time entries.
     
      
      . See note 2, supra.
      
     
      
      . Dwyer argues that she did not "benefit in any way from any alleged wrongdoing at MCDI.” That may be true, but section 666 criminalizes conversion to the use of "any other person.” 18 U.S.C. § 666(a)(1)(A).
     
      
      . Dwyer does not argue that the payments to Ortiz should be considered under the 18 U.S.C. § 666(c) exception.
     