
658 F.3d 35 (2011)
UNITED STATES of America, Appellee/Cross-Appellant,
v.
Muhamed MUBAYYID and Emadeddin Z. Muntasser, Defendants, Appellants/Cross-Appellees. *36 
United States of America, Appellant,
v.
Samir Al-Monla, Defendant, Appellee.
Nos. 08-1846, 08-1985, 08-1986, 08-2103, 10-1094, 08-2102.
United States Court of Appeals, First Circuit.
Heard October 4, 2010.
Decided September 1, 2011.
*40 Michael C. Andrews for Muhamed Mubayyid.
Kathleen M. Sullivan, with whom Faith E. Gay, Susan R. Estrich, Adam M. Abensohn, William B. Adams, and Quinn Emanuel Urquhart & Sullivan, LLP were on brief, for Emadeddin Z. Muntasser.
Judith H. Mizner, Assistant Federal Public Defender, for Samir Al-Monla.
S. Robert Lyons, Attorney, Tax Division, U.S. Department of Justice, with whom John A. DiCicco, Acting Assistant Attorney General, Alan Hechtkopf, Attorney, Tax Division, U.S. Department of Justice, and Carmen Milagros Ortiz, United States Attorney, were on brief, for United States of America.
Before TORRUELLA and LIPEZ, Circuit Judges, and SMITH,[*] District Judge.
LIPEZ, Circuit Judge.
This complex appeal arises out of the joint criminal prosecution of Emadeddin Muntasser, Muhamed Mubayyid, and Samir Al-Monla for conspiring to defraud the United States by obstructing the functions of the Internal Revenue Service ("IRS"), for corruptly endeavoring to obstruct the due administration of the Internal Revenue laws, for filing false tax returns, for making false statements to agents of the Federal Bureau of Investigation ("FBI"), and for scheming to conceal material facts from a federal agency. The charges stem from each defendant's involvement with Care International, Inc. ("Care"), a charitable organization incorporated by Muntasser in 1993 with a stated purpose of providing worldwide humanitarian aid.
The defendants' twenty-four day jury trial focused on the circumstances motivating Muntasser's formation of Care in 1993; the defendants' failure to disclose some of Care's activities, such as the publication of certain newsletters from 1993 to 1997; and Care's support for, and promotion of, Islamic jihad and fighters known as "mujahideen."[1] The government's central theory at trial was that Muntasser had established Care in order to fraudulently obtain a tax exemption, so that contributions being used to finance mujahideen overseas could be deducted from individual tax returns as charitable donations.
*41 At the close of the government's case, the district court acquitted Muntasser and Al-Monla of endeavoring to obstruct the administration of the Internal Revenue laws. It found that their tax filings, which formed the basis of the charge, occurred outside of the relevant statute of limitations period. The jury then acquitted Al-Monla of making a false statement to an FBI agent, but otherwise convicted the defendants of all counts. Following that verdict, the district court acquitted Muntasser and Al-Monla of having schemed to conceal material facts from a federal agency, and acquitted all three defendants of having conspired to defraud the United States. With respect to the scheme to conceal, it found that the government's proposed jury instruction, accepted by the court, had narrowed the charge in a way that rendered Muntasser's and Al-Monla's acts of concealment immaterial. As to the conspiracy, the court concluded that the government offered insufficient evidence that the defendants had reached the specific agreement described in the indictment.
Muntasser, Mubayyid, and the government have appealed. Muntasser argues that the evidence introduced at trial linking Care to organizations financially supporting the mujahideen and jihad, including an alleged predecessor organization that received negative publicity in connection with the 1993 World Trade Center bombing, biased the jury in the appraisal of the government's evidence on his sole count of conviction, a false statement charge. He also challenges his sentence. Mubayyid appeals from his convictions for filing false tax returns and for endeavoring to obstruct the administration of the Internal Revenue laws, contending that the question that the jury found he answered falsely was fundamentally ambiguous. He also claims that the evidence was insufficient to support his conviction for scheming to conceal material facts. Additionally, with respect to all of his convictions, he claims that he was prejudiced by the introduction of a recorded telephone conversation and joins Muntasser in claiming prejudicial spillover from what the defendants characterize as "terrorism evidence." The government, for its part, seeks to reinstate the jury's guilty verdict against all three defendants on the charged conspiracy to defraud the United States.[2] In its view, the district court erred by acquitting the defendants when the government successfully proved a conspiracy that was narrower than, but wholly included within, that alleged in the indictment.
After careful consideration, we reverse the district court's acquittal of the defendants on the conspiracy count, reinstate the jury's verdict, and affirm the defendants' other convictions.

I.

A. Factual Background
We recount the essential facts of the case, drawn from the trial record, in the light most favorable to the verdict. E.g., United States v. Poulin, 631 F.3d 17, 18 (1st Cir.2011). Due to the complexity of the issues, we reserve additional factual detail for the analysis that follows.

1. Care's Formation and Operations
Emadeddin Muntasser is a Libyan citizen and a permanent resident alien in the United States. In the early 1990s, Muntasser served as Director of the Boston branch of the Al-Kifah Refugee Center *42 ("Al-Kifah"), the American face of Maktab al-Khidmat ("MAK"), a Pakistan-based organization that openly advocates violent, Islamic jihad and actively supports mujahideen in Afghanistan. In a letter of solicitation introduced at trial, Muntasser described Al-Kifah as "an organization founded by Sh[eikh] Abdullah Azzam to serve the cause of Jihad," and which "actively supports the Mujahideen in the front."[3] Among its activities, Al-Kifah's Boston branch published a pro-jihad newsletter entitled "Al-Hussam," which translates from Arabic as "The Sword"; it sold books and audiotapes extolling the cause of jihad; and it promoted sermons and lectures by like-minded Muslim leaders. It also solicited substantial charitable donations through the publication of an annual Zakat Calculation Guide.[4] Although the organization advertised itself as a tax-exempt charity, it had never been granted charitable status by the IRS.
In early 1993, shortly after the World Trade Center bombing in New York City, both Newsweek and The New York Times ran articles linking the Brooklyn branch of Al-Kifah to "Islamic Militant groups, fighters in Afghanistan, and individuals who were alleged to have committed acts of violence." Within days, Muntasser dissolved the Boston branch of Al-Kifah and incorporated Care in Massachusetts. According to its articles of incorporation, Care was "organized exclusively for charitable, religious, educational, and scientific purposes including . . . human welfare, charitable and relief activities." The articles listed Muntasser as Care's President, Munther Baara as Treasurer, and Ahmad Nawras as Secretary, and identified Afif Kadri, Mohamad Akra, and Waseem Abu Yasin as board members. Baara, Nawras, Kadri, Akra, and Yasin had all served in identical positions for the Boston branch of Al-Kifah. The articles also stated, "It is intended that the corporation shall be entitled to exemption from federal income tax under Section 501(c)(3) of the Internal Revenue Code."
Following its incorporation, Care effectively replaced Al-Kifah's Boston branch. It took over Al-Kifah's mailbox address and deposited financial contributions into Al-Kifah's bank account (though these contributions were eventually transferred to an account in Care's name). Care's activities also substantially mirrored those of Al-Kifah's Boston branch, including the sponsoring of pro-jihad speakers, the sale of books and tapes advocating jihad, and the continued publication of the "Al-Hussam" newsletter.[5]
Within the organization, individuals referred to Care as "Maktab," a shorthand reference to MAK. In its own newsletters, Care referred to itself as "the office of services," a name by which MAK was known in the United States. Like Al-Kifah, Care also represented itself to the public as "founded by Imam Abdullah Azzam," even though Abdullah Azzam had died more than three years prior to Care's formation. At trial, the government presented *43 two experts who testified regarding the overseas operations of MAK, Abdullah Azzam's philosophy on violent jihad, the general trend of using charitable organizations to covertly finance jihad and mujahideen, and the concept of "economic jihad"the precept that, "[i]f you cannot be a fighter, fund a fighter." It also asked a witness to read fifty-five pages of the "Al-Hussam" newsletters into the record, primarily those sections that demonstrated Care's commitment to violent jihad and its financial solicitations for the mujahideen.
Defendants Al-Monla and Mubayyid had both been associated with Care in some form since 1993, and with Al-Kifah before it. In 1996, Al-Monla replaced Muntasser as President of Care. He served in that capacity until 1998, when he became Treasurer. Mubayyid, who is Al-Monla's brother-in-law, eventually replaced Al-Monla as Care's Treasurer in 1998 or 1999. He filled that role through at least 2002.

2. Care's Tax Filings
Approximately six weeks after incorporating Care, Muntasser applied to the IRS to have Care designated as a tax-exempt charity. In order to obtain tax-exempt status, an organization must file an initial application for tax exemption, IRS Form 1023, in which the organization demonstrates that it is organized and operated exclusively for a qualifying purpose.[6] In Care's Form 1023 filing, Muntasser represented that Care had not yet become operational, an inaccurate statement, but that "within a couple months" it would engage in humanitarian projects such as providing "assistance to victims of natural and man-made disasters," sponsoring "orphans in disaster areas overseas," and developing "rehabilitation programs for refugees coming from overseas." Although the form asked for "a detailed narrative description of all of the activities of the organization past, present, and planned," Muntasser did not disclose Care's hosting of religious speakers, its sale of materials advocating jihad, or its publication of the "Al-Hussam" newsletters (by that point, Care had already published at least two "Al-Hussam" newsletters in its own name). Nor did he disclose that Care's orphan sponsorship program would target the orphans of martyred mujahideen.[7] In response to a question asking for the details of the organization's fundraising program, Muntasser stated that "mailings" "will commence within the next couple of months." He did not specifically describe the "Al-Hussam" newsletters or the Zakat Calculation Guide as fundraising devices, nor did he attach them in response to the form's request for "representative copies of solicitations for financial support." Lastly, Muntasser denied that Care was an outgrowth of or successor to any other organization, despite Care's obvious ties to Al-Kifah's Boston branch.
Based on the information provided, the IRS approved Care's application for tax-exempt *44 status without requesting additional verifying information. At trial, the IRS employee who approved Care's application testified that he would have requested copies of the "Al-Hussam" newsletter and the Zakat Calculation Guide if their existence had been disclosed in the application. He further testified that, if he had seen the Zakat guide, he would have requested further documentation of Care's day-to-day activities. Similarly, if Muntasser had disclosed the relationship between Al-Kifah and Care, he would have requested information about Al-Kifah, including whether it was a tax-exempt organization in the United States.
In order to maintain its tax exemption, Care had to file annually IRS Form 990, disclosing the earnings and activities of the organization. Between 1993 and 2002, each of the three defendants signed and filed at least one Form 990 on Care's behalf. In 1996, Muntasser filed delinquent Form 990s for the tax years 1993, 1994, and 1995. In 2000, Al-Monla signed and filed the delinquent 1998 Form 990. In 2000, 2001, and 2002, Mubayyid filed amended Form 990s for the 1997, 1999, and 2000 tax years.
None of the Form 990s filed by the three defendants revealed that Care was publishing or had published the "Al-Hussam" newsletters, that Care was operating a website through which it solicited donations and provided access to articles from the "Al-Hussam" newsletters, that Care was regularly hosting pro-jihad speakers, or that Care was selling books and tapes on the subject of jihad. Although Muntasser had failed to disclose these same activities in Care's initial application, Form 1023, each of the defendants answered "No" when the Form 990s asked whether the organization engaged in any activities that had not previously been reported to the IRS. Instead, each Form 990 filed by the defendants depicted Care as engaging in just four program services: food distribution, cash assistance to orphans and widows, medical assistance to refugees, and grants to other welfare organizations.

3. The Federal Investigation
By at least 1999, Care's activities had drawn the attention of the FBI, which began a formal investigation of both Care and Muntasser.[8] In April of that year, Muntasser was interviewed by the FBI. During that interview, he disclosed that he had traveled to Pakistan in 1994 or 1995. However, he did not volunteer the fact that, during that trip, he had also traveled to Afghanistan and had met with the Afghan warlord Gulbuddin Hekmatyar.[9] He was not asked a question that required such a disclosure.
In August of 2001, Mubayyid transferred all of Care's records out of its offices and into a rented storage unit. Shortly thereafter, Mubayyid was recorded pursuant to a court-approved wiretap conversing with Mohammed Chehade, the executive director of the Global Relief Foundation ("GRF"), about the federal investigation.[10] During the conversation, Chehade implored Mubayyid to remove *45 Care's records from the storage unit. However, Mubayyid demurred, insisting that he was "afraid that they may think that there is something. . . . I don't want to touch anything, so that there is no."[11] Three days later, the FBI covertly searched the storage unit, pursuant to a court-issued warrant, in order to gather intelligence about the activities of Care and its officers. It catalogued the contents of the unit and copied numerous documents, but it did not remove any materials at that time.
In 2003, the FBI executed a search warrant, seizing the contents of the storage locker as well as documents discovered at Mubayyid's residence. Among the items at the residence was a copy of Care's Form 1023 filing. Several documents that had been in the storage unit during the 2001 search were not recovered in 2003: the minutes of a 1995 meeting at which officers of Care and of GRF discussed jihad and supporting the "battalion"; a letter signed by Muntasser and Al-Monla pledging support to the Afghan warlord Hekmatyar; and an e-mail sent to Care from a London-based pro-jihad organization that announced an impending war involving "Kosovah-Mujahideen" and requesting aid from Care in the form of money and fighters.
Around the time of the seizure, the FBI once again interviewed Muntasser. This time, Muntasser was asked directly whether he had ever traveled to Afghanistan. He repeatedly denied having done so, and he also denied having ever met Hekmatyar. Although an investigating agent testified that he thought Muntasser had been to Afghanistan, he had no information linking him to Hekmatyar. He testified that a truthful response by Muntasser regarding his travel to Afghanistan would have drastically changed the nature of the interview. Later in 2003, Muntasser disclosed his trip to Afghanistan on an Application for Naturalization and admitted the same to an Immigration and Naturalization Service officer in a subsequent interview.

B. Procedural History
On May 11, 2005, a grand jury returned an indictment charging Muntasser and Mubayyid with one count of scheming to conceal material facts from a federal agency and one count of conspiring to defraud the United States. The indictment also charged Mubayyid with three counts of filing a false tax return for his submission of the Form 990s for the tax years 1997, 1999, and 2000,[12] and it charged Muntasser with one count of making a false statement to a federal agency during his April 2003 FBI interview.
On March 8, 2007, a grand jury returned a superseding indictment charging all three defendants with scheming to conceal material facts from a federal agency (Count 1), conspiring to defraud the United States (Count 2), and endeavoring to obstruct the administration of the Internal Revenue laws (Count 8). The 2007 indictment retained the tax return charges against Mubayyid (Counts 3-5) and the false statement charge against Muntasser (Count 6). Additionally, it charged Al-Monla with one count of making a false statement to a federal agency (Count 7) for allegedly lying to the FBI when he *46 denied knowing a man by the name of Bassam Kanj.[13]
Following the government's presentation of evidence at trial, the defendants moved for a judgment of acquittal on Counts 1, 2, and 8, arguing that the evidence at trial was insufficient to prove the charged crimes, and also that the relevant statutes of limitation precluded convictions on Counts 1 and 8. See Fed.R.Crim.P. 29. The trial judge acquitted Muntasser and Al-Monla on Count 8, obstructing the Internal Revenue laws, because those defendants' tax filings on behalf of Care, Forms 1023 and 990, were outside the statute of limitations, and their more recent statements to the FBI, even if proven false, could not have been material to the IRS. It otherwise denied the motions. With respect to the Count 2 conspiracy charge, however, the judge expressed significant reservations about the sufficiency of the evidence.
The defendants called just one witness a tax expert[14]before the case was submitted to the jury. The jury acquitted Al-Monla on Count 7, the false statement count,[15] and returned a guilty verdict on all other charges. In response to the defendants' renewed Rule 29 motion, the district court set aside the jury's verdict against all three defendants on Count 2 and against Muntasser and Al-Monla on Count 1. According to the district court, Count 2 charged a conspiracy with a single, unitary objectobtaining Care's tax-exempt status in 1993 and maintaining it thereafterbut the government had presented insufficient evidence that Muntasser conspired with anyone prior to obtaining Care's tax-exempt status in 1993. The district court's ruling on Count 1, which charged them with scheming to conceal material facts from a federal agency, was a function of the government's proposed jury instruction restricting the federal agency affected to the IRS alone. As with Count 8, the district court again concluded that the only conduct by Muntasser and Al-Monla that would be material to the IRS was time-barred.
The district court's combined rulings left Al-Monla acquitted of all charges, and Muntasser convicted only of his 2003 false statement to the FBI (Count 6). Mubayyid, however, was convicted of five counts: one count of scheming to conceal material facts from the IRS (Count 1), one count of endeavoring to obstruct the administration of the Internal Revenue laws (Count 8), and three counts of filing a false tax return (Counts 3-5).
Muntasser received a twelve-month sentence of incarceration, twice that recommended by the United States Sentencing Guidelines for a false statement conviction. Mubayyid was sentenced to eleven months' incarceration and thirty-six months of supervised release.

II.
This appeal involves the following claims:
The government appeals from the district court's post-verdict acquittal of all three defendants on the conspiracy *47 charged in Count 2.[16] It claims that the district court erred by finding evidentiary insufficiency in a variance in proof that did not prejudice the defendants. It does not appeal the district court's acquittal of Muntasser and Al-Monla for scheming to conceal material facts from the IRS, and for obstructing the due administration of the IRS.
Mubayyid argues that his convictions for filing false tax returns are legally unsupportable because they rest on his answer to a fundamentally ambiguous question. He also claims that the government's evidence was insufficient with respect to the charged scheme to conceal, and that both the erroneous admission of certain evidence and a statement by the prosecutor in closing arguments prejudiced his trial.
Muntasser contends that the admission of inflammatory terrorism evidence, relevant only to the conspiracy and the tax-related counts of which he was acquitted, spilled over into the jury's consideration of his false statement charge. He also contends that his twelve-month sentence is unreasonable.
We address the parties' claims seriatim.

A. The Government's Claim
We begin by addressing the government's appeal because the correctness vel non of the district court's post-verdict acquittal informs our analysis of several of the defendants' claims of error. Our review is de novo, and we may uphold the judgment of acquittal only if the evidence, viewed in the light most favorable to the government, could not have persuaded any trier of fact of the defendants' guilt beyond a reasonable doubt. E.g., United States v. Merlino, 592 F.3d 22, 29 (1st Cir.2010). "So long as `the guilty verdict finds support in a plausible rendition of the record,' it must be allowed to stand (and the acquittal must be reversed)." United States v. Rivera Rangel, 396 F.3d 476, 482 (1st Cir.2005) (quoting United States v. Rivera-Ruiz, 244 F.3d 263, 266 (1st Cir.2001)).
Count 2 of the indictment charged the defendants with conspiring to defraud the United States by obstructing the functions of the IRS, in violation of 18 U.S.C. § 371. See generally United States v. Klein, 247 F.2d 908 (2d Cir.1957). Specifically, the indictment alleged that the purpose of the conspiracy was as follows:
impeding, impairing, interfering, obstructing and defeating through deceit, craft, trickery, and dishonest means the lawful functions of the [IRS] in the ascertainment, assessment, and determination of whether [Care] qualified and should be designated as a 501(c)(3) organization in 1993 and should continue to be accorded status as [a] 501(c)(3) organization thereafter.
The district court acquitted the defendants on Count 2 based on its finding that the above language of the indictment described a conspiracy with a "specific purpose: impairing the IRS's determination as to whether Care qualified for, and should continue to be accorded, charitable status." The district court acknowledged that, where a single conspiracy embraces multiple unlawful objects, a jury may convict upon proof that the defendants agreed to any one of those objectives. See Griffin v. United States, 502 U.S. 46, 57, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991). It held, however, that "this was not a multiple-object conspiracy," but rather a conspiracy with "a single, unitary object." Because the evidence at trial was insufficient to prove that anyone agreed with Muntasser to obstruct the IRS prior to Care's initial application *48 for tax-exempt status in 1993, the district court reasoned that the government had failed to prove the specific conspiracy charged:[17]
Again, the government charged a single agreement, an agreement to obtain and maintain tax-exempt status for Care. There was no evidence that there was a conspiracy to obtain that status, and no evidence that there was a conspiracy of any kind in or about 1993. Even if Mubayyid or Al-Monla, or both, agreed with Muntasser in 1995 or later to maintain the charitable status of Care or to commit another offense, that is not the agreement charged in the indictment. To sustain a conviction there must be sufficient evidence of the conspiracy charged in the indictment that conspiracy and not some other conspiracy.
On appeal, the government concedes that it presented insufficient evidence at trial to prove that any of the defendants conspired to obtain Care's tax exemption in 1993. It also fails to pursue its argument, made in the district court, that Count 2 of the indictment alleged a conspiracy with multiple objects.
Nevertheless, the government urges us to reinstate the jury's verdict, casting the issue as one of evidentiary variance, rather than insufficiency.[18] A variance occurs when the facts proved at trial differ materially from those alleged in the indictment without altering the crime charged. United States v. Tormos-Vega, 959 F.2d 1103, 1115 (1st Cir.1992). Traditionally, a claim of variance is raised on appeal by a defendant seeking to overturn a judgment of conviction. In those situations, we have said that a variance is not a ground for acquittal, provided that the facts actually proven at trial are sufficient to convict the defendant of the charged crime and the variance did not prejudice the defendant. See United States v. Glenn, 828 F.2d 855, 858 (1st Cir.1987) (Breyer, J.). The government claims that it succeeded in proving a narrower conspiracy prohibited by the same statutory provision charged, 18 U.S.C. § 371, and comprised wholly of acts clearly set forth in the indictment, amounting to no more than a non-prejudicial variance.
The defendants offer three rejoinders. First, they claim that a variance is only permissible where the indictment is narrowed in a way that does not alter an "essential element" of the charged offense. Alterations to the object of a unitary conspiracy, they contend, fundamentally change the crime of conviction from that charged. Second, they claim that, even if the variance was otherwise permissible, it was prejudicial to their defense, requiring that we affirm the district court's acquittal. Third, they claim that, in any event, the government failed to produce sufficient evidence of a narrower conspiracy among the defendants.

1. Did the Variance Alter the Crime Charged?
In general, a defendant can hardly be heard to complain when the government's *49 proof at trial establishes "a scheme similar to but somewhat narrower in breadth and malignity than that charged in the indictment." United States v. Mueffelman, 470 F.3d 33, 38 (1st Cir.2006). The defendants argue, however, that the object of a conspiracy is an "essential element" of the crime charged, see United States v. Roshko, 969 F.2d 1, 5 (2d Cir.1992), and that permitting a variance as to that object is improper. They suggest that the government's failure to establish the precise object of the conspiracy charged is substantively different from the cases in which we have permitted a variancetypically where the government has failed to establish a particular manner or means, or that the crimes occurred in the particular time frame alleged. As the defendants put it, "An agreement to maintain a tax-exempt status may encompass a narrower range of activity than a conspiracy to obtain and maintain tax-exempt status, but it is also a different agreement."
The defendants' claim implicates a number of often-overlapping limitations on the government's power to prosecute its citizens.[19] As far as is relevant to the government's appeal, these limitations are encapsulated by the distinction in our law between mere variance and the constructive amendment of an indictment.[20]See United States v. Brandao, 539 F.3d 44, 57 (1st Cir.2008) ("The prohibition on constructive amendment exists to preserve the defendant's Fifth Amendment right to indictment by grand jury, to prevent reprosecution for the same offense in violation of the Sixth Amendment, and to protect the defendant's Sixth Amendment right to be informed of the charges against him."). In contrast to a variance, a constructive amendment occurs where the crime charged has been altered, "either literally or in effect," after the grand jury last passed upon it. E.g., United States v. Bunchan, 626 F.3d 29, 32 (1st Cir.2010) (quoting United States v. Celestin, 612 F.3d 14, 24 (1st Cir.2010)). "The concepts of constructive amendment and variance are closer to a continuum than exclusive categories." Mueffelman, 470 F.3d at 38. "Save at either end of the spectrum," it is not always clear what distinguishes a permissible variance from an impermissible constructive amendment. Haines v. Risley, 412 F.3d 285, 291 (1st Cir.2005); see also United States v. Adamson, 291 F.3d 606, 615 (9th Cir.2002) ("The line between a constructive amendment and a variance is at times difficult to draw."); 3 Charles Alan Wright & Sarah N. Welling, Federal Practice and Procedure, Criminal § 516 (4th ed.2011) ("The distinction between *50 variances and constructive amendments is a matter of degree, and the distinction is rather shadowy." (footnote omitted)).
The Supreme Court has interpreted the Fifth Amendment's Presentment Clause to mean that, "after an indictment has been returned[,] its charges may not be broadened through amendment except by the grand jury itself." Stirone v. United States, 361 U.S. 212, 215-16, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960); see also id. at 217-19, 80 S.Ct. 270 (holding that an indictment was unconstitutionally broadened where prosecution offered evidence of two theories of liability, but the grand jury indicted defendant only on the first theory). It has also expressly rejected the proposition that "a narrowing of the indictment constitutes an amendment that renders the indictment void." United States v. Miller, 471 U.S. 130, 144, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985). The Miller Court held that the Fifth Amendment was not violated where the government's variance "added nothing new to the grand jury's indictment and constituted no broadening," id. at 145, 105 S.Ct. 1811, but rather proved "a significantly narrower and more limited, though included, fraudulent scheme," id. at 131, 105 S.Ct. 1811. We have since embraced, as a "well-established" principle, that a court may "narrow the indictment's charges without adding any new offenses." Celestin, 612 F.3d at 25 (alteration omitted) (quoting Miller, 471 U.S. at 138, 105 S.Ct. 1811) (internal quotation marks omitted).
The defendants seek to distinguish Miller on the ground that "what was removed from the case was in no way essential to the offense on which the jury convicted."[21]See Miller, 471 U.S. at 145, 105 S.Ct. 1811. They rely on a Second Circuit case, United States v. Roshko, for the proposition that, "[w]ithout question, the object of a conspiracy constitutes an essential element of the conspiracy offense." 969 F.2d at 5. Thus, they claim, "a variance may be permissible where it alters the means of a charged conspiracynot where it alters the object."
To the extent that the defendants argue that the object of a conspiracy is always an improper subject for a variance, they are wrong. In United States v. Glenn, this circuit's pathmarking precedent articulating the variance analysis, we upheld a defendant's conviction for a narrower conspiracy than the one charged. There, the indictment charged two defendants with a single, overarching conspiracy to import both marijuana and hashish. Glenn, 828 F.2d at 857. The government's proof at trial, however, evidenced two separate conspiracies, each with a narrower, distinct object of importing only a single drug. Id. Explaining that "conspiracy law, like most criminal law, focuses on the activities of an individual defendant," id., the Glenn court set out to determine "what kind of agreement or understanding existed as to each defendant," id. (emphasis omitted) (quoting United States v. Borelli, 336 F.2d 376, 384 (2d Cir.1964)) (internal quotation mark omitted). Although it concluded that the evidence was insufficient to convict the *51 defendants "of the conspiracy that the indictment charged, namely, the conspiracy to import and possess both marijuana from Thailand and hashish from Pakistan," it concluded that a permissible variance had occurred because the evidence remained sufficient to permit a jury, under a proper set of instructions, to convict one defendant of a "related, similar conspiracy" to import just one of the drugs. Id. at 858-61.
Roshko is not to the contrary. It involved a conspiracy to defraud the United States whose object was expressly defined as "seeking changes in the immigration status of an alien based on a sham marriage to a United States citizen that was falsely represented to be genuine." Roshko, 969 F.2d at 2. At trial, the government introduced evidence that the defendant had conspired in the marriage of her future husband, an immigrant from Israel, to a United States citizen, in order to secure his green card. Id. at 3. It further offered evidence of that couple's subsequent divorce and of the defendant's marriage to her now-permanent-resident-alien husband (which ultimately resulted in her successful application for a green card). Id. When the defendant raised a statute of limitations challenge to the evidence of her husband's sham marriage, the government argued that the conspiracy broadly embraced both marriages, and that the prosecution was therefore timely. Id. at 4. The Second Circuit, emphasizing that the indictment specifically charged a purpose to change the status of "an alien" through marriage to "a United States citizen," found that the indictment was not so broad as the government claimed. Id. at 5-6 (emphasis added). It held that the unlimited introduction of evidence related to the second marriage, combined with the government's arguments that such conduct was part and parcel of the conspiracy, was impermissible because it "could easily have created a basis for conviction which the grand jury did not intend to create." Id. at 6. Roshko thus stands for the unobjectionable proposition that the government's broadening of an indictment's charges through proof at trial constructively amends an indictment.
To the extent that the defendants instead argue that the object of the conspiracy here, because of the way in which it was charged, may not be narrowed without fundamentally changing the offense, their claim is unpersuasive. "[T]he line between `the crime charged' and `the facts charged' is inherently fuzzy." Mueffelman, 470 F.3d at 38. Hence, our practice has been to look to statutory elements in response to claims by defendants that "the crime charged" has been changed.[22] We have said that, "[s]o long as the statutory violation remains the same, the jury can convict even if the facts found are somewhat different than those charged." United States v. Twitty, 72 F.3d 228, 230 (1st Cir.1995); *52 cf. Glenn, 828 F.2d at 858 (noting that one question in variance analysis is whether sufficient evidence exists of "related, similar conspiracy" to one charged).
Here, the titular crime was not altered. The defendants were indicted under 18 U.S.C. § 371, which criminalizes conspiracies with an object "to defraud the United States, or any agency thereof in any manner or for any purpose." Cf. Mueffelman, 470 F.3d at 38 (finding no constructive amendment where "Mueffelman was charged with mail fraud and convicted of mail fraud"). Pursuant to that provision, the government was required to prove three elements: "an agreement, the unlawful objective of the agreement, and an overt act in furtherance of the agreement." United States v. Barker Steel Co., 985 F.2d 1123, 1127-28 (1st Cir.1993) (quoting United States v. Hurley, 957 F.2d 1, 4 (1st Cir.1992)). "The objective of the agreement is unlawful if it is `for the purpose of impairing, obstructing or defeating the lawful function of any department of Government.'" Id. at 1128 (quoting Dennis v. United States, 384 U.S. 855, 861, 86 S.Ct. 1840, 16 L.Ed.2d 973 (1966)). These elements were fully satisfied by so much of the indictment as charged the defendants with conspiring "to defraud the United States for the purpose of impeding, impairing, interfering, obstructing and defeating through deceit, craft, trickery, and dishonest means the lawful functions of the [IRS]."[23] That language is also consonant with the narrower conspiracy proven.
To be sure, the government's indictment did not stop there. It specifically alleged that the agreed-upon purpose of the defendants' fraud was to obstruct the IRS "in the ascertainment, assessment, and determination of whether Care International, Inc., qualified and should be designated as a 501(c)(3) organization in 1993 and should continue to be accorded status as [a] 501(c)(3) organization thereafter." As the district court noted, this language appears in the key charging paragraph, is identified as a component of the conspiracy's "purpose," and appears prior to and apart from the five paragraphs of the indictment setting forth the "manner and means by which the conspiracy was sought to be accomplished" and the nine paragraphs identifying the overt acts committed in furtherance of the conspiracy. The question is whether, and to what extent, this additional charging language precluded the government from proving a narrower conspiracy that embraced only the agreement of the defendants to act unlawfully to maintain Care's tax-exempt status.
We have found no indications in our case law that, as an element of the offense, the unlawful object of a § 371 conspiracy must be defined with the level of specificity to which the defendant now seeks to hold the government. To the contrary, we have previously declined to parse the conspiratorial object so finely. See United States v. Goldberg, 105 F.3d 770, 774 (1st Cir.1997) ("[W]e see no sharp distinction under section 371 between *53 a purpose to file [false tax] documents and a purpose to interfere [with the functions of the IRS]."); cf. Dennis, 384 U.S. at 863, 86 S.Ct. 1840 (rejecting claim that defendants' specific purpose of filing false documents in violation of another statute precluded trial under general charge of conspiracy to defraud, noting that indictment under the broader charge is permissible so long as it "properly reflects the essence of the alleged offense"). We have also held, in other contexts, that where the government's charging language identified an element of the crime with greater specificity than was required by the statute, the alteration of that additional language had "no bearing on the substance of the charge." United States v. Dowdell, 595 F.3d 50, 68 (1st Cir.2010) (finding no constructive amendment in government's clarification of drug type identified in indictment where charged crime "prohibits distribution of any controlled substance regardless of type," and thus "the government could technically have omitted reference to a particular controlled substance altogether"). This approach is consistent with the approach taken in other circuits. See, e.g., United States v. Kuenstler, 325 F.3d 1015, 1022 (8th Cir.2003) (treating as surplusage language in the indictment that described the object of the conspiracy in detail exceeding that which was needed to make out the statutory offense); United States v. Garcia-Paz, 282 F.3d 1212, 1215-17 (9th Cir.2002) (holding that language preceded by the phrase "to wit" in the indictment is mere surplusage that may be disregarded and need not be proven); United States v. Pumphrey, 831 F.2d 307, 309 (D.C.Cir. 1987) ("[E]xcess allegations in an indictment that do not change the basic nature of the offense charged need not be proven and should be treated as mere surplusage.").[24]
Thus, what is striking about the language relied upon by the defendants for the unitary conspiracy theory is that it is needless in the purpose portion of the indictment. If the indictment's reference to "the ascertainment, assessment, and determination of whether [Care] qualified and should be designated as a 501(c)(3) organization in 1993 and should continue to be accorded status as [a] 501(c)(3) organization thereafter" had appeared in the section of the indictment describing the conspiracy's "manner and means," rather than its "purpose," the defendants would have no argument at all. Hence, the defendants' argument challenging the government's right to prove a narrower conspiracy elevates form over substance. All of the material in the "manner and means" portion of the indictment, along with the overt acts alleged, is the specification of the ways in which the defendants sought to accomplish the conspiracy. Given the sufficiency of the more broadly stated purpose of the conspiracy and the detailed specification of conduct in its "manner and means" portion, the language at issue could have been omitted altogether without affecting the sufficiency of the indictment. See United States v. Troy, 618 F.3d 27, 34 (1st Cir.2010) ("[T]he statutory language may be used in the indictment to describe the offense, `but it must be accompanied with such a statement of the facts and circumstances as will inform the accused of the specific offence, coming under the general description, with which he is charged.'" (quoting Hamling v. United *54 States, 418 U.S. 87, 117-18, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974))).
In light of the foregoing considerations, the government has demonstrated that variance, rather than constructive amendment, is the proper lens through which to view the narrowing of the conspiracy that occurred in this case.[25] The allegations in the indictment charging, in the words of the district court, a conspiracy with a "single, unitary object" are not indispensable or "essential" to the integrity of that document. Indeed, they were effectively surplusage. The government is not seeking to reinstate the defendants' conviction on the basis of a crime other than the one with which they were charged. Although we hold the government to its charging decisions, we must also hold defendants to so much of their criminal conduct that the government has properly charged and successfully proven.

2. Was the Variance Prejudicial?
As noted, to be grounds for reversal, a variance must be severe enough to affect the defendant's substantial rights. Tormos-Vega, 959 F.2d at 1115 (citing Berger v. United States, 295 U.S. 78, 82, 55 S.Ct. 629, 79 L.Ed. 1314 (1935)). "The `substantial rights' protected by this rule are that the defendant have sufficient knowledge of the charge against him in order to prepare an effective defense and avoid surprise at trial, and to prevent a second prosecution for the same offense." Id. In addition, a variance can affect a defendant's substantial rights where, in cases with multiple defendants, proof that one defendant was involved in one conspiracy leads the jury to believe that another defendant was involved in a separate conspiracy. Id. We review de novo whether a variance affected a defendant's substantial rights. United States v. Fornia-Castillo, 408 F.3d 52, 67 (1st Cir.2005).
The defendants claim that they tailored their defense strategy at trial to their expectation that the government was obligated to prove the entire conspiracy as charged. Thus stated, the defendants' claim of prejudice is not one about fair notice of the charges or conduct at issue. Instead, their claim of prejudice rests uneasily on their misunderstanding about the legal sufficiency of the government's narrower proof. To the extent that the defendants believed that the government's conspiracy charge would fail because the government could only prove the narrower conspiracy to maintain Care's tax-exempt status, they misunderstood the law of conspiracy in this circuit. That misunderstanding cannot support a claim of prejudice. We have previously rejected similar claims in analogous circumstances. See Mueffelman, 470 F.3d at 38-39 (rejecting a claim of prejudice where the defendant structured his defense to combat a claim that the government was not required to prove); accord United States v. Davis, 679 F.2d 845, 852 (11th Cir.1982) ("Appellants' contention that they suffered prejudice because they were prepared to defend against the larger conspiracy but not the smaller one is nothing more than an argument that they had less of a defense against the smaller conspiracy since the larger one may not have existed.").
Moreover, even if the nature of the prejudice claimed by the defendants was legally relevant (which it is not), the defendants have not pointed to any evidence in the voluminous trial record that reflects a less-than-vigorous *55 defense. Although the defendants do not elaborate in their briefs on their prejudice claim, counsel for the defendants asserted at oral argument that, because they believed the government's inability to prove a conspiracy to obtain Care's tax-exempt status in 1993 would be fatal to the conspiracy charged, their defense did not emphasize the weaknesses of the government's circumstantial evidence of any narrower agreement to maintain that status. Our own review of the record does not support the defendants' claim.
To begin with, although the government has conceded on appeal that it charged a unitary conspiracy to both obtain and maintain Care's tax exemption, it argued below that the indictment charged a multiple-object conspiracy. The trial judge did not reject that argument until after the close of the government's evidence. In their initial Rule 29 motion, the defendants challenged Count 2 only on the ground that the government had failed to demonstrate that the defendants had, in fact, reached an agreement among themselves sometime after 1993.[26] It was not until their memorandum in support of a renewed Rule 29 motion that the defendants first suggested that the indictment did not charge a conspiracy with separate objects. Similarly, the defendants' proposed jury instruction on the conspiracy count merely specified that the jury must be required to find "that the object of their agreement was to impede or thwart the IRS as alleged in the indictment. . . . If you find that tax fraud was not the object of the conspiracy, then even if you find that tax fraud was a foreseeable consequence of the conspiracy, you must find the defendants not guilty." Again, the defendants' own conduct reveals no particular emphasis on the unity of the charged object.
Nor have we found that the defendants placed an undue emphasis on defending against the government's proof of Muntasser's agreement with unindicted co-conspirators in 1993. In fact, Muntasser's principal defense to the Count 2 conspiracy was that he withdrew from the conspiracy by 1996.[27] He expressed this position through the opening statement of his defense counsel, through cross-examination of witnesses, including Afif Kadri, one of Care's founding officers, and again through closing argument.
The absence of outward indications of prejudice is not a surprise: a less-than-vigorous defense of the conduct underlying the narrower conspiracy would have compromised the defendants' defense of other charges. For example, the evidence supporting the narrower conspiracy was directly relevant to Count 1, which charged all three defendants with a scheme to conceal material facts from the FBI, IRS, and INS, and Count 8, which charged all three defendants with endeavoring to obstruct the due administration of the Internal Revenue laws. Thus, even if the defendants *56 subjectively believed that the government's failure to prove a conspiracy to fraudulently obtain Care's tax exemption in 1993 was fatal to the conspiracy claim, the defendants had strong incentives to continue to challenge the evidence that most demonstrated their willing agreement to fraudulently maintain that exemption in subsequent years.
Finally, in a different version of their prejudice argument, the defendants claim that the variance affected their substantial rights because, by charging a larger conspiracy than it could ultimately prove, the government was permitted to introduce much of the so-called "terrorism" evidence, relevant to Muntasser's initial motivation for incorporating Care, which would not have been admissible if the government had charged only the narrower conspiracy at the outset. According to the defendants, "The government should not be permitted to have it both ways" (i.e., securing the admission of potentially inflammatory evidence through a broadly worded charge while securing a conviction on a narrower ground).
The defendants have underestimated the extent to which the challenged evidence was relevant to the narrower conspiracy. The most inflammatory evidence presented at trial was the content of Care's "Al-Hussam" newsletters, with its accounts of the violent jihad being conducted overseas, described by the district court as "blood curdling." While the newsletters were probative of whether Care was a successor to Al-Kifah and whether Muntasser incorporated Care to legitimize the tax exemption Al-Kifah incorrectly claimed, they also played a central role in explaining why Care's Form 990 filings were fraudulent. Similarly, the expert testimony explaining the concept of economic jihad, and thus the way in which Care's "orphan sponsorship program," among other things, promoted and supported the mujahideen and jihad, would have been independently admissible to prove the pattern of conscious concealment that reflected agreement among the defendants when they filed the Form 990s. Consequently, in this way as well, the variance in proof at trial did not prejudice the defendants' substantial rights.[28]

3. Did the Government Prove the Narrower Conspiracy?
The defendants contend that the government may not rely on a variance to reinstate their conspiracy conviction because the evidence at trial was insufficient to demonstrate a narrower conspiracy among the defendants. As noted, the general conspiracy statute, 18 U.S.C. § 371, criminalizes the conspiring of two or more people "to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner *57 or for any purpose." The defendants were charged under § 371's defraud clause with conspiring to defeat the IRS's proper assessment and collection of tax revenue, commonly known as a Klein conspiracy. See Goldberg, 105 F.3d at 773. To prove a Klein conspiracy, the government is required to establish both "an agreement whose purpose was to impede the IRS (the conspiracy)," and the knowing participation of each defendant in that conspiracy. United States v. Adkinson, 158 F.3d 1147, 1154 (11th Cir.1998). Although "[v]olumes could be written" on the "subtle problems in discriminating `purpose' from `knowledge' and in separating the objects of a conspiracy from its more remote consequences," it is well settled in this circuit that, "where the conspirators have effectively agreed to falsify IRS documents to misstate or misattribute income, . . . the factfinder may infer a purpose to defraud the government by interfering with IRS functions." Goldberg, 105 F.3d at 774. We therefore turn our attention to the evidence at trial that indicates the defendants' knowing agreement to falsify Care's tax filings.[29]
The government presented no direct evidence of an agreement either among the defendants or between any defendant and an unindicted co-conspirator. Of course, this is unsurprising. By their very nature, criminal conspiracies are clandestine and inchoate, and "may be completed in the brief period needed for the formation of the agreement and the commission of a single overt act in furtherance of the conspiracy." Boyle v. United States, 556 U.S. 938, 129 S.Ct. 2237, 2246, 173 L.Ed.2d 1265 (2009); see also United States v. Rodriguez-Velez, 597 F.3d 32, 39 (1st Cir.2010). Accordingly, the government is not required to offer proof of an express agreement. Rather, it is a "well-established legal principle that a conspiracy may be based on a tacit agreement shown from an implicit working relationship." United States v. Patrick, 248 F.3d 11, 20 (1st Cir.2001). As we detail below, there was sufficient evidence here of a deliberate, coordinated effort among the defendants reflecting just such a tacit agreement.
The government's theory at trial was that the defendants, through a series of fraudulent Form 990 filings, intentionally concealed from the IRS the fact that Care's activities substantially advanced two non-charitable purposes: financial support of the mujahideen and promotion of jihad. During their tenure with Care, each defendant filed at least one Form 990. Muntasser signed and filed Care's Form 990s for the 1993, 1994, and 1995 tax years. He did so with considerable assistance from Waseem Yassin, an unindicted co-conspirator and an officer of both Care and Al-Kifah. For example, Yassin contacted an attorney to assist in the preparation of the forms, he provided the attorney with Muntasser's materially false Form 1023 application for tax exemption, and he gave an incomplete description of Care's activities to the attorney when that information was requested.
Al-Monla had been involved with Care since 1993, became more involved in 1995, and eventually succeeded Muntasser as Care's President in 1996. The government introduced evidence that showed how, prior to becoming President, Muntasser *58 and Al-Monla worked closely together to advance Care's non-charitable purposes. For example, the evidence showed that the two defendants jointly met with Mohammed Chehade, the executive director of GRF, to discuss the solicitation of donations and "coordinating with the battalion." It also introduced a written pledge of support to the Afghan warlord Gulbuddin Hekmatyar, which was signed by Muntasser, Al-Monla, Yassin, and another unindicted co-conspirator. In 1996, the year Muntasser became president, Yassin stated in a recorded conversation that his involvement in Care was waning and that he would be handing the reigns over to someone else. Yassin subsequently provided Al-Monla with Care's financial information. Following his tenure as President, Al-Monla served as Care's Treasurer in 1998. He signed and filed Care's Form 990 for that year.
Mubayyid, Al-Monla's brother-in-law, performed volunteer work for Care in 1993 and 1994 before leaving the country for several years. In 1998 or 1999, Mubayyid succeeded Al-Monla as Care's Treasurer. He signed and filed amended Form 990 returns for the 1997, 1999, and 2000 tax years.
The Form 990s filed by the defendants were nearly identical, regardless of the preparer. Substantially mirroring the Form 1023 submitted by Muntasser in 1993, each return listed only the same four program accomplishments: food distribution, cash assistance to orphans and widows, medical assistance for refugees, and grants to other welfare organizations. As we explain below, however, the evidence showed that Care's day-to-day activities and objectives were markedly different than those reported to the IRS. The consistency of the misrepresentations over a span of nearly ten years and the failure of the defendants to disclose precisely those activities that were most likely to jeopardize Care's tax-exempt status provide strong circumstantial evidence that the defendants were operating under an implicit agreement. See, e.g., United States v. Shea, 211 F.3d 658, 665 (1st Cir.2000) (pointing to evidence of "a common and continuing aim, similar methods of operation, continuity in personnel, and interdependence" to prove conspiracy); cf. United States v. Niemi, 579 F.3d 123, 127 (1st Cir.2009) ("[I]nterdependence may be shown where one participant knows that his own success depends on the continued existence and health of the [unlawful] organization as a whole."). That the misrepresentations came from defendants who had assumed substantial leadership roles in the organization; who, in those roles, had primary authority over Care's tax filings, which were central to the fraud; and who succeeded one another in those roles, further negate the alternative possibility that any falsity was the product of separate, individual misunderstandings about the required disclosures. Cf. United States v. Peters, 732 F.2d 1004, 1007 (1st Cir.1984) ("The jury could reasonably have disbelieved that [defendants], as cousins and as president and vice president, respectively, of a relatively small company, acted entirely independently of one another. . . ." (footnote omitted)).
While the above evidence demonstrates an implicit agreement among the defendants, other evidence shows that the defendants had knowledge that their Form 990 submissions were materially false. To begin with, the evidence showed that Care was a small, tight-knit organization whose members were actively and intimately involved in its cause. Its officers were volunteers whose roles were not rigidly segregated.[30]*59 We have previously held that an organization's small size and informal structure may support a jury's inference that the organization's officers had knowledge of and voluntarily participated in a conspiracy. See United States v. Pesaturo, 476 F.3d 60, 72 (1st Cir.2007).
Additionally, the evidence at trial indicated that financial support of the mujahideen and promotion of jihad were Care's primary purposes. The "Al-Hussam" newsletters were replete with exhortations to join the jihad or to finance the mujahideen. The Zakat Calculation Guide distributed by Care described it as "imperative" to "give part of your Zakat to Mujahideen" (which it defined as "those who are going out for Jihad, fighting in the path of Allah") because "the Mujahideen represent the most needy category today since they are facing a shortage of financial support." Care's website similarly contained overt solicitations for support of the mujahideen. Witnesses testified that, in addition to distributing the "Al-Hussam" and the Zakat guide, Care was selling books and tapes advocating jihad at the lectures of religious speakers that it hosted. Indeed, the government even introduced a recorded phone conversation between Al-Monla and the head of another Islamic charity, in which Al-Monla described Care as existing on "the rear lines" and "financing the brothers picking apples," a reference to Care's financial support of the mujahideen.
Through its solicitations, Care collected nearly two million dollars in untaxed donations. Many of the donation checks received by Care during this time expressly indicated that the funds were to be used for "mujahideen," "fighters," "martyrs," and "Jihad." Some checks specified particular countries, or even particular groups of fighters, for which the funds should be used. For example, three checks presented to the jury bore the memo lines: "Bosnia mujahideen," "Jihad Bosnia," and "mujahideen Bosnia, 9th Battalion." During this time, Care deposited checks made out to Al-Kifah and even to "Human Services Office," referring to MAK.
The government introduced evidence of personal checks from each of the defendants to Al-Kifah or Care containing similar instructions. Muntasser made a donation to Al-Kifah shortly after Care's formation in April 1993 in which he indicated that the funds were "Zakat for the mujahideen in Afghanistan . . . Zone 1." He subsequently made a donation to Care in which he stated that his donation was for "renewing the sponsorship of the family of a martyr." Despite not being a formal officer at the time, Mubayyid made two donations to Care in 1993 for "Printing of the Al-Hussam" and "Al-Hussam and pilgrimage." A check from Al-Monla in 1993 simply reads, "Buying Bosnia." This evidence makes plain the defendants' intimate knowledge of the very activities and purposes of Care that were concealed through the submission of incomplete and inaccurate Form 990s.
We are of course always wary of the dangers associated with a § 371 conspiracy. See Goldberg, 105 F.3d at 775 ("[T]he defraud clause of section 371 has a special capacity for abuse because of the vagueness of the concept of interfering with a proper government function."). Its broad *60 sweep can capture the innocent as well as the culpable. Cf. Dennis, 384 U.S. at 860, 86 S.Ct. 1840. This is not such a case. The defendants, well known to each other, succeeded each other as authority figures in a small organization that benefitted from the perpetuation of a fraudulent tax status. Given the significance of the factual misrepresentations when juxtaposed with the single-mindedness of Care's apparent mission, given the overlap among the defendants and the closeness of their working relationships, and given the consistency of the misrepresentations necessary to sustain the fraud for so long, the government's evidence sufficed to prove a narrower conspiracy to fraudulently maintain Care's tax exemption.

B. Mubayyid's Claims
Mubayyid makes several challenges to his convictions on appeal. First, he argues that his convictions for filing false tax returns and for obstructing the functions of the IRS rest on his answer to a tax-form question that is fundamentally ambiguous, precluding the jury from finding deliberate falsity. Second, he challenges the legal sufficiency of the government's evidence on his conviction for scheming to conceal material facts from the IRS. Finally, he claims that he was prejudiced on all counts by the admission of a recorded phone conversation in which another speaker urged him to remove Care's documents from the storage unit eventually searched by the FBI.[31]

1. False Tax Filings
Mubayyid was convicted on three counts (Counts 3-5) of filing false tax returns, in violation of 26 U.S.C. § 7206(1), and one count (Count 8) of corruptly endeavoring to obstruct the administration of the Internal Revenue laws, in violation of 26 U.S.C. § 7212(a). All four counts rest on Mubayyid's answers to Question 76 on Care's Form 990 for the tax years 1997, 1999, and 2000. Question 76 asks, "Did the organization engage in any activity not previously reported to the IRS? If `Yes,' attach a detailed description of each activity." The instructions accompanying Form 990 clarified the inquiry as follows:
Attach a statement explaining any significant changes in the kind of activities the organization conducts to further its exempt purpose. Include new or modified activities not listed as current or planned in the organization's application for recognition of exemption [IRS Form 1023], or not yet reported to the IRS by a letter to its key district director or by an attachment to the organization's return for any earlier year. Also include any major program activities that are being discontinued.
For each of the charged years, Mubayyid answered "No" to Question 76. The government alleges that, in so doing, he intentionally concealed from the IRS the fact that Care was "engaged in activities involving the solicitation and expenditure of funds to support and promote the mujahideen and jihad."
To support a conviction for filing false tax returns, the government was required to prove, inter alia, that Mubayyid filed a return that was "false as to a material matter" and that he "signed the return willfully and knowing it was false." United States v. Boulerice, 325 F.3d 75, 79-80 (1st Cir.2003) (quoting United States v. LaSpina, 299 F.3d 165, 179 (2d Cir. 2002)). Count 8 charged the same underlying *61 conduct, with a purpose "to obstruct or impede the due administration of the Internal Revenue laws." United States v. Marek, 548 F.3d 147, 150 (1st Cir.2008). The filing of false tax documents to mask an organization's non-charitable purposes falls within the purview of § 7212. See United States v. Mitchell, 985 F.2d 1275, 1279 (4th Cir.1993). Thus, for all four tax-filing charges, the government needed to show that Mubayyid knew when he answered Question 76 on Care's Form 990 for the 1997, 1999, and 2000 tax years that the answer was false.[32]
The government argued at trial that Question 76 required the reporting of any activities ever conducted by Care that had not previously been reported. Mubayyid asserts that he reasonably understood the question to require reporting only of changes in Care's activities and only when those changes occurred during the single tax year for which the Form 990 was filed. Mubayyid's version of the question is thus more limited both temporallycovering only one year, rather than the organization's lifetimeand in contentcovering only new undertakings or activities that had significantly changed from the previous year, rather than all activities Care had not previously reported. Mubayyid maintains that, under his version of the question, the record does not allow a finding beyond a reasonable doubt that he knew his answers on the tax forms were false.
Mubayyid thus claims that the government failed to show that his answers were willfully false because Question 76 is fundamentally ambiguous and, hence, cannot legally support a jury's finding that his answer was willfully false. It is not unusual for the defendant in cases such as this to argue that the question he is alleged to have answered falsely was ambiguous, that his understanding of the question differed from the government's, and that, under his understanding, he answered the question truthfully. United States v. Posada Carriles, 541 F.3d 344, 362 (5th Cir.2008). Traditionally, it is the province of the jury to decide whether the defendant "intended to and did in fact give a response that was literally false." United States v. Richardson, 421 F.3d 17, 33 (1st Cir.2005) (quoting United States v. Finucan, 708 F.2d 838, 848 (1st Cir.1983)) (internal quotation mark omitted).
We have recognized, however, that in the exceptional case a question may be so fundamentally ambiguous as to foreclose a jury's resolution of a perjury or false statement charge because "it could never be said that one intended to answer such a question untruthfully." Id. (quoting United States v. DeZarn, 157 F.3d 1042, 1049 (6th Cir.1998)). As we shall explain, this is not such a case. Any ambiguity in the substantive scope of Question 76 is, at most, the sort of imprecision that is appropriately evaluated by a jury. As for the question's temporal scope, any ambiguity is irrelevant to our analysis because the government produced sufficient evidence for a jury to find that Mubayyid provided false answers to the question even as he claims to have understood it. We expand on these two conclusions in turn.

a. The Substantive Scope of Question 76
As noted, Question 76 asks simply whether "the organization engage[d] in any activity not previously reported to the IRS." In elaborating on the reporting obligation, *62 the guiding instructions demand an explanation of "any significant changes in the kind of activities the organization conducts to further its exempt purpose." Taking his lead from the instructions, Mubayyid argues that the question asks only about "changes," and that he was thus not required to report activities that were ongoing and unchanged, even if they had never previously been included in Care's filings. He asserts that Care had engaged in no new activities in the relevant tax years, and that his answer to Question 76 could therefore not be found to be false. We consider this view of Question 76 to be unreasonable.
A straightforward reading of Form 990 and its instructions makes plain that Question 76 seeks the disclosure of information about activities not accurately depicted in the organization's application for recognition of exemption, Form 1023, or in any other year's return. Indeed, reading Question 76 together with Form 1023 confirms that, in posing Question 76, the IRS's purpose was to require organizations to update their initial filings on an annual basis. Like Question 76, Form 1023 contains a broad request for information regarding every activity of the organization. It asks organizations to provide "a detailed narrative description of all the activities of the organization." It instructs filers to list "each activity separately in order of importance" and to include, "as a minimum," "(a) a detailed description of the activity including its purpose; (b) when the activity was or will be initiated; and (c) where and by whom the activity will be conducted." The interpretation of Question 76 advanced by Mubayyid would defeat the IRS's clear intent to obtain an accurate, current report of the organization's activities. It defies common sense to conclude that the IRS sought, under penalty of perjury, detailed information about a tax-exempt organization's activities if begun, altered, or ended in the current tax year, but that it was wholly uninterested in such an organization's ongoing, previously unreported activities if begun in any other year.
Hence, in context, the instruction's references to "changes" cannot reasonably be understood to circumscribe the broad request for disclosure of "any activity" required by the text of Question 76 itself. Mubayyid's proffered reading does not take into account the IRS's justifiable assumption, built into the instruction, that an organization would have complied with its obligation to disclose previously existing reportable activities in either its Form 1023 or in a prior Form 990. In other words, the instructions focus on "significant changes" because the IRS expects that "changes" will be the only information not previously reported. The question itself, however, clearly requires disclosure of "any activity not previously reported to the IRS." Further, the request in the instruction for disclosure even of those activities that are being discontinued highlights that the IRS is seeking to correct and update all information previously submitted to it about the organization's activities. A defendant who has previously filed a fraudulent or incomplete return, in contravention of the government's reasonable expectation, may not then "`twist the meaning of a question in his own mind into some totally unrecognizable shape and then hide behind it' by alleging its fundamental ambiguity." Richardson, 421 F.3d at 35 (quoting United States v. Reveron Martinez, 836 F.2d 684, 691 (1st Cir.1988)).
In urging an interpretation of Question 76 that disregards its obvious context, Mubayyid falls far short of demonstrating a fundamental ambiguity that would preclude a jury's evaluation of his defense. Of course, a defendant is entitled to argue even an unreasonable interpretation of a *63 question to the jury.[33] Here, Mubayyid did so, and the jury rejected it. But the unreasonableness of his claimed interpretation shows that Question 76 is, at most, only arguably ambiguous. Where a question is only arguably ambiguous, the issue of the defendant's guilt is properly one for the jury. Id. at 33.
There is no question that sufficient evidence supported the jury's rejection of Mubayyid's claim that he understood Question 76 to require reporting only of changes. The jury reasonably could have found that Mubayyid, as Care's treasurer, understood the context described above and, specifically, knew that the IRS sought through Question 76 to determine whether the organization remained entitled to its charitable tax status. To that end, the IRS plainly needed to know what the organization was currently doing. The interpretation Mubayyid posits is so inconsistent with the plain intent of the question when considered in context thatparticularly given his role as the organization's financial managera reasonable jury could readily reject his claim that he understood the question in the way he describes.
In sum, we conclude that Question 76 is, at most, only arguably ambiguous in its demand that the filer advise the IRS of all activities, not simply changes. It was well within the jury's capability to find that Mubayyid in fact understood that the obligation imposed by Question 76 required reporting of more than just Care's new or modified activities.

b. The Temporal Scope of Question 76
At trial, the government's position was that Question 76 required a Form 990 filer to disclose any previously unreported activity in which the filing organization had ever engaged, irrespective of whether that activity had taken place during the year that was the subject of its tax filing. Mubayyid argues that the question is reasonably understood to require reporting only of activities occurring during the subject tax year. He asserts that "common sense argues that if one is filing a 1999 tax form the questions pertain to 1999."
Mubayyid's claim of fundamental ambiguity with respect to the temporal scope of Question 76 need not detain us. A question is not fundamentally ambiguous if "a reasonable jury, given the language of the question to the defendant and the context in which it was asked, could conclude beyond a reasonable doubt that the defendant knew that the answer he gave was false." United States v. Boskic, 545 F.3d 69, 90 (1st Cir.2008); see also Richardson, 421 F.3d at 33 ("In determining whether a statement made in response to an ambiguous question could be said to be false, `the context of the question and answer becomes critically important.'" (quoting United States v. Farmer, 137 F.3d 1265, 1269 (10th Cir.1998))). Even when the temporal scope of the question is viewed as Mubayyid claims to have understood it, the jury's verdict was supported by the evidence presented at trial. Specifically, as detailed below, the record supports a finding *64 that Mubayyid answered Question 76 falsely by failing to disclose three distinct activities: the publication of the "Al-Hussam" newsletter in 1997; the operation of Care's website in 1999 and 2000; and, in all three years, an orphan sponsorship program that targeted the families of martyred mujahideen.[34]

c. The Evidence of Falsity

i. The Newsletter in 1997
It is undisputed that Care published a single issue of the "Al-Hussam" newsletter in January 1997. Dawn Goldberg, an IRS employee, testified that she would "certainly" expect the publication of a newsletter such as the "Al-Hussam" to be disclosed in response to Question 76 because the instructions "say it should be, but, also, it's an activity of the organization." She later repeated that she would expect it to have been disclosed "because, as we read in the directions, it falls in the category of `program service.'"
Consistent with this testimony, a thorough reading of the Form 990 instructions illuminates that the phrases "activities" and "major program activities," used in Question 76 and the Form 990 instructions, encompass an organization's newsletters. In explaining a part of the form preceding Question 76, the Form 990 instructions define the term "program services" as "mainly those activities that the reporting organization was created to conduct and which . . . form the basis of the organization's current exemption from tax." That section then includes the following explanation:
Program services can also include the organization's unrelated trade or business activities. For example, publishing a magazine is a program service even though the magazine contains . . . advertising, the income from which is taxable as unrelated business income.
Similarly, the instruction for Part III, "Statement of Program Service Accomplishments," states:

*65 A program service is a major (usually ongoing) objective of an organization, such as adoptions, recreation for the elderly, rehabilitation, or publication of journals or newsletters. Specify the service outputs, products, or other measures of a program service, such as clients served, days of care, therapy sessions, or publications issued.
Thus, in the full context of the Form 990 instruction, it is clear that the term "activity" used in Question 76 encompasses all "program services," which are by definition "major objective[s] of an organization" and which, at the very least, include the publication of journals or newsletters.
It is also clear that the publication of the "Al-Hussam" newsletters, in particular, was a major objective of Care. The evidence revealed that thousands of copies of the newsletters were printed and distributed internationally. Witnesses testified to the newsletters' "underlying theme" of the promotion of jihad. The newsletters contained "descriptions of ongoing fighting happening in different corners of the world, interviews of fighters, and encouraging people to participate in the fight and, . . . if they can't participate, to provide funding." The jury heard excerpts from numerous issues of the newsletters in which readers were exhorted to finance the mujahideen if they could not otherwise join the jihad. The government combined this evidence with expert testimony explaining the concept of "economic jihad," the belief that individuals who "cannot participate in that fighting themselves . . . should at least finance someone who can." A reasonable jury could have considered the centrality of the "Al-Hussam" newsletters to Care's organizational mission as evidence both that Mubayyid would have recognized that publication of the "Al-Hussam" was an activity that should be disclosed, and that the "Al-Hussam" was willfully not disclosed to the IRS precisely because it reflected Care's non-charitable purposes.
Mubayyid attempts to obfuscate Question 76's otherwise clear instruction by pointing to testimony by Dawn Goldberg on cross-examination. When questioned about a separate section of the Form 990 that asks filers to segregate the organization's expenses among three categories program services, managerial services, and fundraisingGoldberg admitted that the filer must use some amount of judgment. She acknowledged that, depending on the facts and circumstances, it might not be unreasonable for a filer to identify all of the printing expenses associated with a newsletter as fundraising expenses. Mubayyid claims that the possibility that he reasonably categorized the expense of publishing the "Al-Hussam" newsletters as a fundraising expense rather than a "program service" expense invalidates the argument that the newsletters are necessarily program services that would need to be disclosed in response to Question 76.
This argument is unavailing. First, Mubayyid did not attribute Care's printing and publication expenses to fundraising on the Form 990 for 1997. Rather, all of Care's printing expenses for that year were categorized as managerial service expenses. The evidence thus belies Mubayyid's claim that his statement was not false because Care had consistently treated the "Al-Hussam" newsletters as merely a fundraising device, rather than an activity of the organization.
Second, even if the attribution of printing expenses in 1997 was a mere scrivener's error, a reasonable jury could have concluded that Care's designation of the "Al-Hussam" newsletters as a fundraising activity would not have been a reasonable accounting choice. Dawn Goldberg testified that she looked at thirty-five "Al-Hussam" *66 newsletters and saw "a handful, maybe six or eight little blurbs" related to fundraising. Referencing the Form 990 instructions' directive to "allocate expenses that relate to more than one functional category," she acknowledged that "a small amount of [the publication expenses for the "Al-Hussam"] might be attributable to `fundraising,'" but that the newsletter is primarily "educational and informative," and should therefore properly be designated as a "program service."
In light of the Form 990 instructions including the specific example of newsletters as a program service activityand Goldberg's testimony on the inappropriateness of designating the "Al-Hussam" as a fundraising device, it would have been reasonable for the jury to conclude that the designation instead reflected an intent to conceal Care's true nature. In any event, the jury was entitled to conclude that Mubayyid understood that Question 76's request for "any activity" of the organization not previously disclosed called for disclosure of Care's publication of the "Al-Hussam" newsletters, regardless of whether Care was permitted to allocate the associated expenses as "fundraising" in other parts of the Form 990.
Taking another tack, Mubayyid claims that his answer was not false because the "Al-Hussam" newsletters had arguably already been disclosed to the IRS on Care's initial application for tax exemption, Form 1023, and therefore were not required to be disclosed in answer to Question 76. Here, Mubayyid refers to a statement in Care's initial Form 1023 that the organization's fundraising efforts would comprise "[s]ubstantial efforts . . . by means of: . . . mailings." Again, his argument fails.
A reasonable jury could have readily concluded that the "Al-Hussam" newsletters were not, in fact, the type of mailings disclosed to the IRS in the cursory reference to "mailings" on the Form 1023. To begin with, the Form 1023 refers to such mailings prospectively, yet the evidence at trial demonstrated that two "Al-Hussam" newsletters had already been published in Care's name at the time the Form 1023 was filed. Likewise, neither the "Al-Hussam" newsletters nor the Zakat Calculation Guide were submitted with the Form 1023 as "representative copies of solicitations for financial support."
Moreover, Robert Charnoff, a former IRS employee who had been responsible for reviewing Care's Form 1023 application, testified for the government that fundraising mailings are typically "just a one- or two-page solicitation letter," while the evidence presented at trial demonstrated that the "Al-Hussam" newsletters primarily consisted of multi-page descriptions of the successes of jihad, exhortations to join the fighting, and reminders of the duty to engage in jihad. They contained only a few small blurbs that might be fairly characterized as overt fundraising. On this basis, Charnoff explained that he would have expected the "Al-Hussam" newsletter to be identified elsewhere because "it's an activity in its own right."
We thus conclude that, based on the evidence presented at trial, a reasonable jury could find that Mubayyid understood that the "Al-Hussam" newsletter was required to be disclosed in response to Question 76 on the 1997 Form 990.[35]

ii. The Website in 1999 and 2000
The government's evidence at trial showed that, by 1999, Care was operating *67 a website that was described as "similar in content" to the "Al-Hussam" newsletters. A witness testified for the government that Mubayyid had approached him in 1997 or 1998 to discuss the construction of a website for Care. The two men worked together over the course of nearly a year on designing and naming the website, and on hiring a local business to host it. According to the witness, Mubayyid provided a CD of content that he wanted uploaded to the website, the witness constructed the website, and he provided Mubayyid with the administrative privileges to modify and update the website once it was up and running. The website was operational by early 1999.
The government also introduced printed copies of the content of Care's website as of June 4, 2000, and March 1, 2001. Those printouts reveal that Care was providing regularly updated content to its website's readers. As one example, Care maintained a page entitled "News from the Battlefields of Chechnya" that provided daily news bulletins throughout late December 1999. The website also republished selected articles from the "Al-Hussam" newsletters, including a collection explaining the duty of jihad, an article entitled "Story of a Muhajid," and an exhortation for readers to "Do Something!" Additionally, the website contained information about calculating Zakat and a contact page informing readers where to send their donations (with Care's United States tax identification number prominently displayed).
In these respects, Care's website effectively replaced the publication of the "Al-Hussam" newsletter following its discontinuation in 1997. It provided an important communications link between the organization and potential supporters, and it sought to generate affirmative conduct to benefit the mujahideen. Hence, based on the website, the jury properly could have found that Mubayyid knowingly made a false statement about a material matter when he declared that the organization had engaged in no previously unreported activity in 1999 and 2000.

iii. The Orphan Sponsorship Program
The third activity to which we turn our attention spanned all three years covered by Counts 3-5 and 8, and the alleged falsity was a matter of inaccurate disclosure rather than nondisclosure. Throughout the trial, the government argued that Mubayyid's failure to correct substantial misrepresentations in Care's Form 1023, through the attachments requested in Question 76, concealed the organization's support for and promotion of the mujahideen and jihad. In particular, the government alleged that Care's initial application for tax exemption was false because it failed to disclose to the IRS that Care's orphan sponsorship program focused on the orphans of martyrs. When asked to provide "(a) a detailed description of the activity including its purpose," Muntasser stated in the Form 1023 that Care would develop a program for orphan sponsorship in Bosnia, Afghanistan, and Kashmir. Consistent with this representation, each of the Form 990s submitted by Mubayyid reported a substantial amount of cash assistance to orphans and widows.
At trial, an expert for the government, who testified that he had reviewed the materials and solicitations associated with Care's orphan sponsorship program, opined that the purpose of the program's focus on the orphans of martyrs was to promote violent jihad:
In the context of encouraging people to go and participate in fighting, it's important to remove anything that may prevent them from doing so, to remove disincentives. If a person who is inclined *68 to go fight knows that if something should happen to him that his family would be taken care of, that removes the disincentive, and he's more likely to be able to go and fight.
The witness also testified that he had seen similar, targeted solicitations used by organizations to support mujahideen activities "many times." This focus was reflected in Care's website solicitation, which depicts a child to be sponsored as "an orphan whose father died in defense of the faith."
Because orphan sponsorship was, from Care's own perspective, a responsive answer to the call for "activities" on the Form 1023 and "program services" on the Form 990s, Mubayyid cannot sensibly deny that it was also an "activity" within the understood meaning of Question 76. Instead, as with the "Al-Hussam" newsletter, Mubayyid suggests that this activity had already been disclosed to the IRS on Care's Form 1023 and on Care's Form 990s for previous years. Although those forms did not reveal that the organization's orphan sponsorship focused on the children of martyred fighters, Mubayyid argues that, because the Form 1023 disclosed that the program would focus on orphans in war-torn countries, "[i]t is no great inferential leap to conclude some of the widows and orphans became such because husbands and fathers died fighting." He also notes that the sole defense witness, a former IRS employee, testified that the program's focus would not have changed his opinion of Care's entitlement to tax exemption "because widows and orphans are traditional objects of charitable aid. It's not significant for tax purposes how they became widows and orphans."
The defense testimony was directly contradicted, however, by Robert Charnoff, the IRS employee who actually reviewed Care's application. Charnoff testified that he "almost certainly" would have denied Care's initial application for tax exemption if Care had disclosed that its orphan sponsorship program targeted children of martyred mujahideen because "it's telling would-be fighters in foreign conflicts that if something happens to them, if they're killed say, this organization will provide funds to their orphans. So the net effect is it's an inducement for them to go to these areas of conflict." Likewise, Dawn Goldberg testified that evidence indicating that Care was "soliciting people to go out and fight, or soliciting money to help fighters," could have led to the revocation of Care's tax exemption because "one of the basic things [a 501(c)(3) charity] can't do is they can't do anything that's illegal or violate[s] public policy."
The materiality to the IRS of the undisclosed focus of Care's orphan sponsorship program demonstrates why the simple listing of an orphan sponsorship program on the Form 1023 and prior Form 990s was not an adequate disclosure of the activity that was in fact being carried out by Care. To employ a counterfactual, if Care had initially conducted the unfocused orphan sponsorship program described in the Form 1023, but later elected to focus its donations on the orphans of martyrs, the testimony by Charnoff and Goldberg makes clear that the change in the program's focus should have been disclosed in response to Question 76 as a substantial modification. On the same basis, it would have been reasonable for the jury to have concluded that Care's Form 1023 described an orphan sponsorship activity that Care had never conducted, and hence Mubayyid was required to report Care's actual orphan sponsorship program in response to Question 76 as an ongoing activity that had never been accurately disclosed.
*69 The 990s themselves, though incomplete in the way we have described, provide evidence that the orphan sponsorship program was ongoing during each of the tax years in question. In addition, a government witness who volunteered for Care in 1996 and 1997 acknowledged that Care was actively raising money for orphan sponsorship during those years, and authenticated a flyer soliciting donations for orphans in language substantially similar to that contained on the website. In 2000 and 2001, as described above, the website featured the program in a way that made clear its true purpose. Although there was no direct testimony or record evidence confirming the program's operation in 1999, the other evidence permits the reasonable inference that it was an ongoing activity.
We thus conclude that the government presented sufficient evidence from which a reasonable jury could have found that, in response to Question 76 on Care's Form 990s, Mubayyid willfully failed to disclose at least one reportable activity that occurred in each of the 1997, 1999, and 2000 tax years. Any arguable ambiguity in the temporal scope of Question 76 could not, therefore, have precluded Mubayyid's conviction for making a false statement; Mubayyid's answers would have been false even under the interpretation of the question consistent with his claimed understanding.
For the foregoing reasons, we affirm Mubayyid's convictions on Counts 3, 4, and 5, for filing false tax returns in violation of 26 U.S.C. § 7206(1), and his conviction on Count 8, for corruptly endeavoring to obstruct the administration of the Internal Revenue laws in violation of 26 U.S.C. § 7212(a).

2. Scheme to Conceal
Mubayyid claims that Count 1 of the indictment, which charged him with a scheme to conceal material information from a federal agency, in violation of 18 U.S.C. § 1001(a)(1), was not supported by sufficient evidence. The crime under § 1001(a)(1) is the concealment of a material fact by scheme, trick, or device.[36] The charge in the indictment, which covered all three defendants, alleged that the defendants concealed "material facts . . . to wit: the Defendants concealed the fact that Care International, Inc., was an outgrowth of and successor to the Al-Kifah Refugee Center and was engaged in non-charitable activities involving the solicitation and expenditure of funds to support and promote mujahideen and jihad."
Mubayyid emphasizes that the language of the indictment following "to wit" stated that the defendants concealed "the fact that" before proceeding to describe two facts. Then, with echoes of his challenge to the Count 2 conspiracy, he asserts that the government necessarily charged each defendant with a "single-object scheme" that embraced both facts as if one. He notes that the government presented insufficient evidence at trial to demonstrate that his scheme encompassed one of those facts "for the simple reason that the Form 990 does not request any information regarding *70 whether the organization filing the return is the outgrowth or successor of another organization." As he did with the conspiracy charge, Mubayyid thus contends that his conviction must be vacated because the government failed to prove the specific scheme charged.
The government was not required to prove that Mubayyid schemed to conceal that Care was an outgrowth of, or successor to, Al-Kifah. It is well established that an indictment may charge alternative theories of guilt in the conjunctive, and that, "[w]hen a jury returns a guilty verdict on an indictment charging several acts in the conjunctive, the verdict stands if the evidence is sufficient with respect to any one of the acts charged." United States v. Murray, 621 F.2d 1163, 1171 n. 10 (1st Cir.1980); see also Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 24 L.Ed.2d 610 (1970). Moreover, indictments are to be read in a plain and commonsense manner. United States v. Flemmi, 245 F.3d 24, 29 (1st Cir.2001). The indictment charged Mubayyid with concealing two facts by scheme, trick, or device. Under our settled precedent, proof that he concealed either fact is sufficient to support his conviction. Mubayyid attempts to extend the defendants' constructive amendment argument from the conspiracy charge in Count 2 to the charge in Count 1; the argument is as unconvincing here as it was there. Cf. Dowdell, 595 F.3d at 68; Garcia-Paz, 282 F.3d at 1212 (holding that language preceded by the phrase "to wit" in the indictment is mere surplusage that may be disregarded and needs not be proven).
As a second line of attack, Mubayyid contends that his false statements on the Form 990s are legally insufficient to support his conviction under § 1001(a)(1) because they were not affirmative acts of concealment in the face of a legal duty to disclose.[37] As just described, § 1001(a)(1) criminalizes the concealment of material facts from a government agency by scheme, trick, or device. A separate provision of the statute, under which Mubayyid was not charged, criminalizes the making of materially false or fraudulent statements. 18 U.S.C. § 1001(a)(2). Reflecting this statutory separation, we have held that simple omissions fall short of constituting affirmative acts of concealment, which are required to prove a "scheme, trick, or device." United States v. St. Michael's Credit Union, 880 F.2d 579, 589 (1st Cir.1989). Additionally, under § 1001(a)(1), the concealment must occur in the face of a legal duty to disclose the material fact. See generally United States v. Anzalone, 766 F.2d 676, 682-83 (1st Cir.1985).
Mubayyid fails to acknowledge that one has a legal duty to disclose information when a response is required by statute, government regulation, or government form. See, e.g., United States v. Calhoon, 97 F.3d 518, 526 (11th Cir.1996); United States v. Kingston, 971 F.2d 481, 489 (10th Cir.1992); United States v. Bucey, 876 F.2d 1297, 1307 (7th Cir.1989). Moreover, by filing the false Form 990s, which he signed under penalty of perjury, Mubayyid did not passively fail to disclose material facts; he engaged in an affirmative act of concealment. Cf. St. Michael's *71 Credit Union, 880 F.2d at 590-91. His conduct is therefore sufficient grounds for a conviction under § 1001(a)(1).
Lastly, Mubayyid contends that, if the government did not charge Count 1 as a unitary scheme, his conviction needs to be set aside under the rationale of Yates v. United States, 354 U.S. 298, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957). See generally United States v. Nieves-Burgos, 62 F.3d 431, 434-37 (1st Cir.1995) (explaining Yates). Yates stands for the principle that a conviction must be vacated where the charged crime was submitted to the jury on two independent theories of guilt, one of which depends upon conduct that falls outside of the relevant limitations period, and where "it is impossible to tell which ground the jury selected." See id. at 312, 77 S.Ct. 1064 (emphasis added).
Yates is inapplicable to Mubayyid's conviction under § 1001(a)(1) because it is not "impossible to tell" whether the jury rested their verdict upon evidence of time-barred conduct. Cf. United States v. Zvi, 168 F.3d 49, 55 (2d Cir.1999); United States v. Hudgins, 120 F.3d 483, 487 (4th Cir.1997) (describing Yates's "impossible to tell" requirement as "integral to the rule's application"). The indictment charged all three defendants with scheming to conceal two facts: that Care was a successor to Al-Kifah, and that Care was engaged in non-charitable activities that included supporting the mujahideen and jihad. In separate counts, the jury convicted Mubayyid of filing false tax returns within the five-year limitations period by failing to disclose that Care was involved in non-charitable activities that involved supporting the mujahideen and jihad. As noted above, the filing of false tax returns is an affirmative act of concealment sufficient to support a conviction for scheming to conceal material facts under § 1001(a)(1). By contrast, there was no evidence at trial that Mubayyid engaged in any effort to conceal the fact that Care was a successor to Al-Kifah (the conduct which Mubayyid now claims would have occurred outside of the limitations period, if it had been proven). Thus, far from being "impossible to tell" whether the jury based its verdict on a theory of guilt that depends on time-barred conduct, it is obvious that Mubayyid's conviction under § 1001(a)(1) rests exclusively on his false Form 990 filings within the limitations period. The argument fails.

3. Recorded Telephone Conversation
Mubayyid also challenges the admissibility of a recorded telephone conversation between himself and the executive director of GRF, Mohammed Chehade, in which he declined the advice to remove Care's documents from a storage unit in response to the FBI's investigation of Care. In the telephone call, Mubayyid informs Chehade that the FBI had attempted to search Care's former offices. The relevant portion of the call was as follows:
Chehade: What did you have? Did you have things?
Mubayyid: Actually, we had already moved, we were not there. . . . We had moved our effects to uh-wha do you call it? To storage.
. . .
Chehade: Alright. What do you have? Storage? What-what do you have for storage? Take the things out of storage.
Mubayyid: They were originally locked, in- in- in-, uh, in- the ugh- the office, and we moved them to the storage.
. . .
Chehade: Remove them.
Mubayyid: It need uh, one is afraid that they may think that there is something, I mean

*72 Chehade: No.
Mubayyid: I don't want to touch anything so that there is no.
Chehade: No, no, no, remove them, remove them.
The government introduced the conversation to show that, notwithstanding his statement to the contrary at the time, Mubayyid ultimately removed and destroyed documents from the storage unit, evidencing his consciousness of guilt. To that end, the government tied this conversation to evidence indicating that three particularly damning documents, one of which involved GRF, had been removed from the storage unit between the time of the FBI's covert search in October 2001 and the time of the FBI's subsequent search in April 2003. It also explained this theory of the evidence to the jury in closing argument.
Appropriately, the district court instructed the jury that it could not consider Chehade's statements for the truth of the matter asserted, and that the conversation was being offered to show the impact upon Mubayyid. The evidence was admissible for this limited purpose. Cf. United States v. Walter, 434 F.3d 30, 34 (1st Cir.2006) (concluding that informer's out-of-court statements during taped "sting" were admissible as context for defendant's taped responsive admissions).
In any event, the admission of this phone conversation was harmless. "[A] non-constitutional evidentiary issue will be treated as harmless if it is highly probable that the error did not contribute to the verdict." United States v. Rose, 104 F.3d 1408, 1414 (1st Cir.1997). At trial, the government introduced evidence that the storage unit was rented by Mubayyid and remained under his control during the time between the two FBI searches. It further showed that many of Care's documents were retrieved from Mubayyid's residence during the 2003 search, that the documents in question were not recovered from either the storage unit or the residence, and that the storage unit contained a paper shredder in 2003 that had not been present in 2001. Thus, the government had substantial other evidence from which it could have asked the jury to draw the same conclusion. Moreover, by choosing to demonstrate consciousness of guilt as it didi.e., by emphasizing that Mubayyid had been asked to remove documentsthe government necessarily highlighted for the jury that Mubayyid, in fact, refused to do so. For these reasons, it is highly probable that the introduction of the challenged phone conversation and the prosecutor's reference to it in closing argument did not contribute to the verdict.

C. Muntasser and Mubayyid's Joint Claim[38]
Muntasser, in an argument adopted by Mubayyid, contends that so-called "terrorism" evidence admitted to prove the conspiracy of which both defendants were ultimately acquitted by the district court was so extensive, inflammatory, and prejudicial that it necessarily spilled over into the jury's consideration of their guilt on other charges. In effect, they argue that their acquittal produced a "retroactive misjoinder."[39]See generally United States v. *73 Hamilton, 334 F.3d 170, 181-82 (2d Cir. 2003). Because we reinstate the conspiracy conviction against all three defendants on Count 2, the defendants' contention is without merit. As we explained when addressing the defendants' claim that the variance was prejudicial, the challenged evidence was properly admitted to prove the conspiracy.
Additionally, the defendants are unable to show that, though properly admitted for the conspiracy charge, this evidence was so inflammatory that it prejudiced the jury against them on the discrete counts for scheming to conceal material facts from the IRS, filing false tax returns, endeavoring to obstruct the administration of the Internal Revenue laws, and making a false statement to the FBI. In order to determine whether a new trial is warranted, we look for a "serious risk" that the joinder of offenses compromised a specific trial right or "prevent[ed] the jury from making a reliable judgment about guilt or innocence." United States v. Houle, 237 F.3d 71, 75-76 (1st Cir.2001) (quoting Zafiro v. United States, 506 U.S. 534, 539, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993)).
Here, the district court went to considerable lengths to safeguard against the possibility of prejudicial spillover.[40] The court's timely use of cautionary instructions weakens the inference of prejudice to be drawn from any evidence that would not have been independently admissible. See United States v. Ofray-Campos, 534 F.3d 1, 35 (1st Cir.2008) (citing United States v. Sabatino, 943 F.2d 94, 96-97 (1st Cir.1991)). We have "no basis to suppose that the jurors disregarded the trial judge's admonitions and departed on a frolic of their own." United States v. Pierro, 32 F.3d 611, 616 (1st Cir.1994).
Additionally, the charges on which Muntasser and Mubayyid were convicted are distinct from the conspiracy charge to which the challenged evidence had primary relevance. This factor increases the likelihood that the jury engaged in the "individualized factfinding" to which each defendant was entitled. See United States v. Josleyn, 99 F.3d 1182, 1188 (1st Cir.1996). Indeed, the jury asked several incisive questions during deliberation that demonstrated its discriminating appraisal of all the evidence.[41] Moreover, the jury's acquittal of Al-Monla on his false statement charge, pursuant to the same statute under *74 which Muntasser was convicted, further undercuts the defendants' spillover argument. Cf. United States v. Edgar, 82 F.3d 499, 504 (1st Cir.1996) (jury's acquittal on one of several counts demonstrated harmlessness of spillover evidence). Where the jury renders a judgment of conviction against only some of the defendants or on only some of the charges, we are particularly reluctant to presume that the jury was unable to compartmentalize the evidence of each offense. United States v. Casas, 425 F.3d 23, 50 (1st Cir. 2005).
Most importantly, however, the evidence against both defendants on the relevant charges was simply overwhelming. We have already detailed the evidence supporting Mubayyid's convictions. Muntasser's conviction is similarly supported by substantial evidence, in part because the offense itself is so straightforward. Cf. Josleyn, 99 F.3d at 1189. FBI Agent Peet testified at trial that he interviewed Muntasser in 2003 as part of an active investigation into both Muntasser and Care. During the interview, Muntasser indicated that he had traveled to Peshwar, Pakistan in 1994 or 1995. Because Agent Peet was aware that Peshwar is only about fifty kilometers from the Afghanistan border, and is a main route into Jalalabad, Afghanistan, he specifically asked whether Muntasser had traveled to Afghanistan or had ever met Gulbuddin Hekmatyar. Muntasser responded that he "had never, ever traveled to Afghanistan" and that he "had never met" Hekmatyar. During the interview, the agents inquired several more times into whether Muntasser had visited Afghanistan, but, each time, Muntasser denied having done so. Agent Peet testified that, if Muntasser had told him the truth about visiting Afghanistan in 1994 or 1995, it "would have drastically changed the course the interview took."[42]
At trial, Muntasser conceded that he lied, arguing to the jury only that the lie was not material because Agent Peet already had credible information that he had traveled to Afghanistan and was therefore not misled by Muntasser's statements to the contrary. Thus, although the evidence against Muntasser on this count constituted only a small fraction of that produced over the twenty-four days of trial, we are hard-pressed to imagine that a reasonable jury would have been unable to evaluate such clear evidence objectively.

III.
For the foregoing reasons, we reverse the district court's judgment of acquittal on Count 2, thereby reinstating the jury's verdict of guilty. We affirm the defendants' other convictions. The case is remanded to the district court for the sentencing of defendant Al-Monla, and the resentencing of defendants Muntasser and Mubayyid.
So ordered.

APPENDIX


______________________________________________________________________________
Count        Charge                 Muntasser   Al-Monla    Mubayyid
______________________________________________________________________________
1     Scheme to conceal material    Post-verdict   Post-verdict   Guilty
      facts.                        acquittal      acquittal
      18 U.S.C. § 1001(a)(1)



*75
______________________________________________________________________________
2   Conspiracy to defraud the       Post-verdict   Post-verdict   Post-verdict
    United States.                  acquittal      acquittal      acquittal
    18 U.S.C. § 371
______________________________________________________________________________
3   False tax filing.                                             Guilty
    26 U.S.C. § 7206(1)
______________________________________________________________________________
4   False tax filing.                                             Guilty
    26 U.S.C. § 7206(1)
______________________________________________________________________________
5   False tax filing.                                             Guilty
    26 U.S.C. § 7206(1)
______________________________________________________________________________
6   False statement.                Guilty
    18 U.S.C. § 1001(a)(2)
______________________________________________________________________________
7   False statement.                               Not Guilty
    18 U.S.C. § 1001(a)(2)
______________________________________________________________________________
8   Corruptly obstructing IRS       Pre-verdict    Pre-verdict    Guilty
    administration.                 acquittal      acquittal
    26 U.S.C. § 7212(a)
______________________________________________________________________________

NOTES
[*]  Of the District of Rhode Island, sitting by designation.
[1]  At trial, witnesses for the government testified that "jihad" means "holy struggle," and specifically refers to the duty to fight against the enemies of Islam, while "mujahideen" refers to Islamic "holy warriors." In its own materials, Care defined "mujahideen" as "[t]hose who are going out for Jihad, fighting in the path of Allah."
[2]  The government does not challenge the district court's acquittal of Muntasser and Al-Monla on the charges of scheming to conceal material facts from a government agency or obstructing the administration of the Internal Revenue laws.
[3]  At trial, the government presented evidence that Abdullah Azzam founded MAK in the 1980s in Peshwar, Pakistan, and was largely credited with attracting foreign fighters to Afghanistan to fight alongside the mujahideen.
[4]  Zakat, one of the Five Pillars of Islam, is a form of obligatory charitable giving, similar to the Christian concept of "tithing." Zakat may only be given to a limited class of recipients, including those "in the path of Allah." Both Care and Al-Kifah construed this requirement to include the mujahideen.
[5]  A witness for the government testified that Care's "Al-Hussam" newsletter was "indistinguishable" from Al-Kifah's: "I mean, the format, the font, the little logo up on the top right, same exact newsletter."
[6]  Section 501(c)(3) of the Internal Revenue Code exempts from taxation designated entities that are "organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition . . . or for the prevention of cruelty to children or animals," provided that "no part of the net earnings of [the entity] inures to the benefit of any private shareholder or individual." 26 U.S.C. § 501(c)(3). An organization may serve non-qualifying purposes only if such purposes are not substantial and are merely incidental to the organization's qualifying operations.
[7]  One of the government's expert witnesses testified at trial that, as used by the mujahideen, the word "martyr" refers to "someone who is killed in combat, someone who is killed while defending or fighting in the cause of Islam."
[8]  The details of the federal investigation are sketchy, as the trial judge appropriately limited the jury's exposure to them.
[9]  According to testimony at trial, Hekmatyar was an Afghan warlord in the 1990s who was of particular interest to the FBI.
[10]  GRF was a charitable organization based in Chicago, Illinois. It was one of the recipients of Care's contributions. Muntasser informed an FBI agent during a 2003 interview that Chehade had previously lived in Boston and had been responsible for introducing Muntasser to Al-Kifah. GRF had a sister publication to Care's "Al-Hussam" entitled "Al-Thilal."
[11]  Although this language does not read like the end of the sentence, it is an accurate rendition of the recording.
[12]  In 2000, 2001, and 2002, Mubayyid amended Care's filings for the tax years 1997, 1999, and 2000, respectively. Consequently, his filings fell within the six-year limitations period set by 26 U.S.C. § 6531, whereas the Form 990 filings of the other two defendants did not.
[13]  For ease of reference, a table of the charges brought and their dispositions below is appended to this opinion.
[14]  The witness was examined by counsel for Muntasser, and primarily spoke to the sufficiency of Care's disclosures on its initial application for tax exemption, Form 1023.
[15]  As noted, Al-Monla was charged with denying that he knew a man named Bassam Kanj during an interview with the FBI in 2003. The evidence at trial indicated that Al-Monla admitted to knowing someone named "Bassam," but denied knowing his last name.
[16]  Because he was acquitted of all charges, Al-Monla is participating in this appeal only to defend his post-verdict acquittal on this count.
[17]  The government's theory of the case was that Muntasser had conspired with two unindicted co-conspirators, Mohammed Akra and Waseem Yassin, prior to seeking Care's tax exemption, and that Al-Monla and Mubayyid joined this conspiracy when they subsequently agreed with Muntasser and each other to aid in maintaining Care's fraudulent tax status.
[18]  Despite the strenuous arguments of the defendants to the contrary, the government preserved this argument by raising it in the district court. Although the court did not rule on the argument in its opinion and order, it expressed doubts during arguments on the defendants' Rule 29 motions that the government could permissibly "charge a conspiracy that began in '93 and prove that it began in '96."
[19]  The Fifth Amendment's Presentment Clause guarantees the defendants the right to be free from a trial for any offense other than that alleged in the grand jury's indictment. United States v. Miller, 471 U.S. 130, 134-35, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985). Its prohibition on double jeopardy requires that the record show with accuracy the extent to which the defendants' convictions bar subsequent prosecution. Hagner v. United States, 285 U.S. 427, 431, 52 S.Ct. 417, 76 L.Ed. 861 (1932). Due process precludes the defendants' conviction on any ground that was neither charged in the indictment nor presented to the jury. Dunn v. United States, 442 U.S. 100, 106, 99 S.Ct. 2190, 60 L.Ed.2d 743 (1979). The Sixth Amendment, meanwhile, ensures that the indictment provide the defendants with fair notice of the charges against which they are called to defend. Russell v. United States, 369 U.S. 749, 763-64, 82 S.Ct. 1038, 8 L.Ed.2d 240(1962).
[20]  They are also reflected in our test to determine whether a variance has affected a defendant's substantial rights, which we discuss infra. See United States v. Cruz-Arroyo, 461 F.3d 69, 77 (1st Cir.2006) ("There is no prejudicial variance so long as an indictment provides the defendant with sufficient detail to allow him to prepare a defense, avoid unfair surprise at trial, and plead double jeopardy when appropriate.").
[21]  The defendants further point to language in both Miller and our subsequent decision in United States v. DeCicco, 439 F.3d 36 (1st Cir.2006), that (outwardly) suggests that an indictment may be narrowed only where the narrowing removes "distinct and segregable components." See id. at 46. They argue that, because the maintenance of Care's fraudulent tax exemption was dependant on Care's initial fraudulent application for tax exemption, the latter is not distinct and segregable. The language to which the defendants point does not aid them here. That language refers to the principle that a variance is permissible so long as the indictment's remaining allegations are independently sufficient to constitute the charged crime. That is the case here.
[22]  See, e.g., Celestin, 612 F.3d at 25 & n. 4 (upholding a conviction where the trial judge's instruction to the jury "eliminated a theory of liability rather than removed an element of the crime" under the applicable statute, and thus merely "narrowed the permissible bases for conviction"); United States v. Dowdell, 595 F.3d 50, 68 (1st Cir.2010) (upholding the literal alteration of an indictment to change the controlled substance involved because the nature of the substance is not a statutory element); United States v. Gomez-Rosario, 418 F.3d 90, 104 (1st Cir.2005) (finding no constructive amendment where jury found defendant "guilty of the crime charged but responsible for a lesser quantity of drugs than that specified in the indictment" because drug quantity is not a statutory element); cf. United States v. Bello-Perez, 977 F.2d 664, 669 (1st Cir.1992) (holding that, in conspiracy with no overt act element, "the government is not limited at trial to proof of the [gratuitously] alleged overt acts").
[23]  Certainly, the Sixth Amendment's right to notice of one's criminal charges requires that the indictment do more than parrot the words of a statute; "the statutory language `must be accompanied with such a statement of the facts and circumstances as will inform the accused of the specific offense, coming under the general description, with which he is charged.'" United States v. Mojica-Baez, 229 F.3d 292, 309 (1st Cir.2000) (quoting Hamling v. United States, 418 U.S. 87, 117-18, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974)). Any claim that upholding their convictions on the ground of variance would deprive the defendants of fair notice of their crime is more properly a claim of prejudice, however. See infra. It does not inform our analysis of whether the government's failure to prove all that it included in the indictment impermissibly altered "the crime charged."
[24]  The cases that reflect the opposite conclusion involve situations where the government's failure to prove the crime as it was charged in the indictment opens the possibility that the jury convicted on the basis of conduct that was never charged. See, e.g., United States v. Narog, 372 F.3d 1243, 1247-49 (11th Cir.2004).
[25]  We note that the defendants conspicuously avoided almost any reference to the concept of constructive amendment in their briefing to this court. The government, on the other hand, aptly pointed out that the defendants were "[c]onflating and confusing the distinct concepts of variance and constructive amendment."
[26]  The memorandum accompanying Muntasser's motion read as follows:

The defendants are charged, in count two, with a conspiracy to defraud the United States. . . . But the government has introduced absolutely no evidence, direct or circumstantial, of any agreement, express or implied, between these three defendants. There is no evidence of what, if anything, they agreed to, nor any evidence tying Mr. Muntasser to any agreement, whatever it might have been, after September 1996.
[27]  The government's theory at trial was that Muntasser had conspired with unindicted co-conspirators in 1993 to fraudulently obtain Care's tax exemption, that Al-Monla joined that conspiracy at some later time by agreeing with Muntasser, an unindicted co-conspirator, or both, to fraudulently maintain Care's tax status for the indefinite future, and that Mubayyid subsequently conspired with Al-Monla to do the same.
[28]  As we have explained, the notice and "prejudicial spillover" arguments that were persuasive in United States v. Dellosantos, 649 F.3d 109 (1st Cir.2011), are not persuasive here. Unlike Dellosantos, this case does not involve two or more distinct conspiracies with "different products, a different source of supply, different goals, and a different history." See id. at 121. Rather, the defendants in this case claim a lack of notice because they erroneously believed that the conspiracy charge would fail if the government could not prove that the single tax-related conspiracy in which the defendants participated extended for the entire period of time and involved all of the tax filings alleged in the indictment. Additionally, we found the variance in Dellosantos prejudicial because it allowed the government to introduce "voluminous testimony relating to unconnected crimes in which [the appellants] took no part" perpetrated by sixteen co-defendants. Id. at 125. That evidence, wholly irrelevant to the conspiracy involving the appellants, created an impermissible risk that the jury would find the appellants guilty of one conspiracy solely because their co-defendants engaged in a different conspiracy. Id. That risk does not exist here.
[29]  Title 18, § 371 also requires proof of an overt act in furtherance of the conspiracy by at least one conspirator. However, there can be no serious debate that this requirement has been met here: in the years covered by the indictment, each of the three defendants filed at least one Form 990 with the IRS, through which Care maintained its fraudulently obtained tax exemption.
[30]  Affif Kadri, one of Care's founding directors, testified for the government in this respect. He explained that, for example, Waseem Yassin, also listed as a director, was heavily involved in the organization simply as "the go-around guy. . . . Anything that needs to be done, or you know, whatever it is, he's there when that person or people make it happen." Al-Monla eventually told the FBI during his 2003 interview that Yassin was one of the officers primarily responsible for directing Care's charitable disbursements.
[31]  As we noted previously, Mubayyid also joins Muntasser in claiming prejudicial spillover from the introduction of so-called "terrorism evidence." We address Muntasser and Mubayyid's joint claim separately, infra.
[32]  Mubayyid does not challenge the other elements required to show a violation of § 7206(1): that he filed a verified return for the year(s) at issue and that the return contained a written declaration that it was made under penalty of perjury. See Boulerice, 325 F.3d at 79-80.
[33]  In a footnote in United States v. Boskic, 545 F.3d 69, 91 n. 22 (1st Cir.2008), we stated, correctly, that "the question of objective reasonableness was for the judge to decide in considering whether the government had presented enough evidence to allow the jury to find the statement false." However, the fact that the judge has concluded that a defendant's interpretation of the question is unreasonable, and hence has rejected a defendant's argument that the question, so interpreted, is fundamentally ambiguous, does not mean that the jury cannot still consider the defendant's interpretation of the question in deciding whether the defendant willfully and knowingly gave a false answer to the question. To the extent that our statement in Boskic suggests otherwise, it is inaccurate.
[34]  Both understandings of the timing were argued to the jury. The prosecutor urged the jury to convict Mubayyid for failing to disclose in the 1997, 1999, and 2000 tax returns that Care had published the "Al-Hussam" newsletters from 1993 to 1997. Mubayyid's counsel argued that the evidence was insufficient based on the more limited temporal scope, asserting, "In 1999 there was no newsletter. In 2000 there was no newsletter. There was only this website." In rebuttal, the government argued that Mubayyid's failure to report the website was also a material non-disclosure. The court then instructed the jury to "consider whether a defendant's response was actually false under each reasonable interpretation of the question or instruction." The jury's verdict may thus be upheld if the evidence showed that Mubayyid knew that reportable activities had taken place during 1997, 1999, and 2000i.e., that he knowingly replied falsely when asked whether, during each of those years, "the organization engage[d] in any activity not previously reported to the IRS." See United States v. Gobbi, 471 F.3d 302, 309 (1st Cir.2006) ("The law is crystalline that, when the government has advanced several alternate theories of guilt and the trial court has submitted the case to the jury on that basis, an ensuing conviction may stand as long as the evidence suffices to support any one of the submitted theories.") (citing Griffin, 502 U.S. at 49-51, 112 S.Ct. 466).

On appeal, Mubayyid also argues that a statement by the prosecutor"That question was not limited to that tax year. . . . The question was: `Has the organization ever engaged in any activity not disclosed to the IRS?'" was prosecutorial misconduct because it incorrectly recites the language of Question 76. In the context cited above, however, the statement is most sensibly read as the prosecutor's suggestion to the jury of how to interpret the question. It is therefore not error. See, e.g., United States v. Henderson, 320 F.3d 92, 105 (1st Cir.2003) (noting that a prosecutor "may attempt to persuade the jury to draw inferences unfavorable to the defense" (quoting United States v. Smith, 982 F.2d 681, 683 (1st Cir.1993))).
[35]  Given our description of the newsletter's importance to the purposes of the organization, we think it beyond debate that the falsity was "material." See Boulerice, 325 F.3d at 79 (stating that the government was required to prove that "the tax return was false as to a material matter" (quoting LaSpina, 299 F.3d at 179)).
[36]  18 U.S.C. § 1001(a) provides in relevant part:

[W]hoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully
(1) falsifies, conceals, or covers up by any trick, scheme, or device a material fact;
. . .
shall be fined under this title, imprisoned not more than 5 years or, if the offense involves international or domestic terrorism (as defined in section 2331), imprisoned not more than 8 years, or both.
[37]  Because the jury was instructed that it was required to find that the fact concealed was material to the IRS, Mubayyid's conviction under § 1001(a)(1) for a scheme to conceal material facts rests on the same conduct that forms the basis of his false tax filing convictions pursuant to 26 U.S.C. § 7206(1), which criminalizes materially false representations on subscribed tax filings, and his conviction for corruptly endeavoring to obstruct the due administration of the IRS pursuant to 26 U.S.C. § 7212(a).
[38]  Because we have ordered that the conspiracy conviction be reinstated, which will require re-sentencing, we do not consider Muntasser's additional claims related to sentencing.
[39]  "Retroactive misjoinder occurs where joinder was proper initially because of a conspiracy allegation, but where later developments, such as the district court's decision in the case months later to set aside a defendant's conspiracy conviction, appear to render the initial joinder improper." United States v. Deitz, 577 F.3d 672, 693 (6th Cir.2009) (alterations omitted) (quoting United States v. Warner, 690 F.2d 545, 553 (6th Cir. 1982)) (internal quotation marks omitted).
[40]  For example, when the government presented expert testimony describing the operations of Al-Kifah and MAK, the judge instructed the jury as follows:

Testimony concerningor testimony has been admitted concerning the organization and activities of Al-Kifah and the organization and activities of Care. And it's to go to this issue, the successor or outgrowth issue. And you may consider that issue only for that purpose. And just to be clear, defendants are not charged with any actions or activities relating to MAK or Al-Kifah. The issue here is the successor or outgrowth issue. And you may not conclude or infer or surmise that the defendants are somehow charged with or responsible for the actions or activities of MAK or Al-Kifah. They are not. Again, it's solely this issue of successor or outgrowth and, in effect, comparing the activities or organization of the two organizations.
[41]  For example, the jury asked, "Does Muntasser asking for a lawyer negate his previous answer `no' twice visiting Afghanistan to Special Agent Peet?" The trial judge correctly instructed that Muntasser's request for a lawyer rendered no part of the FBI's questioning legally impermissible, but that the jury was free to consider all of the evidence concerning the interview and to give it such weight as it deserves.
[42]  According to Agent Peet, he would have asked such additional questions as, "Where was the safe house in Peshwar? Who was guarding that safe house? Are Pakistani authorities in compliance with [sic] that safe house?" Additionally, he stated, "We would have asked if false identification had been used to get across the border; were Pakistani authorities helping him; what Afghans were helping him; where the meeting took place; and, again, under what circumstances did the meeting take place."
