#### UNITED STATES of America v. Richard STADTMAUER, Appellant.

No. 09-1575.

United States Court of Appeals, Third Circuit.

Argued Nov. 17, 2009.

Opinion Filed Sept. 9, 2010.

*240David Debold, Esquire, Miquel A. Estrada, Esquire, (Argued), Scott P. Martin, Esquire, Gibson, Dunn & Crutcher LLP, David M. Zinn, Esquire, Williams & Connolly LLP, Washington, D.C., Robert S. Fink, Esquire, Kostelanetz & Fink, LLP, New York, NY, Counsel for Appellant.

*241Ralph J. Marra, Jr., Acting United States Attorney, George S. Leone, Chief, Appeals Division, Steven G. Sanders (Argued), Assistant U.S. Attorney, Office of the United States Attorney, Newark, NJ, Counsel for Appellee.

Before: AMBRO, ALDISERT, and ROTH, Circuit Judges.

OPINION OF THE COURT

AMBRO, Circuit Judge.

*Table of Contents*

I. Background ..............................................................242

A. Richard Stadtmauer and the Kushner Companies..........................242

B. The Other Players ....................................... 242

C. The Alleged Conspiracy.................................................243

1. The General Ledgers...............................................244

i. Charitable Contributions........................................244

ii. “Non-Property” Expenses ......................................244

iii. Capital Expenditures...........................................245

iv. Gift and Entertainment Expenses................................245

2. EC’s Internal Financial Statements...................................245

3. SSMB’s Preparation of the Partnerships’Tax Returns ..................246

D. Evidence of Stadtmauer’s Knowledge.....................................247

1. “Thursday Meetings”...............................................247

2. “Richard Specials” and Other Special Financial Statements..............248

3. Other Circumstantial Evidence of Stadtmauer’s Knowledge of Tax

Law and Consciousness of Guilt....................................249

i. Rationale for Private School Tuition Payments.....................249

ii. The 1996 IRS Audit............................................250

iii. Dissenting Limited Partners and Executives.......................250

E. The Verdict and Stadtmauer’s Post-Verdict Motions........................251

II. Jurisdiction...............................................................252

III. Discussion................................................................252

A. Willful Blindness.......................................................252

1. Whether the District Court’s Willful Blindness Instruction Applied to

Stadtmauer’s Knowledge of the Law................................252

2. Willful Blindness and Cheek.........................................254

3. Whether the District Court’s Willful Blindness Instruction Applied to

the Element of Specific Intent......................................258

4. Whether Trial Evidence Warranted the Willful Blindness Instruction.....259

B. Lay Opinion Testimony.................................................260

1. Background .......................................................260

2. Analysis...........................................................262

C. Prosecutorial Misconduct ...............................................267

D. Expert Testimony......................................................269

E. Restrictions on Cross-Examination.......................................271

Following a two-month jury trial in the District Court for the District of New Jersey, Richard Stadtmauer was convicted of one count of conspiracy to defraud the United States (in violation of 18 U.S.C. § 371), and nine counts of willfully aiding in the filing of materially false or fraudulent tax returns (in violation of 26 U.S.C. § 7206(2)). On appeal, Stadtmauer raises many challenges to these convictions. We deal principally with the issue Stadtmauer raises last: whether the District Court erred in giving a willful blindness instruction in this case, including whether the Supreme Court’s decision in *Cheek v. United States,*498 U.S. 192, 111 S.Ct. 604, 112 *242L.Ed.2d 617 (1991), forecloses the possibility that willful blindness may satisfy the legal knowledge component of the “willfulness” element of criminal tax offenses. We join our sister circuit courts in concluding that *Cheek*does not prohibit a willful blindness instruction that applies to a defendant’s knowledge of relevant tax law. We reject also Stadtmauer’s other claims of error, and thus affirm.

I. Background1

A. *Richard Stadtmauer and the Kushner Companies*

This criminal case stemmed from an investigation of Charles Kushner, a prominent real estate entrepreneur, political fundraiser, and philanthropist in New Jersey. Kushner controls hundreds of limited partnerships, each of which owns and manages a single commercial or residential property. Kushner is the general partner of each partnership and, for most, his siblings (including his brother, Murray Kushner 2) and their children are the other limited partners. These partnerships have collectively operated under the name “Kushner Companies” (“KC”). KC is not a registered entity and does not own any properties.3

In the mid-1990s, Charles and Murray Kushner accused each other of taking more than his fair share out of their common businesses. During the course of the ensuing civil litigation, Murray alerted federal authorities to potential misconduct by his brother and KC. Following an investigation, Kushner pled guilty in 2004 to, among other things, assisting in the filing of false partnership tax returns and federal campaign contribution offenses.

During the course of its investigation of Kushner, the Government indicted several other individuals, including Stadtmauer — a Certified Public Accountant, a law school graduate, and Kushner’s brother-in-law. He became an employee of KC in 1985, and eventually rose to become an executive vice president. In this role, Stadtmauer oversaw the operations of KC’s residential and commercial properties. Stadtmauer also held a small stake (between 1% and 7%) in many of KC’s partnerships. Stadtmauer and Kushner held equal interests (50% each) in Westminster Management, an entity which collected management fees from the other partnerships.

B. *The Other Players*

Several former KC executives testified against Stadtmauer at trial, including: (1) Chief Financial Officer (“CFO”) Stanley Bentzlin; (2) Chief Operations Officer (“COO”) Scott Zecher; and (3) Alan Lefkowitz, who succeeded Bentzlin as CFO in 2000. Of these three, only Zecher was indicted.4

KC employed the accounting firm of Schonbraun, Safris, McCann, Bekritsky & Company, LLC (“SSMB”) as its main “outside” accountant. The lead SSMB accountant for KC matters was Marci Plot-kin, who served as KC’s CFO in the early 1990s before returning to SSMB.5 Though *243Plotkin was technically an employee of SSMB, KC reimbursed SSMB for yearly bonuses it paid to Plotkin6 and certain of Plotkin’s salary increases, and reimbursed Plotkin for the cost of her son’s private school tuition. Kushner did not heed Bentzlin’s warning that paying Plotkin a bonus would impair her independence and preclude SSMB from issuing financial statements on behalf of KC partnerships.

Marci Plotkin was assisted by (among others) SSMB partner Stanley Bekritsky and Anne Amici, a staff accountant who worked almost exclusively on KC matters. Plotkin, Bekritsky, and Amici were indicted along with Stadtmauer and each pled guilty to conspiring to defraud the United States. Of these three, only Bekritsky testified at Stadtmauer’s trial.

C. *The Alleged Conspiracy*

The Government charged that Stadtmauer, Bekritsky, Plotkin, and Amici conspired to file false or fraudulent tax returns for the 1998-2001 tax years for Westminster Management and eleven other KC limited partnerships: “Oakwood Garden Developers,” “Elmwood Village Associates,” “Pheasant Hollow,” “QEM,” “Mt. Arlington,” and six partnerships with variations of the name “Quail Ridge.” The Government alleged that these partnerships fraudulently claimed four categories of expenditures as fully deductible business expenses7 on their tax returns8: (1) charitable contributions, which generally are not deductible as business expenses; (2) expenditures incurred by one partnership but paid by a different partnership (known as “non-property” expenses); (3) capital expenditures, which generally must be amortized and depreciated over the life of the relevant asset (and thus are not immediately deductible in full); and (4) gift and entertainment expenses, which generally are not fully deductible as business expenses.

The Government’s theory was that these four types of expenditures were fraudulently deducted in full as ordinary business expenses on the partnerships’ tax returns through a three-step process. First, the expenses were logged in each limited partnership’s general ledger via a computer-based accounting program that broke down all revenue and expenses into categories called “accounts.” Second, KC used the general ledgers to prepare internal financial statements that automatically categorized these four types of expenditures as “expenses.” Finally, SSMB used the general ledgers and internal financial statements to prepare external financial *244statements and tax returns for each partnership that falsely claimed these four categories of expenditures as fully deductible business expenses.

To illustrate, below we discuss primarily the 2000 tax return for one of the limited partnerships, Elmwood Village Associates (“Elmwood Village”).

1. *The General Ledgers*

i. *Charitable Contributions*

Kushner and Stadtmauer frequently directed that charitable contributions be paid out of partnership funds, which were logged into the general ledger under the “contributions” account. In 2000, Elm-wood Village paid approximately $186,000 to various charitable organizations, including donations to the Suburban Torah Center — the “personal synagogue” of Kushner and Stadtmauer — and to the Center’s Rabbi, Stadtmauer’s “rabbinical advisor.” (App.2846-47.)

Also logged under the “contributions” account were donations made to various political campaigns and political action committees, and $25,384 in private school tuition payments for Zecher’s and Plotkin’s children. Because the latter payments were logged as partnership expenses (rather than entered into the payroll system as taxable income), no taxes were withheld and no Form 1099 was issued to Zecher or Plotkin. Zecher testified that he generally left the descriptions blank on the checks for tuition payments because “[tjhere was nothing [he] really could write. It was not an appropriate business expense.” *(Id.*at 2817.)

ii. *“Norir-Property” Expenses*

Whenever a particular KC partnership incurred an expense that it could not satisfy out of its current funds, Kushner would direct that a different partnership pay the expense. He referred to this practice as “losing a bill,” and it was a regular agenda item for upper-level management meetings held every Tuesday (referred to as “Tuesday Meetings” or “Cash Meetings”). Typically, either Kushner, the CFO, or the controller chose the source of payment; in other instances, Kushner directed Stadtmauer to choose which partnership would pay the expense. Zecher testified that it was Kushner’s view that an expense could be paid by any partnership that he controlled. Sometimes Kushner would tell Zecher that the partnership actually paying the expense “didn’t matter because it was all family.” *(Id.*at 3116.)

For example, in 1998 various KC partnerships paid more than $1 million in expenses associated with the renovation of KC’s central office building in Florham Park, New Jersey.9 Kushner directed Bentzlin to have several different partnerships, on a rolling basis, pay portions of the total expenses incurred as a result of the renovations. These expenditures were logged in the partnerships’ respective general ledgers under the “repairs and maintenance” account. Eventually, Kushner instructed Bentzlin to review with Stadtmauer the list of all bills due for the renovation work, and directed Stadtmauer to “instruct [Bentzlin] on how to lose it,” *i.e.,*to choose “what entity to pay it out of.” *(Id.*at 2130.)

In addition to one partnership paying another partnership’s expenses, KC partnerships also paid for expenses that had no relation to any partnership’s business. In 2000, Elmwood Village paid approximately $30,000 in “non-property” expenses that were booked to various general ledger accounts, including “advertising,” “semi*245nars,” “legal fee-other,” and “other professional fees.” This amount included (among other things): (1) $10,000 paid to a consulting firm to research the viability of a comeback by then-former Israeli Prime Minister Benjamin Netanyahu; (2) $10,000 toward a $100,000 fee to pay Mr. Netanyahu to speak at a breakfast sponsored by NorCrown Bank (an entity not affiliated with KC in which Kushner held an interest); and (3) $3,815 toward a $50,000 fee to pay former Chairman of the Federal Reserve Paul Volcker to speak at another NorCrown Bank event.

iii. *Capital Expenditures*

From 1998 through 2001, various KC partnerships purchased capital assets and made capital improvements to their properties. In general, these expenses were logged in the partnerships’ general ledgers under the “repairs and maintenance” account rather than the capital expenditures account. As Lefkowitz explained at trial, “[tjhere [were] a few instances where things might have been capitalized, but as a general rule ... everything went through expenses.” *(Id.*at 2604.) Bentzlin explained that, although each general ledger had a capital improvement “account,” capitalizing assets “wasn’t the way it was done at Kushner Companies.” He added that

> [w]e regularly and routinely expensed [capital assets] under one of the repairs and maintenance or capital improvement accounts ... [;] that was the way they were doing it upon my arrival, and it didn’t change throughout my tenure with a few — just with a few exceptions.

> ... You didn’t question it. You know, it was ruled with an iron fist. They controlled pretty much everything.

*(Id.*at 2190.)

In 2000, Elmwood Village spent $269,323 on improvements that allegedly should have been capitalized, which included adding new bathrooms and kitchens to apartments — including new cabinets and $49,318.40 worth of new appliances (such as washers and dryers) — and a new truck (for $25,126). All of these expenses were logged in the partnership’s general ledger under the “repairs and maintenance” general ledger account rather than a capital account.

iv. *Gift and Entertainment Expenses*

Kushner and Stadtmauer frequently directed various partnerships to pay gift and entertainment expenditures that had no specific connection with the partnership paying the expense. In 2000, Elmwood Village paid: (1) $12,640 to cater a brunch at the New Jersey Performing Arts Center; (2) $7,027 to a wine store for alcohol delivered to Kushner’s and Stadtmauer’s private homes during the holidays; (3) $5,905.23 to cater a fundraiser for former New Jersey Governor Jon Corzine; and (4) thousands of dollars for New York Yankees, New York Mets, and New Jersey Nets season tickets. Each of these expenditures was logged in Elmwood Village’s general ledger under a “miscellaneous,” “gifts/entertainment,” or “travel” account.

2. *KC’s Internal Financial Statements*

KC used the general ledgers to generate internal financial statements for each partnership. The accounting template (or “skeleton”) used to produce these statements automatically grouped certain accounts from the general ledgers — including the “contributions,” “gifts/entertainment,” “miscellaneous,” and “seminars” accounts — under the category of “office expenses.” In addition, the “legal fee-other” and “other professional fees” accounts were grouped under the category of “payroll and related expenses.” Each of these categories — in addition to *246the “advertising” and “repairs and maintenance” 10 categories — -were, in turn, grouped under the general category of “expenses,” and thus deducted in full from the partnership’s revenue on the internal financial statement.11 This violated applicable accounting standards, which required the partnerships’ financial statements to be prepared on an income tax basis.

3. *SSMB’s Preparation of the Partnerships’ Tax Returns*

SSMB used KC’s general ledgers and internal financial statements to prepare external financial statements for each partnership. KC would submit a “Management Representation Letter” to SSMB along with its financial statements, in which KC management certified that “[t]here are no material transactions that have not been properly reflected in the financial statements.” Stadtmauer signed most of these representation letters. KC also provided SSMB with the template it used to prepare its internal financial statements.

In preparing the partnerships’ external financial statements and tax returns, SSMB used the groupings applied by KC’s internal accounting software. Thus, the 2000 internal and external financial statements for Elmwood Village reflected virtually identical amounts for “office expenses” and “repairs and maintenance.” As Bekritsky testified, the tax returns were prepared “on the same basis” as the partnerships’ financial statements, meaning that “if [something is] deducted on the financial statement, it is deducted on the tax return and produces income or increases the loss of the partnership.” *(Id.*at 3218.)

Elmwood Village’s 2000 tax return deducted a total of $496,713 in ordinary and necessary business expenses (on lines 3 through 15 of Form 8825, entitled “Rental Real Estate expenses”). Included in this amount was $211,885 in charitable contributions, political donations, and tuition payments (for, among others, Plotkin’s and Zecher’s children). (Line 8 of Schedule K to the return — where partnerships are required to list charitable contributions — was left blank.) The “non-property,” and gift and entertainment, expenses incurred by Elmwood Village in 2000 were similarly claimed as fully deductible business expenses (instead of listed separately as required on Schedule M-l). Finally, Elmwood Village reported no increase in capital assets in 2000. Rather, $269,323 in alleged capital expenditures were included in the $347,939 reported as “repairs” (on line 10 of Form 8825), while other alleged capital expenditures were spread among various items in Statement 10 of Schedule M-2 (entitled “Other Rental Expenses”).12

Around March or April of each year, Stadtmauer met with KC’s CFO and someone from SSMB — usually Plotkin, and infrequently Bekritsky — to review and sign the KC partnerships’ tax returns. During these sessions, Stadtmauer sometimes re*247viewed SSMB’s financial statements for the partnerships; indeed, he refused to “sign a tax return unless he had the financial statements next to him.” *(Id.*at 2958.) He would “flip through” each return, “look at certain things, and then sign it.” *(Id.*at 2194.) Stadtmauer only occasionally asked questions about the returns, and typically spent “30 seconds to a minute” on each. *(Id.*at 2283.) However, he spent more time on EC’s major properties, particularly those that had large annual increases in “repairs and maintenance” expenses. *(Id.*at 2958.)

Stadtmauer reviewed and signed as many as 800 tax returns in a given day. Stadtmauer signed each of the partnerships’ tax returns below a legend declaring, “[ujnder penalties of perjury,” that he had “examined th[e] return, including accompanying schedules and statements,” and that, to the best of his knowledge, the return was “true, correct, and complete.” *(E.g.,*Supp.App. 937.) Stadtmauer signed each return in his capacity as Vice-President of the corporate general partner; as Bentzlin and Zecher testified, Stadtmauer believed that by doing so he would protect himself from personal liability. (App.2209, 2903.)

The Government alleged that, from 1998 through 2001, the twelve EC partnerships identified in the indictment claimed more than $6 million in improper deductions. Capital expenditures that were deducted in full the year they were incurred accounted for more than half of this amount.

D. *Evidence of Stadtmauer’s Knowledge*

To establish that Stadtmauer “willfully” aided in the preparation of materially false or fraudulent tax returns — as required for a violation of 26 U.S.C. § 7206(2)13 — the Government was required to prove beyond a reasonable doubt that he voluntarily and intentionally violated “a known legal duty.” *United States v. Pomponio,*429 U.S. 10, 12, 97 S.Ct. 22, 50 L.Ed.2d 12 (1976). Whether Stadtmauer had knowledge that the deductions claimed on the partnerships’ tax returns were materially false or fraudulent was the critical issue at trial.

At trial, Bentzlin, Zecher, and Bekritsky each testified that they never discussed with Stadtmauer the falsity of any particular deduction or tax return. Accordingly, the Government sought to meet its burden of proving that Stadtmauer acted “willfully” through various forms of circumstantial evidence (some of which have already been discussed), including: (1) evidence of Stadtmauer’s intimate familiarity with the partnerships and how their general ledgers were maintained; (2) evidence that Stadtmauer made decisions on how to treat partnership expenses in the past with tax consequences in mind; and (3) other evidence suggestive of a consciousness of guilt, *e.g.,*evidence that Stadtmauer was aware that the partnerships were making improper expenditures.

1. *“Thursday Meetings*”

In addition to the “Tuesday Meetings” that Stadtmauer regularly attended, for many years he ran weekly “Thursday Meetings” with the limited partnerships’ property managers, as well as EC’s in-house counsel, controller, Bentzlin, and sometimes Plotkin.14 The purpose of each *248meeting was to conduct an in-depth review of one or two KC properties. The managers prepared presentation packages that showed the partnerships’ actual expenses to date. Stadtmauer went through the presentations “line by line,” and asked “specific” questions about each. (App. 2641.) According to Zecher, “there was nothing [Stadtmauer] didn’t see fit to get involved with in property management,” and he was “one of the brightest people [that Zecher had] ever met.” *(Id.*at 2836.)

In 1996, certain property managers started using special letter codes on their general ledgers to identify “non-property” expenses paid for by their respective partnerships. The codes allowed property managers to identify those expenses more easily and exclude them from their Thursday Meeting presentations. According to Bentzlin, the property managers were hesitant to answer Stadtmauer’s questions about such expenses during Thursday Meetings (previously listed as “miscellaneous” expenses on the presentations), because they knew the expenses were for expenses “paid out of other properties,” and “didn’t want to blurt it out in front of a roomful of people.” *(Id.*at 2150.)

Stadtmauer was “quite unhappy” when he learned of the codes, and directed his subordinates to end the practice. *(Id.*at 2186.) Stadtmauer and Bentzlin ultimately decided to lump non-property expenses together under a category called “other.” Doing so obviated the need for Stadtmauer to “interrogate or continue to question the property manager as to the nature of those expenditures” during Thursday Meetings, and made it easier during Tuesday Meetings to “figure out [how] the apartment complex on its own was really operating.” *(Id.*at 2185-86.) In addition, Stadtmauer directed that KC’s accounting software be modified “to allow somebody to go in and change [existing] descriptions within the general ledger.” *(Id.*at 2187.)

Stadtmauer also frequently instructed his subordinates to omit descriptions in check requests to avoid leaving a “trail” when KC “used one property to pay another property’s expenses.” *(Id.*at 2628.) He admonished Zecher to “never put the descriptions in,” because he “d[idn’t] want the descriptions [to show up] in the ledger.” *(Id.*at 2855.) Stadtmauer also “reminded [Zecher,] over and over, [to] be careful what [he] put in emails. Emails never disappear.” *(Id.*at 2858.)

2. *“Richard Specials” and Other Special Financial Statements*

In certain circumstances, Stadtmauer directed that special financial statements for the partnerships be prepared for banks and other entities. These were known as “Richard Specials.” These special financial statements were often prepared when KC wanted to reduce outstanding letters of credit on particular properties. Stadtmauer would direct that “negative items” that tended to depress the partnership’s profitability be removed from these statements, such as capital expenditures (that had been logged as “repair and maintenance” expenses) and “non-property” expenses. *(Id.*at 2077-78.) To prepare these statements, Stadtmauer was given a “detailed report” of the partnership’s general ledger, which he would go through line by line and indicate the items to be removed for the financial statement. *(Id.*at 2077.) KC prepared both internal and external versions of every “Richard Special”; the internal version revealed the adjustments made, while the external version showed only the final numbers after adjustments. *(Id.*at 2225.)

The first time Stadtmauer asked Bentzlin to create a “Richard Special,” Bentzlin objected and told Stadtmauer that he “didn’t think it was the right thing to do” because they “would be sending different financials out other than the ones prepared *249by the accountant.” *(Id.*at 2079.) Stadtmauer argued it would be proper because they would call it a “statement *from*operations” (as opposed to a “statement *of*operations”), supposedly making clear that it wasn’t a true financial statement. *(Id.*(emphasis added).) Bentzlin told Stadtmauer he thought the justification was “ridiculous,” and though Bentzlin ultimately agreed to prepare the “Richard Specials,” he “didn’t want [them] ever to go out with [his] name on [them].” 15*(Id.)*

Similar to “Richard Specials,” on several occasions KC prepared special financial statements in connection with potential acquisitions and joint ventures. For example, in 1995 certain lenders agreed to finance KC’s acquisition of Elmwood Village, provided that KC would commit to making $1.5 million in capital improvements to the property and secure a $1.6 million letter of credit. These expenditures were entered, as usual, under non-capital accounts on the partnership’s general ledger. At the end of the year, however, KC decided to capitalize the items on the partnership’s financial statement “to get the letter of credit cancelled.” *(Id.*at 2348.) This decision was made during a Tuesday “Cash Meeting” in which Stadtmauer participated.

Elmwood Village’s 1996 tax return accurately reported almost $1 million in capital improvements. After the letter of credit was cancelled, however, KC “went back to the usual procedures of expensing those types of expenditures.” *(Id.*at 2210.) Elmwood Village did not capitalize any expenditures after 1996, and its post-1996 returns treated the 1996 renovations that had been capitalized as fully deductible repairs.

Similarly, in 2000 KC paid $280 million to acquire a company called WNY, which owned approximately 40 properties in New Jersey, Pennsylvania, Maryland, and Delaware. KC was required to obtain a $40 million letter of credit in connection with the acquisition. Stadtmauer, Plotkin, and Zecher had a “very detailed meeting” on how they would “do the accounting for the WNY properties.” *(Id.*at 2967.) They agreed that they would “capitalize everything and anything [they] could, instead of expensing it, like [they] always did in the other properties.” *(Id.)*Zecher testified that Stadtmauer was “convinced, because the transaction was so large, and the $40 million [in] letters of credit were so unusual for [KC], that the banks were going to come in and look at not only the tax returns, but ... the actual books and records.” *(Id.)*

When the letters of credit were removed, Plotkin asked whether she should expense the capitalized items. Zecher responded that he and Stadtmauer had determined that the financial statements would “look very weird” if they stopped capitalizing. *(Id.*at 2970-71.)

3. *Other Circumstantial Evidence of Stadtmauer’s Knowledge of Tax Law and Consciousness of Guilt*

i. *Rationale for Private School Tuition Payments*

As noted, for several years KC paid the private school tuition for, among other KC *250employees, Plotkin’s and Zecher’s children. Zecher testified that Stadtmauer came up with the idea of paying the tuition directly to the school instead of increasing Zecher’s year-end bonus by that amount. *(Id.*at 2824.) Stadtmauer told Zecher that he was “trying to' be nice” by paying the tuition directly to the school, which would allow Zecher to avoid thousands of dollars in additional income taxes. *(Id.)*

ii. *The 1996 IRS Audit*

In 1996, the Internal Revenue Service (“IRS”) audited the tax returns for two KC partnerships, focusing on the large deductions taken for repairs (including $850,000 to reconstruct a building’s facade, which was deducted in full as a business expense). The IRS ultimately issued “no change” letters. Following the audit, however, Plotkin sent a letter to Bentzlin — on which Stadtmauer was copied — instructing Bentzlin to change the word “improvements” to “repairs” in the “tenant' improvements,” “apartment renovations,” and “building improvements” general ledger accounts. *(Id.*at 2269-70.) Bentzlin believed the purpose was to make these categories appear as if they contained repair and maintenance expenditures rather than “potentially a capital improvement type item.” *(Id.*at 2270.)

iii. *Dissenting Limited Partners and Executives*

In addition to the Kushner family and Stadtmauer, there were other individuals who held interests in various KC partnerships. As Zecher testified at trial, many of these individuals made repeated requests for information regarding the financial state of their partnership interests. In many instances, Stadtmauer and Kushner ordered Zecher to refuse those requests.

In one instance, a partner of a KC partnership named “K & F Clinton” inquired as to certain political contributions made by that partnership and attributed to him. *(Id.*at 2891.) The partner denied he had ever authorized the contributions, and noted that, “had [he] been informed of the intention to make political contributions, [he] would have advised that such political contributions were inappropriate and [he] would have demanded that they not be made from K *&*F” funds. *(Id.*at 2892.) He further noted that “[n]othing in the partnership agreement authorized the disbursement of K *&*F funds for any unrelated purpose.” *(Id.*at 2892-93.) Zecher got similar responses from several other partners. *(Id.*at 2893.)

Another limited partner — Stanley Greenberg — “constantly” had difficulty obtaining annual financial statements for the partnerships in which he had an interest. *(Id.*at 3356.) When he finally obtained and examined the partnerships’ financial statements for a prior three-year period,16 “it was obvious [to him] that the expenses [claimed for] run[ning] the[ ] properties were way out of line.” *(Id.)*Among other things, Greenberg noticed that the partnerships in which he had an interest had treated capital expenditures as ordinary expenses, and had made numerous charitable contributions to Kushner’s and Stadtmauer’s synagogues, as well as political contributions. *(Id.*at 3363.)

When Greenberg expressed his concerns to Kushner, the latter told him that “if you don’t like it, I will give you your money back.” *(Id.*at 3358.) Greenberg also had conversations with Stadtmauer, both in person and by phone, regarding the im*251proper expenses being paid by the partnerships, and asked Stadtmauer to “stop [KC from] doing what they were doing.” *(Id.)*Though he offered no “excuse ... or any explanation” for the expenses, Stadtmauer rejected Greenberg’s request, explaining that “that was the way they did business.” *(Id.)*Following these conversations, KC attempted to buy out Green-berg’s interests in the partnerships.

In addition to these dissenting limited partners, the Government also introduced testimony that KC executives were expected not to challenge KC’s accounting practices. As Bentzlin explained, “[y]ou had to do pretty much as you were told [at KC]. [Stadtmauer] and [Kushner] often would throw tirades at any number of the meetings on a regular routine basis or in the office, you know, that you really didn’t have latitude to make any changes.” *(Id.*at 2190.)

Former CFO Alan Lefkowitz learned this lesson the hard way. In early 2001, he emailed Kushner to ask whether he should follow the past practice of paying a bill for a Mikvah (a Jewish ritual) with funds from one of the partnerships. Kushner was furious, and admonished Lefkowitz that he “should never write something like th[at] down.” *(Id.*at 2613.) According to Zecher, Kushner was angry that Lefkowitz had “put[ ] in an email in writing that [KC was] paying bills for a ... not-for-profit project out of ... for-profit properties.” *(Id.*at 2858.) Kushner printed out the email and hand-wrote: “This guy is a definite Moron. We must deal with the situation.” Kushner forwarded a copy of the email (bearing his hand-written note) to Stadtmauer, and it was later discussed among upper-level management. Stadtmauer later told Zecher: “This is a stupid thing to do and you better make sure this guy doesn’t do it again.” *(Id.)*

Lefkowitz was eventually barred from Tuesday Meetings and later resigned. He believed that management (including Stadtmauer) had concluded that he was not a “team ... player,” *i.e.,*was “not willing to go along with what they want[ed] to do.” *(Id.*at 2613.)

E. *The Verdict and Stadtmauer’s Postr-Verdict Motions*

Following a two-month trial,17 the jury convicted Stadtmauer of one count of conspiracy and nine counts of aiding in the willful filing of materially false or fraudulent partnership tax returns.18' The District Court denied Stadtmauer’s motions for a judgment of acquittal and to dismiss the indictment.19 In February 2009, the District Court sentenced him to 38 months’ imprisonment. He timely appealed.

*252II. Jurisdiction

The District Court had jurisdiction under 18 U.S.C. § 3231. We have appellate jurisdiction under 28 U.S.C. § 1291.

III. Discussion

Stadtmauer contends that (1) the District Court erred in giving a willful blindness instruction to the jury; (2) the Court improperly admitted prejudicial lay opinion testimony by a Government witness; (3) the prosecutor violated his obligation to correct false testimony by a Government witness; (4) the Court improperly allowed an IRS agent to testify as an expert witness; and (5) the Court violated the Federal Rules of Evidence and his Sixth Amendment rights by restricting the scope of his cross-examination of Government witnesses. We address each claim in turn.

A. *Willful Blindness*

Stadtmauer argues that the District Court erred in giving a willful blindness instruction to the jury for three reasons. Relying on *Cheek v. United States,*498 U.S. 192, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991), he first argues that the “willfulness” element of criminal tax offenses— which “requires the Government to prove that the law imposed a duty on the defendant, [and] that the defendant knew of th[at] duty,” *id.*at 201, 111 S.Ct. 604 — can never be satisfied by willful blindness. Second, he contends that the Court improperly instructed the jury that the element of intent could be satisfied through proof of willful blindness, by analogy in violation of our recent *en banc*decision in *Pierre v. Attorney General,*528 F.3d 180 (3d Cir.2008) *(en*banc). He finally argues that the trial evidence did not warrant a willful blindness instruction.

We exercise plenary review over whether a willful blindness instruction properly stated the law. *United States v. Khorozian,*333 F.3d 498, 507-08 (3d Cir. 2003); *see also United States v. WertRuiz,*228 F.3d 250, 255 (3d Cir.2000). We review a district court’s determination that the trial evidence justified the instruction for abuse of discretion, *United States v. Flores,*454 F.3d 149, 156 (3d Cir.2006), and “view the evidence and the inferences drawn therefrom in the light most favorable to the [G]overnment,” *Wert-Ruiz,*228 F.3d at 255.

1. *Whether the District Court’s Willful Blindness Instruction Applied to Stadtmauer’s Knowledge of the Law*

Before turning to Stadtmauer’s first challenge to the District Court’s willful blindness instruction, we address the Government’s contention that the Court’s instruction applied only to Stadtmauer’s knowledge of facts, not his knowledge of the law.

The Government’s initial proposed willful blindness instruction plainly applied to Stadtmauer’s knowledge of the law. The final sentence of that instruction stated: “You may find that [the] defendant acted knowingly ... if you find either that the defendant actually knew about the applicable IRS requirements for the prosecution years, or that the defendant deliberately closed his ... eyes to what he ... had every reason to believe.” (Supp.App.60.) Stadtmauer submitted a brief objecting to this instruction. Though he conceded that willful blindness may be appropriate to establish knowledge of facts, he argued that, under *Cheek,*“willfulness” requires actual knowledge of the law, which cannot be satisfied through deliberate ignorance.

At the charging conference, the Government submitted a revised instruction that omitted the reference to Stadtmauer’s knowledge of “applicable IRS requirements.” It instead instructed the jury that the “element of knowledge” would be satisfied if the Government proved beyond *253a reasonable doubt “a conscious purpose by the defendant to avoid knowledge [that] the tax returns at issue were false or fraudulent as to a material matter.” (App. at 3973-74.) Though the Government revised its charge to address Stadtmauer’s objections, it nonetheless made explicit its position that willful blindness could cover both knowledge of the law and knowledge of facts, arguing that “it is a little difficult to say that it can’t [apply to] legal [knowledge] at all[,] because it’s really kind of a mixed question of law and fact[ ] in many [tax] cases.”20*(Id.*at 3905.)

In its final instructions, the District Court gave a willful blindness instruction consistent with the Government’s revised instruction. In relevant part, the Court instructed the jury as follows:

> The *element of knowledge*on the part of the defendant may be satisfied by inferences drawn from proof that the defendant closed his eyes to what would otherwise have been obvious to the defendant. A finding beyond a reasonable doubt of a conscious purpose by the defendant to *avoid knowledge that the tax returns at issue were false or fraudulent as to a material matter*would permit an inference that he had such knowledge.

> Stated another way, the defendant’s *knowledge of a fact or circumstance*may be inferred from his willful blindness to the existence of that fact and circumstance.

> No one can avoid responsibility for a crime by deliberately ignoring what is obvious. Thus, you may find that the defendant knew that the tax returns at issue were false or fraudulent as to a material fact based on evidence that you find exists that proves beyond a reasonable doubt that the defendant was *aware of a high probability that the tax returns at issue were false or fraudulent as to a material matter,*and two, that defendant consciously and deliberately tried to avoid learning about this fact or circumstance.

(App. 3973-74 (emphases added).) Thus, though the Court’s willful blindness instruction referred to Stadtmauer’s “knowledge of a fact or circumstance,” it also instructed the jury that the Government could satisfy its burden of proof on “the element of knowledge” by proving that Stadtmauer consciously avoided learning that the returns were *“false*or *fraudulent*as to a material matter,” using language that tracks the applicable statute. *See*26 U.S.C. § 7206(2).

The Government argues that the Court’s reference to Stadtmauer’s knowledge that the tax returns were “false or fraudulent as to a material matter” was merely “addressed to Stadtmauer’s knowledge of the *254contents of the returns.” (Appellee’s Br. at 77.) The Government notes, for example, that regardless of Stadtmauer’s knowledge of the relevant tax laws, he could have consciously avoided learning of “the fact that an expenditure from one partnership was falsely represented as a deduction of another partnership,” a question of fact that did not require proof of Stadtmauer’s knowledge of tax law. *(Id.*at 79.) We disagree.

The Government’s charges in this case were not limited to improper deductions for “non-property” expenses *(i.e.,*expenses paid by a partnership different than the one that actually incurred the expense). Indeed, the bulk of the allegedly improper deductions were for expenditures that should have been capitalized, and it was undisputed that these amounts were paid for work that was actually performed. Rather, for this category of deductions (and others), the Government’s theory was that *legitimate*expenditures were deducted in a fraudulent *manner*on the partnerships’ tax returns.

To prove that Stadtmauer knew the partnership tax returns were “false or fraudulent as to a material matter” with respect to these deductions, the Government needed to establish two “facts” beyond a reasonable doubt: (1) that Stadtmauer knew that these expenditures were claimed as fully deductible business expenses; and (2) that he knew those deductions were impermissible under the relevant tax laws *(i.e.,*that they rendered the tax returns “false or fraudulent as to a material matter”). *Cf. United States v. Schiff,*801 F.2d 108, 113 (2d Cir.1986) (noting that in a criminal tax case the defendant’s “knowledge of tax law [is], itself, a *fact*to be proved as part of the government’s case”) (emphasis in original). In that light, we believe a reasonable juror could have interpreted the District Court’s willful blindness instruction as applying not only to Stadtmauer’s knowledge of facts *(i.e.,*which expenditures were claimed as deductible business expenses on the tax returns), but also his knowledge of the law *(ie.,*whether those deductions were materially “false or fraudulent” under the Tax Code). Accordingly, we turn to Stadtmauer’s argument that the Court’s instruction incorrectly stated the law in that regard.

2. *Willful Blindness and Cheek*

Stadtmauer argues that a willful blindness charge that applies to a defendant’s knowledge of the law is “categorically and unequivocally” inappropriate in a criminal tax case in light of the Supreme Court’s decision in *Cheek.*(Appellant’s Br. at 69.) We disagree.

We begin with the facts of *Cheek.*The defendant there stopped filing federal income tax returns in 1980 and was charged with (1) willfully failing to file federal income tax returns and (2) willfully attempting to evade income taxes. 498 U.S. at 194, 111 S.Ct. 604. Cheek’s defense at trial was that, as a result of “indoctrination” he received as a member of a group that believed the federal tax system is unconstitutional, he “sincerely believed that the tax laws were being unconstitutionally enforced and that his actions ... were lawful,” and thus had “acted without the willfulness required” for the offenses charged. *Id.*at 196, 111 S.Ct. 604.

The trial court instructed the jury that, to satisfy the element of “willfulness,” the Government was required to “prove the voluntary and intentional violation of a known legal duty, a burden that could not be proved by showing mistake, ignorance, or negligence.” *Id.*However, the court also instructed the jury that only *“an objectively reasonable*good-faith misunderstanding of the law would negate willfulness.” *Id.*(emphasis added). The *255Seventh Circuit Court affirmed Cheek’s conviction, holding that “even actual ignorance is not a defense unless the defendant’s ignorance was itself objectively reasonable.” *Id.*at 198, 111 S.Ct. 604.

The Supreme Court reversed. It first reaffirmed that the term “willfully,” as used in criminal tax statutes, “carv[es] out an exception to the traditional rule” that ignorance of the law is not a defense to criminal liability. *Id.*at 200, 111 S.Ct. 604. Second, it reaffirmed its prior decisions establishing that “the standard for the statutory willfulness requirement is the ‘voluntary, intentional violation of a known legal duty.’” *Id.*at 201, 111 S.Ct. 604 (quoting *Pomponio,*429 U.S. at 12, 97 S.Ct. 22); *see also United States v. Bishop,*412 U.S. 346, 360, 93 S.Ct. 2008, 36 L.Ed.2d 941 (1973).

Turning to the jury instruction given in Cheek’s trial, the Court concluded that the trial judge erred in instructing the jury that “a claimed good-faith belief must be objectively reasonable” to “negat[e] ... evidence purporting to show a defendant’s awareness of the legal duty at issue.” 498 U.S. at 203, 111 S.Ct. 604. The Court explained that, in proving that a defendant had “actual knowledge” of the legal duty imposed on him by the tax laws, the Government must also

> negat[e] a defendant’s claim of ignorance of the law or a claim that because of a misunderstanding of the law, he had a good-faith belief that he was not violating any of the provisions of the tax laws. This is so because one cannot be aware that the law imposes a duty upon him and yet be ignorant of it, misunderstand the law, or believe that the duty does not exist. In the end, the issue is whether, based on all the evidence, the Government has proved that the defendant was aware of the duty at issue, which cannot be true if the jury credits a good-faith misunderstanding and belief submission, whether or not the claimed belief or misunderstanding is objectively reasonable.

*Id.*at 202, 111 S.Ct. 604. The Court thus distinguished between two types of persons: (1) a person with “actual knowledge” of a legal duty, and (2) a person who, in good faith, is ignorant of the duty, misunderstands it, or believes that it does not exist. It held that criminal tax liability could not attach to a person in the latter category.

Stadtmauer’s attempt to equate a person who *deliberately*avoids learning of a legal duty with a person falling within the latter category *(e.g.,*one who is ignorant of that duty by virtue of a good-faith belief or misunderstanding) is not persuasive. The willful, blindness charge, also known as a “deliberate ignorance” charge, originates from the Ninth Circuit Court’s decision in *United States v. Jewell,*532 F.2d 697 (9th Cir.1976). *See United States v. Caminos,*770 F.2d 361, 365 (3d Cir.1985). *Jewell*explained that

> [t]he substantive justification for the [charge] is that *deliberate ignorance and positive knowledge are equally culpable.*The textual justification is that in common understanding one “knows” facts of which he is less than absolutely certain. To act “knowingly,” therefore, is not necessarily to act only with positive knowledge, but also to act with an awareness of the high probability of the existence of the fact in question. When such awareness is present, “positive” knowledge is not required.

*Jewell,*532 F.2d at 700 (emphasis added). Thus, willful blindness is a “subjective state of mind that is deemed to satisfy a scienter requirement of knowledge,” *United States v. One 1973 Rolls Royce,*43 F.3d 794, 808 (3d Cir.1994), and “cannot become a safe harbor for culpable conduct,” *WertRuiz,*228 F.3d at 258.

*256We see nothing in *Cheek*— which did not involve a willful blindness instruction— that suggests the Supreme Court intended to exempt criminal tax prosecutions from this general rule. *Cf. United States v. Bussey,*942 F.2d 1241, 1249 (8th Cir.1991) (defendant’s reliance on *Cheek*in challenging willful blindness instruction in criminal tax trial was “seriously misplaced” because *“Cheek*did not involve a willful blindness instruction”). The justification for requiring knowledge of the relevant tax laws is that, “in our complex tax system, uncertainty often arises even among taxpayers who earnestly wish to follow the law, and it is not the purpose of the law to penalize frank difference^] of opinion or innocent errors made despite the exercise of reasonable care.” *Cheek,*498 U.S. at 205, 111 S.Ct. 604 (internal quotation marks and citation omitted); *see also Bryan v. United States,*524 U.S. 184, 195, 118 S.Ct. 1939, 141 L.Ed.2d 197 (1998) (explaining that “[t]he danger of convicting individuals engaged in apparently innocent activity” is what “motivated [the Court’s] decision[]” in *Cheek)-,*United States v. Murdock, 290 U.S. 389, 396, 54 S.Ct. 223, 78 L.Ed. 381 (1933) (“Congress did not intend that a person, by reason of a bona fide misunderstanding ..., should become a criminal by his mere failure to measure up to the prescribed standard of conduct.”), *overruled on other grounds by Murphy v. Waterfront Comm’n,*378 U.S. 52, 84 S.Ct. 1594, 12 L.Ed.2d 678 (1964). By definition, one who *intentionally*avoids learning of his tax obligations is not a taxpayer who “earnestly wishfes] to follow the law,” or fails to do so as a result of an “innocent error[ ] made despite the exercise of reasonable care.” *Cheek,*498 U.S. at 205, 111 S.Ct. 604 (internal quotation marks and citation omitted). Rather, a person who deliberately evades learning his legal duties has a subjectively culpable state of mind that goes beyond mere negligence, a good faith misunderstanding, or even recklessness. *Cf. Wert-Ruiz,*228 F.3d at 237 (“Willful blindness is not to be equated with negligence or lack of due care, for willful blindness is a subjective state of mind that is deemed to satisfy a scienter requirement of knowledge.” (internal quotation marks and citation omitted)); *see also 1973 Rolls Royce,*43 F.3d at 808 (describing the “mainstream conception of willful blindness as a state of mind of much greater culpability than simple negligence or recklessness, and more akin to knowledge”).

Several of our sister circuit courts have similarly concluded that a willful blindness instruction that applies to a defendant’s knowledge of tax law does not run afoul of *Cheek. See United States v. Anthony,*545 F.3d 60, 64-65 (1st Cir.2008); *United States v. Dean,*487 F.3d 840, 851 (11th Cir.2007); *Bussey,*942 F.2d at 1248-49.21 The First and Eleventh Circuit Courts have interpreted *Cheek*as counseling that, though a belief that one is complying with the tax laws need not be “objectively reasonable” to constitute a defense, it nonetheless must be “held in good faith.” Aw*257*thony,*545 F.3d at 65; *see also Dean,*487 F.3d at 851 (reasoning that the *Cheek*Court had, “albeit, not in so many words,” held that “the law would not countenance” willful blindness to one’s tax obligations). Accordingly, “the defense that the accused did not know of his [legal] duty fails if he came by his ignorance through deliberate avoidance of materials that would have apprised him of his duty, as such avoidance undermines the claim of good faith.” *Anthony,*545 F.3d at 65; *see also Dean,*487 F.3d at 851 (“A willful blindness instruction is entirely appropriate where the evidence supports a finding that a defendant intentionally insulated himself from knowledge of his tax obligations.”).

We agree with the reasoning of these Courts and join them in concluding that a willful blindness instruction that applies to a defendant’s knowledge of the law in a criminal tax case (such as the instruction at issue here) does not run afoul of *Cheek.*

The District Court’s willful blindness instruction in this case also adhered to our precedent requiring that such an instruction “ ‘make clear that the defendant himself was subjectively aware of the high probability of the fact in question, and not merely that a reasonable man would have been aware of the probability.’ ” *Werh-Ruiz,*228 F.3d at 255 (quoting *Caminos,*770 F.2d at 365). The Court instructed the jury that it must find beyond a reasonable doubt that Stadtmauer (1) “was aware of a high probability that the tax returns at issue were false or fraudulent as to a material matter,” and (2) “consciously and deliberately tried to avoid learning about this fact.” (App.3974.) The Court told the jury that it could not find the element of knowledge satisfied if it found only that Stadtmauer *“should have known*that the tax returns at issue were false as to a material matter[,] or that a *reasonable person would have known*of a high probability of that fact.” *(Id.*(emphases added).) Finally, the Court stressed that it was insufficient that Stadtmauer “may have been stupid or foolish or may have acted out of inadvertence or accident. A showing of negligence or of a good-faith mistake of law is not ... sufficient to support a finding of ... knowledge.” *(Id.)*

The instruction as a whole thus belies Stadtmauer’s claims that the District Court “allowed the jury to substitute a failure to inquire for evidence of actual knowledge of the tax laws”; allowed the jury to convict him simply for being “ignorant of’ or “for misunderstanding” the law; and instructed the jury to apply an “objective test[ ]” in determining whether he had knowledge of the law.22 (Appellant’s Br. at 70-71.) Accordingly, we conclude that the Court’s willful blindness instruction correctly stated the law.

*2583. *Whether the District Court’s Willful Blindness Instruction Applied to the Element of Specific Intent*

Though we agree with Stadtmauer that the District Court’s willful blindness instruction could be interpreted as applying to his knowledge of the law, we reject his argument that the instruction also (and impermissibly) applied to the element of intent.

In addition to requiring a “known legal duty,” *Cheek*requires proof that the defendant “voluntarily and intentionally violated that duty.” 498 U.S. at 201, 111 S.Ct. 604. “Willfulness” thus requires more than a general intent to accomplish an act; it requires proof that the act was done with the specific intent to do something that the law forbids. *See id.*at 200-01, 111 S.Ct. 604; *Pomponio,*429 U.S. at 12-13, 97 S.Ct. 22; *Murdock,*290 U.S. at 394-95, 54 S.Ct. 223; *see also Carter v. United States,*530 U.S. 255, 268, 120 S.Ct. 2159, 147 L.Ed.2d 203 (2000) (explaining that general intent (as opposed to specific intent) requires “that the defendant possessed knowledge [only] with respect to the *actus reus*of the crime”).

The penultimate paragraph of the District Court’s willful blindness instruction stated:

> [Y]ou may find that the defendant acted knowingly and willfully if you find beyond a reasonable doubt either that the defendant actually knew that the tax returns were false or fraudulent as to a material matter or that the defendant deliberately closed his eyes to what he had every reason to believe.

(App.3974.) Stadtmauer argues that the Court’s instruction that the jury could find that Stadtmauer “acted knowingly *and willfully”*if he “deliberately closed his eyes to what he had every reason to believe” improperly substituted willful blindness for proof of a specific intent, as the element of “willfulness” encompasses both a knowledge and intent component. In that light, Stadtmauer argues that the Court’s instruction by analogy ran afoul of *Pierre,*where we held that, although “[w]illful blindness can be used to establish knowledge,” it “does not satisfy the specific intent requirement” under the Convention Against Torture (“CAT”).23528 F.3d at 190.

Even assuming that the inclusion of these two words (“and willfully”) in the District Court’s willful blindness instruction was technically an incorrect statement of the law,24 we conclude that the Court’s “instructions, taken as a whole, properly instructed the jury as to the proof required” for the element of intent. *United States v. Leahy,*445 F.3d 634, 650 (3d Cir.2006). The Court’s instructions made clear that willful blindness applied only to the element of knowledge. *See*App. 3973 *(“The element of knowledge*on the part of the defendant may be satisfied by inferences drawn from proof that the defendant closed his eyes to what, would otherwise *259have been obvious to him.” (emphasis added)). Indeed, aside from two isolated instances where the Court mentioned the words “willfully” or “willfulness,”25 its eight-paragraph instruction referred only to the “element of knowledge,” Stadtmauer’s “knowledge that the tax returns at issue were false or fraudulent,” or his “knowledge of a fact or circumstance.” It never mentioned “intent,” “purpose,” or any other language that could be reasonably interpreted as applying to the element of intent.

In this context, we cannot agree that a reasonable juror would have concluded from the District Court’s instructions that a finding of willful blindness may also satisfy the element of specific intent. *See United States v. Gurary,*860 F.2d 521, 527 n. 6 (2d Cir.1988) (though the trial court “also mentioned conscious avoidance in connection with willfulness, the components of which are knowledge and intent, a fair reading of ... the charge as a whole indicate[d] that conscious avoidance was to be used only in connection with the knowledge component”). Accordingly, we reject Stadtmauer’s contention that the Court’s willful blindness instruction improperly charged the jury as to the element of intent.

4. *Whether Trial Evidence Warranted the Willful Blindness Instruction*

Stadtmauer finally argues that the trial evidence did not warrant a willful blindness instruction, noting simply that “[n]ot one” of the Government’s witnesses directly claimed that he “deliberately tried to shield himself from learning any fact about the tax returns.” (Appellant’s Br. at 75.) We disagree. The Government need not present *direct*evidence of conscious avoidance to justify a willful blindness instruction. *E.g., United States v. Singh,*222 F.3d 6, 11 (1st Cir.2000). In any event, the District Court did not err in concluding that the instruction was warranted in this case.

At trial, there was abundant evidence that Stadtmauer was intimately involved with the operations of the partnerships and was aware of how the partnerships characterized capital expenditures, charitable contributions, gift and entertainment expenses, and “non-property” expenses in the general ledgers and financial statements. There was also evidence that, despite this knowledge — and despite the logical inference that, as Bentzlin described, “if there is garbage in, [there’s] garbage out” (App.2281) — Stadtmauer spent very little time reviewing the partnerships’ tax returns, and never asked questions of SSMB as to the propriety of the expenses deducted therein. One possible inference from this is what Stadtmauer asked the jury to draw: that he relied in good faith on his accountants to prepare the tax returns consistent with applicable law (and thus had no need to review them closely). However, another possible inference is that Stadtmauer deliberately avoided “ask[ing] the natural follow-up ques*tion[s]”*— e.g., whether the deductions claimed in the tax returns were consistent with how expenses were falsely characterized in the general ledgers and reported on the financial statements — despite his awareness of a high probability of that fact. *Wert-Ruiz,*228 F.3d at 257; *United States v. Brodie,*403 F.3d 123, 158 (3d *260Cir.2005); *see also United States v. Stewart,*185 F.3d 112, 126 (3d Cir.1999) (evidence justified willful blindness instruction in mail fraud and money laundering trial, where the defendant maintained that he “lacked the intent to defraud because he relied upon the findings of solvency reported in state examinations and audit reports,” and where the jury reasonably could have concluded that the defendant “recognized the likelihood of insolvency yet deliberately avoided learning the true facts”).

In this context, we conclude that the Court did not abuse its discretion in giving a willful blindness instruction.26

B. *Lay Opinion Testimony*

Stadtmauer next contends that the District Court admitted impermissible lay opinion testimony as to his knowledge of the falseness of the partnerships’ tax returns by SSMB partner Stanley Bekritsky. We review the admission of lay opinion testimony for abuse of discretion. *United States v. Hoffecker,*530 F.3d 137, 170 (3d Cir.2008).

1. *Background*

About one month into trial, the Government informed defense counsel that, during a recent interview in preparation for his testimony, Bekritsky had recalled a tax return signing session during which Stadtmauer asked him “whether the returns were okay to sign.” The Government disclosed that Bekritsky (1) “understood [Stadtmauer’s] question [to be] about whether the IRS would be likely to detect the problems with the returns,” and (2) stated “I signed them” in response to Stadtmauer’s question. (Supp.App.1049.)

Stadtmauer filed a motion *in limine*to prevent Bekritsky from testifying as to his “ ‘understanding’ of Mr. Stadtmauer’s intended meaning of the question that Mr. Stadtmauer posed to Mr. Bekritsky.” *(Id.*at 1051.) Stadtmauer argued thaj. such testimony would be impermissible lay opinion testimony under Federal Rule of Evidence 701. The Government opposed the motion, arguing that, as a participant in the conversation, Bekritsky should be permitted under Rule 701 to testify as to his understanding of what Stadtmauer was attempting to convey to him. The Government further noted that, unless Bekritsky was permitted to testify as to that understanding, Stadtmauer’s question could be interpreted as having an exculpatory meaning *(ie.,*that he was seeking Bekritsky’s confirmation that the tax returns were accurate27). *(Id.*at 1057.)

The District Court granted the motion *in limine,*reasoning that the jurors could “come to their own conclusions [about] what Mr. Stadtmauer meant” by the question. (App.3217.) The Court nonetheless made clear that the Government was authorized to ask Bekritsky “what ... he mean[t] when he said, T signed it[.]’ ” *(Id.)*

*261At trial, Bekritsky testified on direct examination as follows:

> Q. Did [Stadtmauer] ever ask you generally about the returns?

> A. Yes.

> Q. What did he ask you?

> A. On one occasion, he asked me if he could — if he should sign the returns — if the returns were okay, and-—

> A. —and I said, I signed the returns.

> Q. *What did he**28**mean by that?*

[Defense Counsel]: Objection.

> THE COURT: I don’t want you to tell us what you thought Mr. Stadtmauer [meant] by asking you the question[.] You can testify, however, as to what you meant by your answer.

> A. What I meant by my answer was that I knew that there were problems with these tax returns, *and based upon my understanding of Richard’s involvement, Richard knew*— •

[Defense Counsel]: Objection.

*(Id.*at 3262-63 (emphases added).)

The parties then went to sidebar, where defense counsel objected to Bekritsky “testifying to what [Stadtmauer] knew or didn’t know.” *(Id.*at 3263.) Counsel argued that Bekritsky testifying about “what [Stadtmauer] knew” was “the basis for [the] motion” *in limine. (Id.)*

The District-Court disagreed:

I disagree with you that was the basis of the Court’s ruling. The basis was his interpretation of a statement by Mr. Stadtmauer as to what Stadtmauer’s statement meant, because those words, in my view, did not need interpretation to help the jury.

That is different than this witness testifying about what, based on his perception, he believed Mr. Stadtmauer knew or didn’t know, so I will allow it.

*(Id.)*Bekritsky’s testimony then resumed:

> THE COURT: ... [You] said, what I meant by my answer was that I knew there were problems with these tax returns, and based on my understanding of Richard’s involvement. What did you mean by that?

> A. Richard was involved with the details of the operations of the partnerships. He knew that professional expenses of one entity were being paid by another entity.

[Defense Counsel]: Same objection to his testimony as to what [Stadtmauer] knew or didn’t know.

> THE COURT: ... Overruled.

> THE COURT: ... What did you intend to convey when you said you signed it?

> A. What I intended to convey was there were problems that *we both knew*that existed in the returns. The returns were prepared in a way that I thought that they would get *262by the Government and questions would not be raised.

*(Id.*at 3264 (emphasis added).)

Defense counsel then moved to strike Bekritsky’s statement as to what Stadtmauer “knew”; in the alternative, he moved for a mistrial. Defense counsel argued that Bekritsky’s testimony was “incredibly prejudicial,” had no “probative value at all,” and lacked a foundation. *(Id.*at 3264-65.) The District Court denied Stadtmauer’s motions, reasoning that (1) Bekritsky’s perception of Stadtmauer’s involvement in and knowledge of the partnerships provided a sufficient foundation for his testimony as to what Stadtmauer knew; and (2) in testifying that Stadtmauer “knew that things were being ex-pensed that shouldn’t have been,” Bekritsky was merely “explaining what he meant when he said ... T signed it.’ ” *(Id.*at 3266.)

At the close of its summation, the Government quoted Bekritsky’s testimony and emphasized that, instead of asking whether the returns were “accurate” or “a hundred percent correct,” Stadtmauer had asked whether they were “okay to sign.” *(Id.*at 4060.) In that context — and in light of Bekritsky’s testimony regarding what he intended to convey by his answer, “I signed [them]” — the Government argued that Stadtmauer’s goal was not to file “accurate!,] true returns,” but to file returns that would not raise “flags ... with the IRS.”29*(Id.)*

By contrast, defense counsel urged the jury to draw the opposite inference from Bekritsky’s testimony. Counsel argued in summation that “any reasonable person” would have interpreted Stadtmauer’s question to “mean[] the returns are okay to sign, meaning that they are correct.” *(Id.*at 4062.) In that light, defense counsel contended that “Bekritsky’s testimony [as a] whole ... exonerate^]” Stadtmauer. *(Id.)*

2. *Analysis*

Stadtmauer argues that Bekritsky’s testimony that Stadtmauer “knew” there were “problems” with the tax returns was inadmissible under Federal Rule of Evidence 701. In relevant part, it limits lay testimony “in the form of opinions or inferences” to those “which are (a) rationally based on the perception of the witness, [and] (b) helpful to a clear understanding of the witness’ testimony or the determination of a fact in issue[.]” Fed.R.Evid. 701.

Rule 701 represents “a movement away from ... courts’ historically skeptical view of lay opinion evidence,” and is “rooted in the modern trend away from fíne distinctions between fact and opinion and toward greater admissibility.” *Asplundh Mfg. Div. v. Benton Harbor Eng’g,*57 F.3d 1190, 1195 (3d Cir.1995); *see also Teen-Ed, Inc. v. Kimball Int’l, Inc.,*620 F.2d 399, 403 (3d Cir.1980). The Rule is nonetheless designed to exclude lay opinion testimony that “amount[s] to little more than choosing up sides,” Fed.R.Evid. 701 advisory committee’s note, or that “ ‘merely tell[s] the jury what result to reach,’ ” *United States v. Rea,*958 F.2d 1206, 1215-16 (2d Cir.1992) (quoting Fed.R.Evid. 704 advisory committee’s note on 1972 Proposed Rules). Lay testimony in the form of an opinion about what a defendant did or did not know often comes dangerously close to doing just this. Though “we have *263never held that lay opinion evidence concerning the knowledge of a third party is *per se*inadmissible,” 30 we have explained that “this kind of evidence [is] difficult to admit” under either prong of Rule 701:

> If the witness fails to describe the opinion’s basis, in the form of descriptions of specific incidents, the opinion testimony [should] be rejected on the ground that it is not based on the witness’s perceptions. To the extent the witness describes the basis of his or her opinion, that testimony [should] be rejected on the ground that it is not helpful because the fact finder is able to reach his or her own conclusion, making the opinion testimony irrelevant.

*United States v. Polishan,*336 F.3d 234, 242 (3d Cir.2003) (internal citation omitted).

In our ease, Stadtmauer primarily argues that Bekritsky’s testimony was inadmissible under the first prong of Rule 701. Bekritsky’s opinion that Stadtmauer “knew” there were “problems” in the tax returns was not, according to Stadtmauer, “rationally based” on Bekritsky’s perceptions because he never discussed with Stadtmauer the falseness of any specific tax return (or any deduction claimed on a return). (Appellant’s Br. at 49.) We do not follow this path.

Rule 701’s “rationally based” requirement is essentially a restatement of the personal knowledge requirement necessary for all lay witness testimony. *See*Fed.R.Evid. 701 advisory committee’s note; *see also*Christopher B. Mueller & Laird C. Kirkpatrick, *Federal Evidence*§ 7:3, at 751 (3d ed.2007). We agree with the District Court that Bekritsky’s testimony that Stadtmauer “knew” there were “problems” with the partnership tax returns — specifically, that certain partnerships were claiming deductions for expenses paid on behalf of other partnerships (“non-property” expenses) — was at least “rationally based” on his perception of Stadtmauer’s (1) involvement with and control over the operations of the partnerships, (2) knowledge of how certain kinds of expenditures were characterized in the partnerships’ general ledgers and financial statements, and (3) knowledge that those materials were used to prepare the partnerships’ tax returns. *Cf. Polishan,*336 F.3d at 242 (“Lay opinion testimony may be based on the witness’s own perceptions and ‘knowledge and participation in the day-to-day affairs of [the] business.’ ”) (alteration in original) (quoting *Lightning Lube, Inc. v. Witco Corp.,*4 F.3d 1153, 1175 (3d Cir.1993)); *Rea,*958 F.2d at 1216 (“[T]here are a number of objective factual bases from which it is possible to infer ... that a person knows a given fact,” including what the person “was in a position to see or hear ..., conduct in which he engaged, and what his background and experience were.”).

Indeed, our Court (and other circuit courts) have held far more prejudicial statements to satisfy this Rule 701 requirement (even where such statements violated Rule 701’s helpfulness requirement). *See United States v. Anderskow,*88 F.3d 245, 250 (3d Cir.1996) (lay witness’s testimony that defendant “must have known” of loan fraud scheme satisfied the “rationally based” requirement of Rule 701, as the testimony was based on the witness’s “first-hand knowledge” of the defendant’s frequent exposure to fraudulent loan schedules); *see also United States v. Wantuch,*525 F.3d 505, 512-14 (7th Cir. 2008) (lay witness’s testimony that defen*264dant “knew all the time that everything that he was doing was illegal” satisfied the “rationally based” requirement of Rule 701, as the witness was “deeply involved in” the fraudulent scheme and was the defendant’s “contact every step of the way”); *Rea,*958 F.2d at 1217, 1219 (lay witness’s testimony that defendant “had to” have known of scheme to evade taxes satisfied the “rationally based” requirement of Rule 701, as the witness testified that he repeatedly told the defendant that he lacked a license that would exempt their transactions from federal excise taxes).

Whether Bekritsky’s testimony violated the helpfulness prong of Rule 701 requires closer attention.31 At first blush, Bekritsky’s testimony that Stadtmauer “knew” there were “problems” with the returns seems unhelpful because the basis for Bekritsky’s *opinion*— e.g., Stadtmauer’s intimate knowledge of the partnerships’ operations and how their books and records were maintained — was already in evidence. *Cf. Rea,*958 F.2d at 1216 (“[W]hen a witness has fully described what a defendant was in a position to observe, what the defendant was told, and what the defendant said or did, the witness’s opinion as to the defendant’s knowledge will often not be ‘helpful’ ... because the jury will be in as good a position as the witness to draw the inference as to whether or not the defendant knew.”).

Bekritsky’s testimony is nonetheless different in important respects from the lay opinion testimony we found inadmissible in *Anderskow,*the principal case on which Stadtmauer relies. In that case, a cooperating conspirator in a loan fraud conspiracy testified that he provided one of the defendants, Donald Anchors, with fraudulent loan schedules to be passed along to borrowers. 88 F.3d at 249. On direct examination, the Government asked the witness whether Anchors would have been “deceived by the information that [the witness was] sending him.” *Id.*The witness responded:

> Donald Anchors had probably 20 or 30 borrowers, maybe more for all I know, who had been promised millions of dollars for a long time, some as long as a year. He had never seen one dime funded or loaned, and he kept on with the business at hand. *I had no reason to believe that he wasn’t fully aware of**265*what was occurring,*as long as he was getting paid.

*Id.*at 250 (emphasis added). We held that this testimony was inadmissible under Rule 701’s helpfulness prong, reasoning that “a witness’ subjective belief that a defendant ‘must have known’ [of the object of a conspiracy] is [not] helpful to a factfinder that has before it the very circumstantial evidence upon which the subjective opinion is based.” *Id.*at 251. Stated another way, the witness’s testimony was not helpful — and thus inadmissible under Rule 701 — because the jury was in just as good a position as the witness to infer what Anchors “must have known.”

However, unlike the witness in *Anderskow,*Bekritsky did not offer his opinion as to what Stadtmauer “knew” in a vacuum. Rather, Bekritsky was responding to a question asking him to explain what he meant by his ambiguous answer (“I signed them”) to Stadtmauer’s equally ambiguous questions (whether “he should sign the returns,” and whether “the returns were okay”). Rather than opining as to what Stadtmauer “must have known,” Bekritsky more specifically testified as to what he *believed*Stadtmauer knew at the time of this conversation (in the context of explaining why he answered Stadtmauer’s questions the way he did). In that light, even if Bekritsky’s opinion regarding what Stadtmauer “knew” was unhelpful to “the determination of a fact in issue” *(ie.,*whether ’Stadtmauer had guilty knowledge), it arguably was helpful to “a clear understanding of [Bekritsky’s] testimony.” Fed.R.Evid. 701. *Cf. United States v. De Peri,*778 F.2d 963, 977 (3d Cir.1985) (lay witness’s testimony was helpful to a clear understanding of conversations consisting of “unfinished sentences and punctuated with ambiguous references to events that [were] only clear to [the participants]”); *see also United States v. Urlacher,*979 F.2d 935, 939 (2d Cir.1992) (lay witness’s testimony was helpful to a clear understanding of “statements or words [recorded] on the tape that would be ambiguous or unclear to someone who was not a participant in the conversation”); *United States v. Awan,*966 F.2d 1415, 1430 (11th Cir.1992) (same).32

This question is close. However, even assuming that the District Court erred in refusing to strike Bekritsky’s testimony,33 we conclude that any error was harmless. A non-constitutional error at *266trial does not warrant reversal where “it is highly probable that the error did not contribute to the judgment.” *United States v. Helbling,*209 F.3d 226, 241 (3d Cir.2000) (internal quotation marks and citation omitted); *see also Kotteakos v. United States,*328 U.S. 750, 764-65, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). This “high probability” standard “requires that we have a sure conviction that the error did not prejudice the defendant! ]”; however, “we may be firmly convinced that the error was harmless without disproving every ‘reasonable possibility’ of prejudice.” *United States v. Jannotti,*729 F.2d 213, 220 n. 2 (3d Cir.1984).

When Bekritsky’s testimony is viewed in the context of the record as a whole, we conclude that it is highly probable that any error in admitting that testimony did not prejudice Stadtmauer. *See, e.g., United States v. Zehrbach,*47 F.3d 1252, 1265 (3d Cir.1995) (“The harmless error doctrine requires that the court consider an error in light of the record as a whole.... ”). Though Stadtmauer challenges Bekritsky’s testimony that Stadtmauer “knew” there were “problems” with the returns, he does not challenge Bekritsky’s testimony that, by his answer (“I signed them”), he intended to convey that (1) “there were problems ... that existed in the returns”; and (2) “[t]he returns were prepared in a way that [Bekritsky] thought that they would get by the Government and questions would not be raised.” . (App.3264.) The plain and unmistakable implication of these unchallenged portions of Bekritsky’s testimony is that he believed Stadtmauer also “knew” that there were “problems” with the return. Otherwise, Bekritsky’s explanation of what he intended to convey by answering “I signed [them]” would be nonsensical.34

Moreover, any error in refusing to strike Bekritsky’s testimony regarding what he believed Stadtmauer “knew” was harmless in light of the “mountain of circumstantial evidence supporting the inference that” Stadtmauer knew that improper deductions were claimed in the partnerships’ tax returns, *Anderskow,*88 F.3d at 251, including evidence that Stadtmauer: (1) was intimately familiar with how the partnerships operated and maintained their general ledgers; (2) was involved in deciding which partnerships would pay certain expenditures; (3) was aware that certain expenditures were falsely characterized as expenses in the ledgers and financial statements; (4) mischaracterized expenditures in the partnerships’ financial statements *267when expedient; and (5) made all of these decisions with awareness of their tax consequences *(e.g.,*the tuition payments for Zecher’s children, and the decision to continue appreciating capital expenditures for the partnerships involved in the WNY transaction). In that light, we are convinced that, regardless of Bekritsky’s testimony, the jury would have rejected Stadtmauer’s defense that he genuinely believed that SSMB — led by Plotkin, to whom KC was tunneling yearly bonuses and private school tuition payments — was, for purposes of the partnerships’ tax retxxrns, correcting the extensive mischaracterizations of expenditures as reflected in the partnerships’ general ledgers and financial statements.

In sum, any error in admitting Bekritsky’s testimony is harmless and thus does not require reversal.

C. *Prosecutorial Misconduct*

Stadtmauer claims that the Government violated his due process rights by “improperly standing silent” when one of its witnesses, former COO Scott Zecher, made several statements during cross-examination that the lead prosecutor knew to be false. (Appellant’s Br. at 41.) To succeed on this claim, Stadtmauer bears the burden of establishing that: (1) Zecher committed perjury; (2) the Government knew or should have known that Zecher committed perjury but failed to correct his testimony; and (3) there is a reasonable likelihood that the false testimony could have affected the verdict. *See Hoffecker,*530 F.3d at 183. Because Stadtmauer cannot meet his burden as to the first two of these elements, we need not address the third.

In 2005, Zecher was interviewed several times by FBI agents and prosecutors (in-eluding one of the prosecutors that tried Stadtmauer’s case). During trial, defense counsel sought to impeach Zecher with his statements during these interviews, as recorded in summaries prepared by the FBI agents present (known as “Form 302s”). To take one example, defense counsel asked Zecher during cross-examination whether he recalled telling investigators that Kushner, and not Stadtmauer, had raised the idea of paying Zecher’s children’s private school tuition “rather than paying [Zecher] a bonus.” (App.3045.) Zecher first stated that he did not recall making the statement, and then denied that he made such a statement. Defense counsel then showed Zecher the Form 302 to refresh his recollection, which stated:

> ZECHER stated when he was hired KUSHNER told him that he could not pay ZECHER the salary he wanted, but instead would make up the difference in bonuses in June and December. KC normally issues bonuses to employees in December, but does not issue bonuses in June. ZECHER stated that because no bonuses were paid in June, KUSHNER would pay ZECHER’s ... school tuition rather than paying him a bonus.

*(Id.*at 567.) Zecher denied that the Fo:rm 302 refreshed his recollection, and was adamant that the only conversations he had regarding the issue were with Stadtmauer. *(Id.*at 3045.) Though the District Coxirt permitted Stadtmauer to cross-examine Zecher on the content of his statements, it refused on several occasions to admit the Form 302s themselves as prior inconsistent statements, rulings, we note, that Stadtmauer does not challenge. The Court’s reasoning was that the Form 302s contained the FBI’s characterizations of what Zecher said (which Zecher had not adopted).35

*268After both sides rested, defense counsel moved for a mistrial based on “the perjured testimony of Scott Zecher and ... the Government’s failure to correct that testimony.” *(Id.*at 3731.) Defense counsel argued that, when considered in light of the totality of Zecher’s testimony-which included numerous instances where Zecher testified that he could not recall certain events and conversations-there was enough for the District Court to determine that Zecher’s testimony was demonstrably false. The Court denied the motion, explaining that it could not find that Zecher’s “apparent lack of recollection in some instances ... was due to confusion or mistake or faulty memory or a willful lie.” *(Id.*at 3871.)

We review a district court’s factual finding that a witness’s testimony was not false for clear error, and “will not disturb that finding unless it is wholly unsupported by the evidence.” *Hoffecker,*530 F.3d at 183. We have little trouble concluding that the District Court’s finding in this case was not clearly erroneous. As the Court noted, other than the inconsistencies between the FBI agent’s notes and Zecher’s recollection of his statements, there was no other evidence that Zecher perjured himself. *Cf. United States v. Dunnigan,*507 U.S. 87, 94, 113 S.Ct. 1111, 122 L.Ed.2d 445 (1993) (a witness does not commit perjury if his false testimony is the “result of confusion, mistake, or faulty memory”).

Even assuming the District Court clearly erred in finding that Zecher’s testimony was not false, Stadtmauer has not demonstrated that the Government knew or should have known that Zecher’s testimony was false. *See Hoffecker,*530 F.3d at 183. Stadtmauer relies on *United States v. Harris,*498 F.2d 1164 (3d Cir.1974), where the Government failed to correct a witness who falsely testified during cross-examination that prosecutors had made no promises to help her achieve a reduced sentence on pending state charges in exchange for her testimony against the defendant. In concluding the Government had violated its “duty to disclose a promise made to a Government witness,” *id.*at 1169, we first noted that the witness arguably had not committed perjury by her responses because she may have “believed in good faith” that the questions posed to her “only referred to specific promises concerning her sentence,” which the Government did not (and could not) make. *Id.*at 1168. We reasoned, however, that the prosecution’s duty to disclose false testimony should not be “narrowly and technically limited to those situations where the prosecutor knows that the witness is guilty of the crime of perjury.” *Id.*at 1169. Rather, “when it should be obvious to the Government that the witness’ answer, although made in good faith, is untrue,” it has an obligation to correct that testimony. *Id.*

The circumstances of Zecher’s testimony are far afield from the witness’s testimony in *Harris,*where it was undisputed that the prosecutor had personal knowledge that the witness’s answers were not correct. *See id.*at 1168 (prosecutor admitted that he had promised the cooperating witness that the Government would do “whatever [it] could” to get her state sentence reduced). Here, there was no way for the prosecutor to know whether Zecher was *269giving false testimony when he denied — or could not recall — making certain statements during the 2005 interviews. Thus, Stadtmauer’s assertion that the Government’s counsel refused “to speak up when he knew for a fact that Zecher had made” false statements is simply unsupported by the record. *Cf. Tapia v. Tansy,*926 F.2d 1554, 1563 (10th Cir.1991) (“Contradictions and changes in a witness’s testimony alone do not constitute perjury and do not create an inference, let alone prove, that the prosecution knowingly presented perjured testimony.”).

D. *Expert Testimony*

Over Stadtmauer’s objection, the District Court permitted IRS Agent Susan Grant to testify as an expert (and summary) witness. *See*Fed.R.Evid. 702, 703. Stadtmauer argues that the Court erred in admitting Agent Grant’s testimony because she “opined, with insufficient factual or legal foundation, that the [KC] partnership returns were false and fraudulent.” (Appellant’s Br. at 51.) We review a district court’s admission of expert testimony for abuse of discretion. *Estate of Schneider v. Fried,*320 F.3d 396, 404 (3d Cir.2003).

Prior to trial, the Government disclosed the expert testimony that Agent Grant intended to provide and produced to defense counsel a set of her summary charts. Stadtmauer moved *in limine*to preclude Grant from testifying, arguing that her proposed testimony would improperly bear on the ultimate legal issues in the case, and would be unhelpful and unreliable. The District Court denied Stadtmauer’s motion, finding that Grant’s testimony had “sufficient indicia of reliability and relation to the facts of this case.” (App.89-92.)

In her direct testimony, Grant described how a partnership tax return is prepared, and explained where on the return different categories of deductions were reported. Grant explained how she totaled the expenses she determined were improperly deducted from each partnership return, and carried them through to a summary chart for each partnership for each tax year, illustrating how the total amount of improper deductions affected the net income reported to the IRS. Defense counsel vigorously cross-examined Grant for two days, including questions on many specific deductions, and nearly every category of deductions, she determined were improperly claimed.

Our sister circuit courts that have addressed the issue are unanimous that “expert testimony by an IRS agent which expresses an opinion as to the proper tax consequences of a transaction is admissible evidence.” *United States v. Mikutowicz,*365 F.3d 65, 72 (1st Cir.2004) (internal quotation marks and citation omitted); *see, e.g., United States v. Bedford,*536 F.3d 1148, 1158 (10th Cir.2008); *United States v. Pree,*408 F.3d 855, 870 (7th Cir.2005); *United States v. Sabino,*274 F.3d 1053, 1067 (6th Cir.2001), *modified on other grounds,*307 F.3d 446 (6th Cir.2002); *United States v. Duncan, 42 F.3d*97, 101-02 (2d Cir.1994); *United States v. Moore,*997 F.2d 55, 58-59 (5th Cir.1993). The “primary limitation” on such testimony is that the expert “may not testify about the defendant’s state of mind when the challenged deductions were claimed.” *Mikutowicz,*365 F.3d at 72; *see*Fed.R.Evid. 704(b) (an expert witness may not opine “as to whether the defendant did or did not have the mental state or condition constituting an element of the crime charged”); *see also Sabino,*274 F.3d at 1067.

In our case, it is undisputed that Grant did not opine on Stadtmauer’s knowledge or intent. Stadtmauer nonetheless argues that the District Court impermissibly allowed her to “interpret the tax laws” and *270“add her unreliable and otherwise inadmissible opinion that the tax returns were false and fraudulent.” (Appellant’s Br. at 51.) Stadtmauer seeks to compare Grant’s testimony to expert testimony the Second Circuit Court found objectionable in *United States v. Scop,*846 F.2d 135 (2d Cir. 1988). There an investigator from the Securities and Exchange Commission testified as an expert in securities trading practices, and opined, drawing “directly upon the language of the statute,” that the defendants’ scheme of buying and selling securities to create artificial price levels constituted market “manipulation” and “fraud.” *Id.*at 140. The Second Circuit Court determined that, through this testimony, the expert had “invade[d] the province of the court to determine the applicable law and to instruct the jury as to that law.” *Id.*(internal quotation marks and citation omitted). In addition, the expert conceded on cross-examination that his opinion was largely based not on his expertise in securities trading, but on his “positive assessment of the trustworthiness and accuracy of the testimony of the government’s witnesses.” *Id.*at 142.

Agent Grant’s testimony is far from the expert testimony deemed objectionable in *Scop.*She never used the words “false” or “fraudulent” to describe any of the deductions she concluded were improper, and did not base any portion of her testimony on her assessment of the credibility of other witnesses. Accordingly, *Scop*is unavailing to Stadtmauer. *Cf. Hoffecker,*530 F.3d at 171 (distinguishing the testimony in *Scop*from testimony that defendant’s commodities investment program was a “scam,” where the witness “did not couch his view ... on the language of the mail fraud statute, and did not base his opinion on the credibility or testimony of others”); *see also Duncan,*42 F.3d at 101-02 (distinguishing the testimony in *Scop*from IRS agent’s testimony that did not “use any legally specialized terms” and was “based on [the agent’s] own investigation of the facts and review of the records”).

Stadtmauer also contends that the District Court erred in admitting Grant’s testimony because she made “out-and-out mischaracterizations” and “bald assertions” of the law in explaining her opinions. (Appellant’s Br. at 53, 55.) The record belies these assertions.36 In any event, all expert testimony as to the “proper tax consequences of a transaction” is bound to touch on the law to some extent, *Milcutowicz,*365 F.3d at 72, and we have little trouble concluding that Grant’s testimony did not improperly invade the province of the Court. Indeed, the Court not only gave extensive instructions on the applicable tax laws, and during Grant’s testimony emphasized to the jury that it was “bound to follow the law as [the Court] tell[s] you it applies in this case.” (App.3434.) The Court emphasized that only it, and not Grant, was authorized to instruct the jury as to the law. *See id.*at 3411 (for exam-*271pie, instructing the jury that “to the extent that [Agent Grant] use[s] the word ‘Law,’ I will instruct you as to the law at the end of the case. [Agent Grant] can certainly testify as to what her understanding based on her experience as a tax expert is [and] to what the IRS’ view of things is”).

In sum, to the extent there were (as Stadtmauer contends) shortcomings in the IRS Agent’s conclusions as to the propriety of specific deductions, they were “raised properly on cross-examination and went to the credibility, not the admissibility, of [her] testimony,” *Kannankeril v. Terminix Int’l, Inc.,*128 F.3d 802, 809 (3d Cir.1997), and the record in this case confirms that defense counsel had ample opportunity to cross-examine Grant on her specific conclusions, methodology, and assumptions.37 Accordingly, we conclude that the District Court did not abuse its discretion in admitting Agent Grant’s testimony.38

E. *Restrictions on Cross-Examination*

We end with the argument that Stadtmauer raises first: that the District Court improperly barred him from affirmatively admitting certain exhibits into evidence during cross-examination of Government witnesses. We review a district court’s rulings on the scope of cross-examination for abuse of discretion, *United States v. Casoni,*950 F.2d 893, 902 (3d Cir.1991), “but to the extent the district court’s ruling turns on an interpretation of a Federal Rule of Evidence^] our review is plenary,” *United States v. Velasquez,*64 F.3d 844, 848 (3d Cir.1995) (internal quotation marks and citation omitted).

Stadtmauer contends that the District Court erroneously barred him from admitting several categories of exhibits during defense counsel’s cross-examination of Bentzlin, Zecher, and Bekritsky. For example, during cross-examination of Zecher, defense counsel sought to introduce hundreds of advertisements bearing the name “Kushner Companies” (instead of the name of an individual partnership). Defense counsel sought to introduce the concept of “branding” through these exhibits, and thus to offer an exculpatory explanation for why expenses incurred by one partnership were frequently paid by a different partnership.39

*272The District Court prevented Stadtmauer from admitting these documents because they were “case-in-chief materials” rather than “impeachment materials.”40*See, e.g.,*App. 2405 (excluding proposed defense exhibits during cross-examination because they were “not really specifically impeachment material,” but “more akin to case-in-chief type evidence”); *id.*at 3002-OS (excluding proposed defense exhibits during cross-examination because Stadtmauer was limited to “impeachment material, not case-in-chief material”). Stadtmauer contends that the District Court thereby violated Federal Rule of Evidence 611(b), which provides that cross-examination “should be limited” to (1) “the subject matter of the direct examination,” and (2) “matters affecting the credibility of the witness.” Fed.R.Evid. 611(b). He argues that the Court erroneously barred him from admitting the documents on the grounds that they (1) did not “impeach” the witness (even though they pertained to the “subject matter” of the witness’s direct testimony), and (2) could be introduced in Stadtmauer’s case-in-chief. *Cf. United States v. Segal,*534 F.2d 578, 582-83 (3d Cir.1976) (“the fact that some of the points which defendant sought to explore could have been introduced in the defense ease is not determinative” of whether the evidence is within the “subject matter” of the Government’s direct examination).

From our review of the record, however, it is apparent that the District Court was using the terms “case-in-chief materials” and “impeachment materials” as shorthand to describe those documents that it would (or would not) permit Stadtmauer to introduce during cross-examination so as to manage effectively the presentation of evidence. The Court did not rely on Rule 611(b) in its rulings, and, as it later described, the question was not the admissibility of these exhibits but “the timing of the[ir] introduction.” App. 3570; *see also id.*at 3322 (agreeing that proposed defense exhibit was “within the subject matter” of the Government’s direct examination, but excluding it because it was more akin to a “case-in-chief document[ ]”).

In that light, the more pertinent provision of Rule 611 is subsection (a), which grants district courts broad discretion to “exercise reasonable control over the mode and order of interrogating witnesses and presenting evidence.” Fed.R.Evid. 611(a); *see also*28 Charles A. Wright & Victor J. Gold, *Federal Practice and Procedure*§ 6162, at 338 (1993) (Rule 611(a) “gives trial courts broad powers to control the ‘mode and order’ of what is otherwise admissible evidence”). In our case, we have little trouble concluding that the District Court did not abuse its discretion in postponing the admission of Stadtmauer’s proposed exhibits, even if they were technically within the “subject matter” of the Government’s direct examination. *See, e.g., United States v. Lambert,*580 F.2d *273740, 747 (5th Cir.1978) (district court did not abuse its discretion under Rule 611(a) by excluding defendant’s “proffers of voluminous documentary evidence” during cross-examination); *United States v. Ellison,*557 F.2d 128, 135 (7th Cir.1977) (district court did not abuse its discretion by excluding proposed defense exhibits during cross-examination, even assuming the documents “would have been relevant rebuttal evidence if offered during the presentation of [the defendant’s] own case”).

Finally, even assuming that the District Court relied on an erroneous interpretation of Rule 611(b) in excluding Stadtmauer’s proposed exhibits, the error was harmless. For example, though the Court did not permit Stadtmauer to introduce the KC advertisements themselves, it nonetheless gave defense counsel broad leeway to use them in cross-examining Zecher. The Court allowed defense counsel to show Zecher approximately 20 advertisements, and he agreed that they refreshed his recollection that KC placed advertisements in “newspapers and professional journals” and “spent money advertising the Kushner name.” (App.3010-11.) He also agreed that management used the name “Kushner Companies” in a “generic sense,” rather than “listing all 100 or 200 partnerships” on corporate materials. *(Id.*at 2999.) Through this testimony, defense counsel was able to establish the same basic point: that the partnerships often did business under the name “Kushner Companies” (rather than names of individual partnerships).41 In this context, we conclude that any error in excluding the exhibits during defense counsel’s cross-examination of the Government’s witnesses did not prejudice Stadtmauer.42

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In summary, we conclude that a willful blindness instruction may, where warranted by the trial evidence in a criminal tax case, properly apply to a defendant’s knowledge of his legal duties. The District Court did not abuse its discretion in giving such an instruction in this case, and we disagree with Stadtmauer’s contention that the instruction also impermissibly applied to the element of specific intent.

Though the question whether Bekritsky’s lay opinion testimony was admissible under Rule 701 is close, we conclude that an error here, if any, was harmless. In addition, we reject Stadtmauer’s prosecutorial misconduct claim based on the Government’s supposed failure to “correct” Zecher’s testimony that he could not recall statements he purportedly made to FBI agents (with Government counsel present) during investigatory interviews. Finally, we conclude that the District Court did not abuse its discretion in (1) admitting the *274expert testimony of an IRS agent in this complicated tax fraud case, and (2) preventing Stadtmauer from affirmatively admitting certain categories of exhibits into evidence during defense counsel’s cross-examination of Government witnesses.

For these reasons, we affirm the District Court’s judgment of conviction.

1

. "As required when reviewing convictions, we recite the relevant facts in the light most favorable to the [G]overnment.” *United States v. Leo,*941 F.2d 181, 185 (3d Cir.1991).

2

. We use "Kushner” throughout this opinion to refer only to Charles Kushner.

3

. For descriptive purposes, however, we refer to KC hereafter as if it were an entity.

4

. He pled guilty to conspiring to defraud the United States.

5

.In the late 1990s, Kushner briefly replaced SSMB with the accounting firm of Richard Eisner & Company. Kushner agreed to hire Eisner & Company on the condition that it hire Plotkin as its lead accountant for KC matters. Eisner & Company agreed to hire Plotkin, but shortly thereafter Kushner decided to re-hire SSMB (after SSMB agreed to rehire Plotkin).

6

. KC funneled to Plotkin (through SSMB) bonus payments of $15,000 in 1996, $20,000 in 1997, and $25,000 in 1998. (App.2823-24.)

7

. The Internal Revenue Code provides that an expenditure is fully deductible as a business expense if it: “(1) was paid or incurred during the taxable year; (2) was for carrying on a trade or business; (3) was an expense; (4) was a necessary expense; and (5) was an ordinary expense.” *Neonatology Assocs., P.A. v. Comm’r,*299 F.3d 221, 228 (3d Cir.2002) (citing I.R.C. § 162(a)).

8

. A partnership does not, itself, pay taxes. "Instead, the partners claim a pro-rata share of the partnership’s profits and losses and each pays tax on his share.” *Kantor v. Comm’r,*998 F.2d 1514, 1517 n. 1 (9th Cir. 1993). However, partnerships are still required to file income tax returns.

> [F]or the purpose of computing income and deductions, “the partnership is regarded as an independently recognizable entity apart from the aggregate of its partners.” It is only once the partnership's income and deductions are ascertained and reported that its existence may be disregarded and the partnership becomes a conduit through which the taxpaying obligation passes to the individual partners.

*Brannen v. Comm’r,*722 F.2d 695, 703 (11th Cir.1984) (quoting *United States v. Basye,*410 U.S. 441, 448, 93 S.Ct. 1080, 35 L.Ed.2d 412 (1973)).

9

. The building is owned by "Florham Park Associates," a limited partnership controlled by Kushner and his children.

10

. Included in the “repairs and maintenance” group were the “apartment renovations” and “building improvement” accounts which, as Zecher explained, included, respectively, "capital improvements made to apartments” and “capital improvements made to the general property, *[e.g.,]*the outside of the buildings, the roofs, paving parking lots, things like that.” *(Id.*at 2923.)

11

. Bentzlin and Bekritsky believed that Plot-kin had configured the software before she left KC, but neither was sure. *(Id.*at 2341, 3292.)

12

.Bekritsky explained that this was done so that amounts reported for repairs and maintenance “wouldn't stick out on the return[s].” *(Id.*at 3261.) Bekritsky admitted that he knowingly prepared and filed false tax returns on behalf of KC partnerships to avoid losing a valuable account. *(Id.*at 3352.)

13

. 26 U.S.C. § 7206(2) makes it a crime to [wjillfully aid[] or assist!] in, or procure!], counsel!], or advise!] the preparation or presentation under, or in connection with any matter arising under, the internal revenue laws, of a return, affidavit, claim, or other document, which is fraudulent or is false as to any material matter, whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return, affidavit, claim, or document!.]

14

. Stadtmauer led these meetings until early 1999, when another KC executive began running them. (App.2701.)

15

. Similar to the "Richard Specials,” SSMB often prepared special supplemental schedules, listing various non-property expenses and capital improvements, that were attached to the partnerships' financial statements. These supplemental schedules were called "Schedules of Non-Recurring Expenses,” but were unofficially referred to as "Schonbraun Specials.” However, as Bentzlin explained at trial, these "non-recurring” expenses were essentially "non-recurring every year,” and he feared that KC was "giving the Government a road map" on how to discover, in the event of an audit, expenses that were being improperly deducted on the tax returns. (App.3255.) After Bekritsky raised his concerns to Plotkin, SSMB ended the practice. *(Id.)*

16

. Though Greenberg also requested the partnerships’ general ledgers, he never received any. *(Id.*at 3358.)

17

. We note that Stadtmauer chose not to put on a defense.

18

. The jury acquitted Stadtmauer of six counts of aiding in the willful filing of false or fraudulent tax returns (Counts Six through Eleven), which corresponded to the 1999— 2000 tax returns for three of the Quail Ridge partnerships. As the Government notes, a question asked by the jury during its deliberations suggests that it acquitted Stadtmauer on these counts because it was unable to locate a piece of evidence explaining how expenses from Quail Ridge's unitary general ledger were apportioned among the three specific Quail Ridge partnerships *(i.e.,*“8 Quail Ridge,” "9 Quail Ridge,” and “10 Quail Ridge”).

19

.Stadtmauer moved before trial to dismiss the indictment to the extent it was based on the failure to capitalize expenditures, arguing that the law on capitalization is vague and uncertain. The District Court deferred ruling on the motion, concluding that "[a] determination of whether the tax laws in question are vague and uncertain necessarily involves a fact sensitive analysis.” *(Id.*at 86.) The Court denied the motion after trial, and Stadtmauer does not challenge that ruling on appeal.

20

. Stadtmauer contends that the Government sought a willful blindness instruction solely (and improperly) as a "preemptive measure.” (Appellant's Br. at 76.) He notes that when then the Government requested the instruction, it stated: "[w]e believe [Stadtmauer] has actual knowledge, but we would like to preserve the right to argue willful blindness depending on what we hear from the other side” in closing arguments. (App.3906.)

We disagree with this contention. As our precedent makes clear, there is nothing improper with the Government seeking a willful blindness instruction while also contending that there is sufficient evidence of actual knowledge. *See, e.g., Wert-Ruiz,*228 F.3d at 255 ("[I]t is not inconsistent for a court to give a charge on both willful blindness and actual knowledge, for if the jury does not find the existence of actual knowledge, it might still find willful blindness.”). Moreover, though Stadtmauer argued in his summation that the number of tax returns he signed at a time, coupled with the brief amount of time he spent reviewing each, proved that he lacked actual knowledge of their contents (App.4082, 4135), the Government did not make arguments based on a willful blindness theory in its summation.

21

. The Fifth and Seventh Circuit Courts have also approved of a willful blindness instruction that applies to a defendant's knowledge of the law, though those Courts did not specifically discuss *Cheek. See United States v. Hauert,*40 F.3d 197, 203 n. 7 (7th Cir.1994) (affirming conviction for tax evasion where the facts "supported] the inference that the defendant was aware of a high probability of the existence of the fact in question [tax liability] and purposefully contrived to avoid learning all of the facts” (internal quotation marks and citation omitted; second alteration in original)); *United States v. Wisenbaker,*14 F.3d 1022, 1027-28 (5th Cir.1994) (willful blindness instruction was appropriate in tax evasion case in light of the defense theory, i.e., that the defendant "belie[ved] that he was not responsible for ... taxes,” and evidence that he failed to file tax returns even after his accountants "brought to his attention his duty to do so”).

22

. Stadtmauer suggests that permitting willful blindness to satisfy the element of legal knowledge will "surely alarm the many thousands of taxpayers who provide records to their accountants, let the accountants prepare the returns, and then sign them ... without flyspecking the tax professionals' work.” (Appellant's Reply Br. at 39 n. 23.) We cannot agree. Such a taxpayer cannot be said (without more) to be " 'subjectively aware of [a] high probability' " that the returns being prepared on his behalf are false or fraudulent. *Wert-Ruiz,*228 F.3d at 255 (quoting *Caminos,*770 F.2d at 365). Rather, to prove willfulness beyond a reasonable doubt, the Government would have to negate the taxpayer's claim that he relied in good faith on the advice of his accountant. *Cf. Cheek,*498 U.S. at 202, 111 S.Ct. 604; *Anthony,*545 F.3d at 65 n. 6; *see also United States v. Moran,*493 F.3d 1002, 1013 (9th Cir.2007) (noting that "[t]he burden is on the government to negate the defendant's claim that he had a good faith belief that he was not violating the tax law,” and "[g]ood faith reliance on a qualified accountant has long been a defense to willfulness in cases of tax fraud” (internal quotation marks and citation omitted)).

23

. In *Pierre,*our Court rejected the petitioner’s argument that he could show that he was more likely than not to be tortured if removed to Haiti through evidence that pain and suffering would be the "practically certain result” of his confinement by Haitian authorities upon returning. *Id.*at 189. In so holding, we rejected a *dictum*in an earlier precedent suggesting that "specific intent could be proven through 'evidence of willful blindness.' " *Id.*at 188, 190 (quoting *Lavira*v. *Att’y Gen.,*478 F.3d 158, 171 (3d Cir. 2007)).

24

. The Government suggests that we should review this claim for plain error, as Stadtmauer did not raise a challenge specific to the inclusion of the words "and willfully” in the Government's proposed instruction. (Appellee's Br. at 82 & n. 28.) We need not decide this issue because, as explained below, we would affirm regardless of the standard of review.

25

. In the second instance, not quoted previously, the Court stated: "[A] showing of negligence or of a good-faith mistake of law is *not ...*sufficient to support a finding of willfulness or of knowledge.” *(Id.*at 3974 (emphasis added).) This was, in fact, a correct statement of the law. As discussed, the element of "willfulness" encompasses a legal knowledge component, *see infra*Part III.A.l, which cannot be satisfied by negligence or a good-faith mistake of law, *see infra*Part III.A.2.

26

. Even assuming the trial evidence did not support a finding of willful blindness, we believe that any resulting error was harmless, given that "the instruction itself contained the proper legal standard,” and in light of the "ample evidence” of Stadtmauer’s "actual knowledge” of the falsity of the tax returns. *Leahy,*445 F.3d at 654 n. 15 (collecting cases). *See infra*Part III.B.2.

27

. This potential exculpatory interpretation of Stadtmauer's question is what prompted the Government — "[i]n furtherance of [its] *Brady*obligations” — to disclose Bekritsky’s anticipated testimony to Stadtmauer. *(Id.*at 1049.) Indeed, Stadtmauer contended in his motion *in limine*that the "more plausibl[e]” meaning of his question was that he "relied on Mr. Bekritsky to prepare the tax returns and trusted Mr. Bekritsky to advise him of any concerns.” *(Id.*at 1052.)

28

. Stadtmauer contends that the prosecutor violated the District Court’s order granting Stadtmauer’s motion *in limine*by asking Bekritsky what Stadtmauer meant by his question. The Government maintains that the court reporter mis-transcribed the prosecutor's question, which actually asked, “What did *yon*mean by that?” (Appellee’s Br. at 52 n. 18 (emphasis added).) This dispute is beside the point, as the Court immediately interceded and rephrased the question to make clear that Bekritsky was not to opine on what he thought Stadtmauer meant by the question.

29

. The prosecutor who gave the rebuttal argument on behalf of the Government also referenced Bekritsky’s testimony, and argued that Stadtmauer’s question itself was suggestive of a consciousness of guilt. *See id.*at 4148 ("If he didn’t think there was anything to worry about, why did he ask?”). However, this prosecutor did not quote the portion of Bekritsky’s testimony that Stadtmauer challenges on appeal (i.e., that Stadtmauer "knew” there were "problems” with the returns).

30

. We note that the mere fact that Bekritsky’s testimony related to an ultimate issue to be decided by the *jury*— i.e., whether Stadtmauer had knowledge that the tax returns he signed were false or fraudulent as to a material matter — does not alone render Bekritsky’s testimony inadmissible. *See*Fed.R.Evid. 704(a).

31

. We reach this issue only by construing Stadlmauer’s opening brief as liberally as possible. Though he analogizes Bekritsky's testimony to the testimony we ruled impermissible in *Anderskow*in his opening brief, his argument appears to be limited to the first requirement of Rule 701 (a prong we held was satisfied in Anderskow). (Appellant's Br. at 49.) Stadtmauer first makes an argument specific to the helpfulness prong in his Reply Brief. But "an issue is waived unless a party raises it in its opening brief, and for those purposes a passing reference to an issue will not suffice...." *Skretvedt v. E.I. DuPont De Nemours,*372 F.3d 193, 202-03 (3d Cir.2004) (internal quotation marks and citation omitted).

Moreover, plain error review is arguably appropriate in these circumstances. Though Stadtmauer claimed in his motion *in limine*that allowing Bekritsky to testify as to what *Stadtmauer*meant by his question would violate Rule 701’s helpfulness prong, he raised different arguments in support of his motion to strike Bekritsky's testimony as to what *he*meant by his answer to Stadtmauer’s question *{e.g.,*that the statement was unfairly prejudicial). *See*Fed.R.Evid. 103(a)(1) (an objection to the admission of evidence must "stat[e] the specific ground of objection”); *see also United Stales v. Gomez-Norena,*908 F.2d 497, 500 (9th Cir.1990) ("[A] party fails to preserve an evidentiary issue for appeal not only by failing to make a specific objection, but also by making the *wrong*specific objection." (internal citations omitted) (emphasis in original)).

However, the Government does not argue waiver or forfeiture, and, as we explain below, we would affirm in any event because any error in admitting Bekritsky’s testimony was harmless.

32

. We are not asked to determine whether the District Court was correct in barring Bekritsky from testifying as to what he believed *Stadtmauer*intended to convey by his questions. We note, however, that other courts have upheld the admission of testimony by a participant in a conversation as to what another participant intended to convey. *See, e.g., United States v. Kozinski,*16 F.3d 795, 809 (7th Cir. 1994) (witness was permitted under Rule 701 to testify "about the context and meaning of conversations to which he was a party,” including his "understanding of the thoughts that were being communicated to him”). As Professors Mueller and Kirkpatrick explain:

> [F]irsthand observers often understand the mental state of another in ways not captured in literal meanings of words spoken by the other, nor readily conveyed in close analytical accounts of what exactly transpired. The old adage that "you had to be there” makes this point, and witnesses asked to give "factual” accounts of what another said or did may be confounded by their knowledge that doing so would be misleading, and that the surface of the words carries little of their real meaning. In everyday life, personal interaction is nuanced and nonliteral, ... and knowledgeable witnesses can easily satisfy the rational basis and helpfulness criteria [of Rule 701] in providing interpretive opinions on the mental states of others.

Mueller & Kirkpatrick, *Federal Evidence*§ 7:5, at 775.

33

. We note that even if testimony similar to Bekritsky's could satisfy the requirements of Rule 701, it may be inadmissible on other grounds, *e.g.,*because its probative value (and helpfulness) are substantially outweighed by the potential for unfair prejudice. Fed. *266R.Evid. 403; *see also Rea,*958 F.2d at 1216. Because Stadtmauer does not raise such, an argument on appeal, we express no opinion on whether Bekritsky's testimony should have been struck under Rule 403 (assuming it satisfied the Rule 701 requirements).

34

. This conclusion is bolstered when Bekritsky’s statement is viewed in light of the even more damaging testimony that defense counsel elicited during cross-examination of Bentzlin — who testified before Bekritsky — regarding why Bentzlin similarly told Stadtmauer to "just sign" the returns:

> Q: Isn’t it a fact that you didn't tell [Stadtmauer] ... that the returns were in any way incorrect?

> A. I didn't need to tell Mr. Stadtmauer, *because he was fully aware*between the Richard Specials and the Tuesday signing, and the [practice of "losing” bills] and the Thursday presentations and signing the checks for all the entities, *he was fully aware of the type of information that was in there,*so I didn’t see that there was any need to tell [him]. He was a very accomplished financial leader. He was familiar with the tax returns. *So, no, I didn’t feel the need to tell him, just sign it or not.*

> I kn[ew] the nature of the stuff that was in the tax returns. If you have repair and maintenance items processed on a regular basis through various entities all over the place, ... logic would dictate that that stuff is reflected somewhere in the tax return.

(Id. at 2478-79 (emphases added).)

35

. Federal Rule of Evidence 613 permits a party to examine "a witness concerning a prior statement *made by the witness,*whether written or oral,” Fed.R.Evid. 613(a) (emphasis added), and permits a party to introduce *268"extrinsic evidence” of a witness's prior inconsistent statement as long as "the witness is afforded an opportunity to explain or deny” it, *id.*613(b). Several of our sister circuit courts have affirmed the exclusion, under Rule 613, of interview memoranda prepared by law enforcement that the witness had not adopted. *See, e.g., United States v. Adames,*56 F.3d 737, 744-45 (7th Cir.1995); *United States v. Saget,*991 F.2d 702, 710 (11th Cir. 1993); *United States v. Almonte,*956 F.2d 27, 29 (2d Cir. 1992).

36

. To take one example, Stadtmauer contends that Grant erroneously testified that "only 50% of entertainment expenses may ever be deducted” by a business, *id.*at 53, despite the fact that entertainment expenses may be deducted in full when, among other things, they are made for "recreational, social, or similar activity ... primarily for the benefit of [the taxpayer's] employees generally.” 26 C.F.R. § 1.274-2(f)(2)(v). Contrary to Stadtmauer's characterization, Grant never testified that there is a *per se*rule that such expenses are only deductible up to 50%. Rather, in the portion of her testimony that Stadtmauer cites, Grant simply: (1) identified the line on the tax return where "travel and entertainment” expenses must be recorded (Line 4B); and (2) testified that this line was "for the 50 percent of travel and entertainment [expenses] that [are] ... not deductible by the partnership.” (App.3411.) Moreover, Grant agreed during cross-examination that the 50% rule "has exceptions,” *id.*at 3548-49; *see also id.*at 3422, and the District Court specifically instructed the jury as to four types of exceptions to the general rule, *id.*at 3969.

37

. Indeed, over *the*Government’s objections, the District Court allowed defense counsel to cross-examine Grant regarding her knowledge of specific provisions of the Tax Code, the IRS’s field manual, and federal court and Tax Court decisions. This went far beyond what other courts have permitted. *Cf. Mikutowicz,*365 F.3d at 72 (holding that trial court did not violate defendant's confrontation rights by refusing to allow defense counsel to question the Government’s tax expert, an IRS agent, "about various judicial opinions, which [the defendant] claim[ed] would have established that the deductions were properly taken”).

38

. Stadtmauer also challenges the District Court's decision to allow the Government to admit summary charts prepared by Grant, arguing that they impermissibly summarized her *“pre*trial conclusions.” (Appellant’s Br. at 56 (emphasis in original).) This argument fails outright. Agent Grant-who also served as a summary witness (based on her participation in the Government's investigation of KC’s partnerships)-testified that she reached her conclusions (reflected in her summary charts) based on the voluminous documentary evidence the Government introduced during trial. *Cf. United States v. West,*58 F.3d 133, 140 (5th Cir.1995) (district court did not abuse its discretion in permitting IRS agent to testify as an expert summary witness where her "specialized training and experience ... made her adequately suited to assist the jury in understanding *the*large amount of documentary evidence presented by the [Government and the tax implications”).

39

.The general rule is that a taxpayer may not deduct expenses incurred on behalf of another taxpayer's business. *See, e.g., Deputy v. du Pont,*308 U.S. 488, 494, 60 S.Ct. 363, 84 L.Ed. 416 (1940). An exception to this rule is *272where a taxpayer’s payment of the business expenses of another serves to "protect or promote” his own business. *See, e.g., Lohrke v. Comm'r,*48 T.C. 679, 684-85 (1967). Through the “branding” theory, Stadtmauer sought to argue that the "non-property” expenses deducted by the partnerships qualified under this exception.

40

. The Government contends that the District Court actually excluded all of the documents defense counsel sought to introduce during cross-examination because Stadtmauer had failed to comply with the Court's pre-trial order requiring the reciprocal exchange of trial exhibits. (Appellee’s Br. at 29-30.) We see little in the record to support that blanket assertion. Though the Court sometimes noted in ruling on Stadtmauer’s requests to introduce exhibits during cross-examination that it "could” bar their admission because they had not been produced to the Government before trial, *e.g.,*App. 2353-54, the record reveals that the Court's rulings were ultimately not based on any violation of its pretrial discovery order.

41

. Moreover, these advertisements were only tangentially relevant to the broader theory that defense counsel sought to establish: that non-property expenses and charitable contributions were properly paid by various partnerships because they collectively benefitted from using the KC '‘brand.” Even if Stadtmauer were permitted to introduce these exhibits, we fail to see how they would have meaningfully rebutted the testimony of Bentzlin, Lefkowitz, and Zecher that they never discussed the concept of "branding” as a justification for certain partnerships paying the expenses of other partnerships. *(Id.*at 2224, 2608, 2841.)

42

. For these reasons, we also reject Stadtmauer's claim that the District Court’s exclusion of these exhibits violated his Sixth Amendment right of confrontation. *See Delaware v. Van Arsdall,*475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (though the Sixth Amendment "guarantees an *opportunity*for effective cross-examination,” it does not guarantee "cross-examination that is effective in whatever way, and to whatever extent, the defense might wish” (internal quotation marks and citation omitted) (emphasis in original)).