
514 F.3d 145 (2008)
UNITED STATES, Appellee,
v.
Richard HATCH, Defendant, Appellant.
No. 06-1902.
United States Court of Appeals, First Circuit.
Heard March 8, 2007.
Decided February 1, 2008.
*146 Michael Louis Minns with whom Enid M. Williams and the Law Office of Michael Louis Minns P.L.C. was on brief for appellant.
Donald C. Lockhart, Assistant United States Attorney, with whom Robert Clark Corrente, United States Attorney, Andrew J. Reich and Lee H. Vilker, Assistant United States Attorneys, were on brief for appellant.
Before Boudin, Chief Judge, Campbell, Senior Circuit Judge, Howard, Circuit Judge.
CAMPBELL, Senior Circuit Judge.
Appellant-defendant Richard Hatch, the first winner of the CBS reality tv show "Survivor," appeals from his convictions and sentence on three counts of filing false tax returns, in violation of 26 U.S.C. §§ 7201 and 7206(1), after a jury trial in the United States District Court for the District of Rhode Island.
Hatch makes four arguments on appeal: (1) that the district court violated his Sixth Amendment rights by curtailing Hatch's explanation of why he believed the show's *147 producers had paid the taxes on his "Survivor" winnings; (2) that, in a variety of ways, the court improperly limited the defense's right to cross-examine; (3) that the court wrongly allowed the government to use what Hatch calls "unqualified experts" while excluding some of the testimony of Hatch's own expert; and (4) that his sentence was unreasonably harsh. After reviewing the record and the arguments, we affirm the convictions on all three counts and the sentence.

Background
On September 8, 2005, Hatch was indicted for related tax and fraud crimes.
Count 1 alleged that Hatch had filed a tax return for the year 2000 in which he falsely stated that he had negative income and was owed a $4,483 refund, and that he willfully failed to declare three sources of income: (a) the over one million dollars he won on "Survivor;" (b) $18,708 in rental income from property he owned in Newport, Rhode Island; and (c) $25,000 in charitable donations diverted to his own use.
Count 2 alleged that Hatch had filed a tax return for 2001 which falsely stated that his income was $228,077 and that he was owed a $43,296 refund, and that he willfully failed to declare four sources of income: (a) about $320,000 he received as co-host of a radio show;. (b) $9,396 in rent from the Newport property; (c) $27,074, the value of a car he won as part of his "Survivor" prize; awl (d) $11,500 in charitable donations which he diverted to his own use.
Count 3 alleged that Hatch had filed a tax return for 2001 for an S-corporation[1] called Tri-Whale Enterprises, created to receive his radio show income, and that he falsely stated that Tri-Whale's annual income was $68,173, omitting the $320,000 mentioned in Count 2, above.
Counts 4-9 alleged that Hatch had defrauded four companies which contributed $36,500 in charitable donations, in violation of the mail and wire fraud statutes. Count 10 alleged that Hatch defrauded the People's Credit Union when he altered a $25,000 donation check so that he would appear to be a payee, as opposed to the designated charity, Horizon Bound, to whom the check was originally made out, and then deposited it in his account there.
Following a nine-day trial, the jury convicted Hatch on the three tax counts but acquitted him of the remaining charges. On May 16, 2006, the district court sentenced him to 51 months in prison, at the high end of the sentencing guideline range.

Facts
I. The 2000 Tax Returns (Count One)
For seven weeks in 2000, Hatch competed with sixteen other contestants on "Survivor," a reality television show filmed on the island of Pulau Tiga. As the "survivor" of the competition, Hatch won a prize of one million dollars and a car. He additionally received $10,000 for appearing on the August 23, 2000 televised finale of the show. "Survivor Entertainment Group" ("SEG"), which produced the show, cut two checks to Hatch in these amounts. Hatch deposited the one-million-dollar check in his bank account. He endorsed the $10,000 check over to a construction company at work renovating his residence in Middletown, Rhode Island.
*148 Prior to the show, Hatch had signed a contract stating he was not an employee or agent of SEG and that he would be responsible for all taxes associated with any winnings: "I shall pay all state and federal or other taxes on any prizes I win." After Hatch received his prize, in early 2001, SEG sent Hatch an IRS 1099 form reporting his receipt of $1,010,000 in income from SEG in 2000.
Following his win, Hatch appeared December 7, 2000 on the pilot episode of a show called "For Goodness Sake!," which focused on the charitable causes of celebrities. The show's producer, Chamber's Communication Corporation, paid Hatch's travel expenses and made a $25,000 donation to "Horizon Bound," a charity Hatch had founded. Horizon Bound's ostensible object was to take disadvantaged teens on camping trips to build their self-esteem.
Hatch attempted to deposit the $25,000 Horizon Bound check in his personal account at Newport Federal Savings Bank, but as the check was payable to a corporation, the bank refused the deposit. Hatch then deposited the check in his personal account at another bank, People's Credit Union. The payee of the deposited check was "Horizon Bound/Richard Hatch," and there was conflicting testimony from Hatch and bank employees about alteration of the payee of the check.[2] Hatch subsequently used the money for gifts and the renovation of his home in Middletown, none of it going to Horizon Bound. Hatch's accountant, Daniel J. Urso, called as a defense witness, testified that Hatch's personal use of the funds was justified because Hatch had given other funds to the charity.
Hatch also in 2000 received $18,708 in rent from the tenants on a property he owned in Newport. He often collected the rent himself.
In March 2001, Hatch hired accountant Richard Plotkin to prepare his 2000 tax return. Hatch gave Plotkin the 1099 received from SEG showing his $1,010,000 in "Survivor" income, along with 1099s showing income from other sources, including a book deal and deals with Conde Nast and Reebok. Hatch gave Plotkin a copy of his own accounting of his income (which distinguished 1099 contractor income from W-2 employee income), in which he noted the "Survivor" income but did not list the $25,000 charity income and the $18,708 rental income. Hatch wrote on the accounting sheet that his "Total Income" was "$1,166,626.10." In a second written summary, Hatch referred to the rental property but claimed, wrongly, that it had generated "no rental income" in 2000 because it was "in renovation." Hatch later said he had received sixty days of rent in the sum of $4,000, and Plotkin's assistant accordingly crossed out "no rental income" and wrote "$4,000" underneath it, but this was also a misrepresentation because he had received seven months of rent for a total of $18,708. Plotkin emphasized to Hatch that the "Survivor" income had to be reported to the IRS, and Hatch did not disagree.
In November 2001, Plotkin showed Hatch the 2000 tax return Plotkin had prepared, which included the "Survivor" income but not the $25,000 charity income or the $18,708 rental income, of which Hatch had not informed him. Plotkin's draft 2000 tax return stated that Hatch owed $374,831 in taxes and $66,670 in interest and penalties for late filing. Hatch did not tell Plotkin that he disputed the inclusion of the "Survivor" income in the *149 return. Hatch and Plotkin discussed various IRS payment options, and then Plotkin and Hatch signed the return. Plotkin offered to file the return, but Hatch said he would do it himself. Hatch never filed the return. Instead, in late 2001, Hatch hired a self-employed accountant and family friend, Jodi Rodrigues Wallis ("Wallis"), to prepare a new 2000 tax return. Hatch provided Wallis with a return for the year 1999 prepared by Plotkin, but not the return for 2000 Plotkin had prepared. When Wallis mentioned she wanted to contact Plotkin, Hatch indicated he preferred that she not be in contact with him because Hatch did not want any more to do with Plotkin's firm.
There was conflicting testimony by the two accountants about whether they ever discussed Hatch with one another. Hatch did not give Wallis the 1099s reflecting his non-"Survivor"-related income for 2000 even though he had given those forms to Plotkin. Hatch told Wallis he had been so busy with "Survivor" he had not had time to earn other income that year. As he had once told Plotkin, Hatch again claimed his rental property had earned no income because it was under renovation. Hatch denied receiving any royalties from a book deal, although Wallis knew Hatch had written, a book. Hatch told Wallis he had disclosed all his sources of income for 2000.
Hatch gave Wallis the 1099 furnished by SEG reflecting his "Survivor" income, as well as the original handwritten accounting sheet he had given Plotkin which stated there was no rental income. He did not give Wallis the other handwritten summary of his 1099 and W-2 income. Hatch also advised Wallis, incorrectly, that in connection with his receipt of the "Survivor" prize, he had paid twenty percent in commissions to an agent and a manager; that CBS had required him to retain an agent and manager in advance in order to claim the prize; and that the SEG contract had not contained any language warning him he would be responsible for paying taxes. Notwithstanding, Wallis told Hatch he was still required to pay taxes on the "Survivor" income, although he could deduct the purported commissions.
On March 1, 2002, Wallis handed to Hatch a 2000 tax return she had prepared reflecting the "Survivor" winnings less deductions for the claimed $200,000 in commissions but omitting the $25,000 "charity income," the $18,708 rental income, and the other 1099 income Hatch had divulged to Plotkin but not to Wallis. The return stated that Hatch owed $234,807 in taxes. Hatch left Wallis' house with the return in hand but he never filed it with the IRS.
In July 2002, the IRS sent Hatch a letter telling him it had not received his 2000 tax return. The' IRS listed in that letter the 1099 income it knew. The IRS's letter did not include mention of the "Survivor" income but stated that its list might not be comprehensive. Hatch gave the IRS's notice to Wallis. Wallis advised Hatch he would need to file an amended tax return which included the 1099 income reflected on the IRS notice of which Hatch had not previously informed her. She told him that he was still required to pay taxes on the "Survivor" income even though the IRS's notice had not mentioned that income. Hatch did not follow this advice.
In the fall of 2002, Hatch asked Wallis what his 2000 tax exposure would be if the "Survivor" income were wholly excluded from the tax assessment. Wallis offered to prepare a spreadsheet with that analysis, but Hatch wanted the information to be provided in the form of a completed tax return. Wallis accordingly prepared a hypothetical 2000 tax return which omitted the "Survivor" income and state that Hatch's income was negative $41,087 and that he was owed a $4,483 refund.
*150 On November 19, 2002, Wallis gave Hatch the hypothetical 2000 return she had prepared that omitted reporting the "Survivor" winnings. This document did not bear Wallis' name and signature as preparer. Hatch, orally and in a letter he signed in Wallis' presence, agreed the return was for informational purposes only and that he would not file it with the IRS. Wallis told Hatch she would lose her license if he filed the return. Hatch said he understood. Later that very same day, however, Hatch signed and mailed the return to the IRS.
The draft return Hatch filed omitted three main sources of income discussed earlier: the "Survivor" income; the "charity" money Hatch had converted to personal income; and the rental income. As a result of these omissions on the filed return, Hatch received a $4,483 refund rather than paying any taxes. If Hatch had filed a return properly reflecting the income he received in the year 2000, including the "Survivor" and other income, he would have had to pay $375,652 in taxes.
II. The 2001 Tax Returns (Counts 2 and 3)
Between January and December 2001, Hatch served as a co-host on the morning show of Boston radio station WQSX-FM. In return, the station's operator, Entercom Boston LLC, paid Hatch $70,232 for his appearances from January-March and $321,139 for his appearances from April to December. The $70,232 was paid as W-2 income because Hatch was then an employee of the station. At Hatch's request, Entercom paid the $321,139 to Tri-Whale Enterprises, the S-Corporation founded by Hatch. As noted, Hatch was the sole shareholder of Tri-Whale, and he was required to list any Tri-Whale income on his individual tax return. Hatch deposited the Entercom checks payable to Tri-Whale in a Tri-Whale bank account (labeled "Richard Hatch d/b/a Tri-Whale") at the Newport Federal. Savings Bank. Hatch then transferred most of the funds to his personal account at the same bank. In February 2001, Hatch claimed the final part of his "Survivor" prize: a car valued at $27,074. General Motors sent Hatch a 1099 form reflecting his receipt of $27,074 in income.
On April 14, 2001, Hatch appeared as a contestant on "The Weakest Link," an NBC game show. The show's producers paid Hatch a small fee and made a $10,000 donation to Horizon Bound. Before the $10,000 check was issued to Horizon Bound, Hatch faxed an NBC representative two documents demonstrating Horizon Bound's tax exempt status, both of which bore the forged signature of Ralph Magee, a friend of Hatch who was unaware that Hatch was holding him out as the treasurer of Horizon Bound. Hatch responds on appeal that Hatch and Magee were domestic partners and that "it is a fact of life that spouses and domestic partners sign for each other and Magee had no issue with Hatch using his signature." He further notes that he was acquitted of the charity fraud charges. When Hatch received the $10,000 check payable to Horizon Bound, he deposited it in the Horizon Bound account at Newport Federal Savings Bank. A month later, however, he wrote a $10,000 check on that account to a construction company that was renovating his Middletown home.
On April 17, 2001, Hatch spoke at East Boston Savings Bank about his time on "Survivor" and Horizon. Bound. The bank then wrote Horizon Bound a check for $1,000, which Hatch deposited in the Horizon Bound account. CAM Media and Graphics, which had arranged for Hatch to make his presentation, also wrote a $500 check to Horizon Bound. Hatch deposited *151 this check in his personal account at People's Credit Union. Also in 2001, Hatch received $9,047 in rental income from the Newport property.
As she prepared Hatch's 2001 individual tax return and the 2001 S-corporation tax return for Tri-Whale, Wallis made clear to Hatch he was individually liable for any income of Tri-Whale and that such income also needed to be reported on the S-corporation return. Hatch told Wallis about the January-March wage income from Entercom of $70,232, which Wallis included on his individual return, but he failed to disclose the April-December payments of $321,139 Entercom had made to Tri-Whalethe largest source of income Hatch had received that year. Hatch responds that he never received a 1099 or W-2 showing the Entercom income and states, without record citation, that "Wallis was aware that the income from Entercom, like all other income, went into Hatch's personal account" and thus that she could have discovered the $321,139 by examining the records of Hatch's personal checking account. Hatch's assertion ignores the fact that Wallis testified that Hatch gave her check stubs for which Tri-Whale was the payee, that those stubs did not include anything from Entercom, and that Hatch told her there were no other sources of income for Tri-Whale for that year. When Wallis asked Hatch whether he had opened a bank account for Tri-Whale, suggesting she might want to look at the bank statements, Hatch told her incorrectly that he had not done so.[3] Hatch also failed to tell Wallis about the income from the car, the rental property, and the diverted donations. When Wallis inquired about the car (which she knew Hatch had won), Hatch lied and said he had not yet received it. As he had done the year before, Hatch told Wallis that the rental property had earned no income because it was still being renovated.
Based on what Hatch had told her, Wallis prepared a 2001 individual tax return for Hatch which omitted those four sources of income (the second portion of the Entercom payment, the car, the rental property, and the diverted, donations, totaling $374,510) and which incorrectly stated that his income was $228,077 and that he was owed a substantial refund. Wallis also prepared a 2001 S-Corporation tax return for Tri-Whale which did not include the $321,139 in Entercom payments and which accordingly wrongly stated, based on check stubs provided to Wallis by Hatch, that Tri-Whale had received only $68,173 in income. Hatch filed the Tri-Whale return on October 1, 2002 and the individual return on October 9, 2002. As a result, Hatch paid no taxes and received a $44,874 refund. If Hatch had filed returns disclosing his true income, he would have paid $99,319 in taxes.
For his defense at trial, Hatch called the contractor who renovated his Middletown residence, in an apparent effort to show that the project had something to do with Horizon Bound, though the witness did not recall for certain whether Hatch had actually spoken to him about the charity. Hatch then called his manager to suggest that at the time he filed the returns at issue in the case, he was distraught over *152 an allegation that he had abused his adopted son. The manager, however, testified the child abuse charge had been dismissed in the summer of 2000, more than two years before the relevant tax filings. He also testified that commissions paid him by Hatch had post-dated the "Survivor" prize and had nothing to do with it. The attorney Hatch hired in connection with the child abuse charge confirmed that the charge had been dismissed in 2000 but noted that Hatch had filed two related civil lawsuits that lasted into the period when he filed the tax returns.
A high school teacher testified that he had run a real camping program called Horizon Bound in the 1970s and 80s, that Hatch had been a camper in the summer of 1979, and that he had given Hatch permission to incorporate a new entity under the name after Hatch won "Survivor." He testified, however, that he was unaware Hatch was holding him out as secretary of the new Horizon Bound.
Hatch testified on his own behalf. He said that Wallis knew he was going to file the hypothetical tax return which omitted the "Survivor" income and that she had him sign the letter acknowledging the draft nature of the return so that she could distance herself from what he was doing. He conceded that the commissions he had paid to his manager, agent and attorney had nothing to do with the "Survivor" prize and claimed that the "mistakes" on his tax returns were made in good faith and that he intended to file amended returns correcting those mistakes.
On cross-examination, Hatch admitted that he had received many 1099s over the years and had reported the income stated on those forms and that he received 1099s reflecting the "Survivor" prize and car. He acknowledged that three months after the show ended, he authored a book in which he stated he would have to pay taxes on the prize and he had initially set aside $350,000 with the expectation of using some of it to pay taxes. He further admitted that Plotkin had told him that it was clear he had to pay taxes on the prize, that he had failed to report the $320,000 in Tri-Whale income, and that he deposited the $25,000 donation in his personal account and used the money for personal expenses because he felt Horizon Bound owed him money. He testified he used the other $11,500 in donations in a similar way for similar reasons.
Lastly, Hatch called accountant Urso to attempt to show that there were certain defects in the tax returns prepared by Plotkin and Wallis regarding issues unrelated to the trial. The court found this testimony largely irrelevant. The government then called two witnesses to rebut Hatch's testimony that someone at People's Credit Union added his name as a payee to the $25,000 donation check.

Discussion
III. Limitations Placed Upon Hatch's Testimony About Irregularities in Way "Survivor" Contest Was Run and Producers' Supposed Promise to Pay His Taxes
Hatch argues that the district court violated his Sixth Amendment rights by precluding Hatch's testimony about his alleged discovery during the taping of "Survivor" that the production company, SEG, was "cheating" by giving food to other contestants and otherwise violating its own rules for how the contest would be run. Hatch's discovery of these irregularities, he now says in his appellate briefs and argument, led the show's producer, Mark Burnett, to promise Hatch, in exchange for his silence, that SEG would pay his taxes if he were to win the prize. In his briefs, Hatch states, "the district court refused to *153 allow [his] testimony about the consideration for the deal Burnett proposed, that if Hatch won the show, his taxes would be paid"; the alleged "encounter with the show's producer . . . was excluded from evidence"; the court would not allow him to testify that the "show's producers . . . agreed that if he won, they would pay his taxes"; the court "shut down" his proposed defense based on "Burnett's proposed deal"; the court barred him from describing "the quid pro quo arrangement offered by Burnett when Hatch caught the show's producers cheating"; the court "decided the jury would not hear about the agreement with Burnett"; and the court precluded him from testifying that "Burnett told him. CBS/SEG would pay his taxes if he did not blow the whistle on the network."
The government responds that, far from preventing Hatch from testifying to an agreement with Burnett for SEG to pay his taxes, the court several times encouraged Hatch to present, and said that it would allow, evidence that the "Survivor" producers promised to pay his taxes, yet neither Hatch nor anyone else ever testified to such a promise, nor was such testimony proffered. Without evidence of a promise to pay the taxes, the government says, the other evidence concerning irregularities in the way the shown was run was immaterial. We agree and find no error in the district court's rulings on the permissible scope of Hatch's testimony. We review rulings excluding evidence for an abuse of discretion. United States v. Maldonado-Garcia, 446 F.3d 227, 231-32 (1st Cir.2006).
a. Background
As necessary background to the disputed rulings, we first describe the relevant testimony and rulings at the trial, noting first that the man who Hatch asserts on appeal to have brokered a purported deal to pay Hatch's taxes, Burnett, testified as the government's first witness. Burnett said nothing during his testimony about a deal to pay Hatch's taxes, and defense counsel never asked him on cross-examination whether he or others at SEG had promised that SEG would pay Hatch's taxesnor did the defense later call Burnett as its own witness and seek to elicit such testimony.
The court's complained-of limitations upon Hatch's testimony to the show's sponsors' misdeeds and Burnett's purported promise to pay the taxes on Hatch's winnings, arose during the defense's case. During the direct examination of defense witness Alan David, a former agent of Hatch's, defense counsel suggested that SEG had portrayed. Hatch in a negative light in the way it edited footage from the show. When Hatch was called, his counsel continued along the same path, trying to portray aspects of the "reality" show as having been improperly "staged" by SEG, including Hatch's encounter with a shark while he was fishing for food. After sustaining an objection from the government, the court told defense counsel that the inquiry about the shark encounter did not seem "relevant to any issues in the case." When defense counsel argued it was relevant, the court called a sidebar and asked for an explanation. Defense counsel responded, "It shows there's staging. He caught the shark, they made him release it and catch it again, and that time it bit him." The court asked again how the information was relevant to the case at hand. Defense counsel replied, "Because a great deal of this has been staged to make him appear to be evil and that sort of thing." The court responded that, "The issue in this case isn't what his behavior was on the Survivor, we went through that during voir dire, that was the time to inquire, and I did inquire about whether *154 any jurors who viewed the Survivor show formed any opinions of Mr. Hatch. So let's move on to the issues in this case, which are the tax evasion charges and the fraud charges."
Defense counsel responded that his next planned area of questioning was that "part of the reason that there was miscommunication on the million dollars was that there were problems with the show, things that people were not doing, and that led them to ask questions about the way this was going to be done." The court replied, "I don't think the manner in which the show was filmed has anything to do with that, so let's move on." Counsel then clarified that he wanted to show that the contest rules had been changed midstream and "that's part of the thing with the 1099s, the rules were changed." When the court asked whether counsel was referring to the rules regarding how Hatch would be paid, counsel stated, "Well, it's a continuing course of conduct, the rules are not changed just for the payment. They also were changed during the contest." The court responded that it would rule on objections as made but that counsel needed to "move off of the details or the manner in which the show was filmed."
This warning prompted counsel to ask again whether he could ask Hatch about the "rule change on the show." The court said, "The rules [on] how he would be paid?" Counsel responded, "No, that led right up to that, that led him to believe that the rules were continuing to change that created an ambiguity in how he was going to be paid." The court concluded, "If it has anything to do with the terms of his payment and who was going to pay taxes on the money he won, you can certainly get into it. Let's get back to it" (emphasis supplied).
The court thus opened the door for defense counsel to ask Hatch whether Burnett or someone else at SEG had promised to pay the taxes on the money he won. Hatch's counsel, however, did not follow up with questions of this sort. Instead, counsel questioned Hatch as follows: "Rich, did there come a time when you realized that the production was not going to completely go by the rules as they had been described to you?" When the government objected, the court asked, "The rules of what? . . . [t]he rules as to how the competition was conducted or how Mr. Hatch would be paid if he won anything?" Counsel replied, "Well, first, that, which leads into the second, your Honor." The court said, "Well, let's talk about the second. To the extent you're asking about the first, the objection is sustained." The court added, "You can certainly get, into anything that Mr. Hatch has to say on the rules of how he was to be compensated if he won" (emphasis supplied). The court's statement offered defense counsel yet another chance to elicit from Hatch that the producers had promised SEG would pay his taxes. Counsel thereupon asked Hatch whether he had had discussions with other contestants about their plans to pay taxes on their winnings. Counsel next asked, "The `Survivor' show, was there a time when you met with anybody on the show and had discussions which began to convince you that the show might pay the taxes for you?" Hatch responded,
Yes. Not contestants. I met with the producers when, for all intents and purposes, we probably shouldn't have been meeting with the producers, but the show almost stopped filming as a result of a number of things that took place, and Mark Burnett, who testified here, and the other executive producer, Craig Pelligian, came in and spent a significant amount of time with the final four who were remaining. And I personally had discussions with both and each of them.
*155 At this juncture defense counsel might logically have asked Hatch whether any of these "discussions" had pertained to the payment of taxes, and what Burnett and Pelligian had said on the topic. Instead of doing so, counsel inquired whether he could make an additional proffer. The court heard the proffer at the morning recess. Counsel said during the recess:
For the record, were we permitted to do so, I would elicit testimony that during the show there were rules, but they were constantly being changed, and that one of the rules were [sic] no outside attention, and that people with the program who did not want Richard Hatch to win, began to try to manipulate it for him to lose, and they started smuggling food to some of the competing contestants. This led to an encounter with Mr. Hatch and Mr.I believe the gentleman who was on the stand, Mr. Burnett, I don'tit led to some interviews with different people on the show in which Mr. Hatch was complaining about this. And during those moments, they apologized to him. And from the conversations and gatherings, Mr. Hatch left with the understanding that if he won the show, the studio would pay his taxes. And this was a result of them breaking the law with trying to manipulate the results of the contest.
The district court expressed hesitation about the relevance of the proffer: "Well, you kind of lost me on the connection. I think I indicated that if you had evidence that Mr. Hatch wanted to present evidence that the individuals who were running the show had told him something or led him to believe that they would be paying the taxes on any earnings, you can certainly do that" (emphasis added). The judge thus repeated the court's earlier invitation to Hatch to testify that Burnett or someone at SEG had expressly promised or led him to believe that SEG would pay his taxes on any earnings. But no such testimony of an express promise was thereafter elicited, nor was the proffer enlarged so as to encompass any indication of an express promise having been made. The court was left to believe merely that Hatch wanted to testify at length about rule violations in the show's conduct and apologies, accompanied by some unconnected assertion that Hatch left "with the understanding that if he won the show," the studio would pay his taxes.
In the circumstances, the court understandably observed that the "details of how the show was being staged" were not in themselves relevant to Hatch's state of mind when he filed his tax returns almost two years later, but it once again emphasized that Hatch, if he would, could still provide the necessary connective. "Now, as I say, if there is evidence as to what the persons running the `Survivor' show and responsible for compensating him may have told him about the taxability of his prize money or who would pay the taxes on the prize money, that's a different matter. I thought I made that clear, that you could go into that" (emphasis added). Defense counsel withdrew, stating without elaboration that "if it's not put in context, I do not believe it makes any sense whatsoever." There was no further questioning of Hatch, and no additional proffer, concerning testimony as to statements by Burnett or others that might have caused Hatch to believe SEG had agreed to pay the taxes on his "Survivor" winnings.
b. Hatch's Argument on Appeal
Hatch argues that the limits placed by the district court on discussion of the rules of "Survivor" wrongly impaired his ability to introduce evidence that he had a subjective belief he had no legal duty to pay' his taxes, an argument which would negate the element of willfulness required to *156 prove his guilt. Cheek v. United States, 498 U.S. 192, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991); United States v. Bonneau, 970 F.2d 929, 931-34 (1st Cir.1992). He argues that the district court "repeatedly set up roadblocks, withdrew invitations previously extended, and closed doors." According to the appellant, "The message was clear: Hatch could testify that he believed his taxes would be or had been paid, but he could not testify why."
We find little merit in this contention. Neither defense counsel's proffers nor Hatch's courtroom testimony ever described conversations with SEG's representatives in which they made offers or promises to pay Hatch's taxes if he won the prize. Yet Hatch's argument in his appellate brief is now apparently premised on the assumption that either such a "deal" was shown at trial or had been the subject of an offer of proof declined by the court. According to the brief, if Hatch had been allowed to testify to what happened behind the scenes on the "Survivor" show, "his testimony would have shown the context for testimony that Burnett proposed a quid pro quo deal: if Hatch remained silent about the fact that the show's outcome was being staged, the cheating would stop, and CBS/SEG would pay Hatch's taxes if he won" (Appellant's brief, p. 17). But Hatch, a principal witness to whatever, if anything, took place, never testified at trial to the events and words by Burnett or others that might constitute such a supposed "quid pro quo deal" with the producers of the show, although specifically invited to do so by the court on several occasions. To quote the judge's words on one of these occasions, Hatch could testify "that the individuals who were running the show had told him something or led him to believe that they would be paying the taxes on any earnings." Hatch was thus put on clear notice that testimony to such a "deal" was allowed and was indeed invitedno offer of proof was even needed as a predicate to his so testifying, if he would. But, notwithstanding the invitations, Hatch, for whatever reason, evaded the giving of any direct testimonyand no proffer was madeto the very deal which his counsel, on appeal, now alludes to as if firmly planted in the trial record. And nowhere else in the record, including in Burnett's own testimony, is there evidence of the making of such a deal. As the government points out in its brief, any wound stemming from this fatal gap in the record is entirely "self-inflicted."
The district court was well within its discretion to insist that appellant first supply specific, evidence of what Burnett or others actually said that might have led Hatch to believe that SEG would pay the taxes. Such evidence was plainly a predicate to the materiality of any other evidence that was offered as "context" to the alleged agreement. Hatch's conclusory assertion that he left the show "with the understanding that the taxes would be paid" was not a sufficient substitute for the recounting of what Burnett or the others had actually said to him, if anything, in the nature of a promise to pay his taxes.
The district court enjoys broad discretion to control the ordering of proof. See, e.g., United States v. Holmquist, 36 F.3d 154, 163 (1st Cir.1994). Even Hatch does not now argue that the mere evidence by itself of SEG's alleged improper "staging" of events during the show, and Hatch's annoyance about this, are probative of Hatch's innocent state of mind when he filed his incorrect tax returns. It could be material only if there were also evidence of an express undertaking by SEG to pay Hatch's taxesan agreement Hatch says was forged in light of his threats to reveal SEG's misconduct in its running of the show. But no promises to pay taxes made *157 by Burnett or others were testified to by Hatch, even though the court several times expressly invited testimony as to such promises.
The district court accordingly in no way violated Cheek by rejecting further testimony by Hatch about the producers' alleged mismanagement of the show. The court could properly have determined that to permit Hatch to testify further to the producers' alleged misdeeds, without assurance of evidence of their actual promise to pay the taxes, would, besides being irrelevant, simply confuse the jury and might cause it to make unwarranted assumptions, See Fed.R.Evid. 401-403; Bonneau, 970 F.2d at 932-33 (rejecting claim that Cheek required admission of certain evidence in the absence of a clear proffer, and noting that even where Cheek evidence is concerned "trial judges have ample latitude to weigh the importance of the evidence against the risk of jury confusion"); United States v. Lussier, 929 F.2d 25, 31 (1st Cir.1991) (exhibit properly excluded despite Cheek where they "lacked a foundation of evidence or offer of proof to link them to the willfulness issue" and they "could only have confused the jury").
The defendant suggests that his proffer was clear enough for the court to realize that the evidence of the producers' misconduct would in due course lead to, and be tied into, testimony to a promise to pay Hatch's taxes. We disagree. The court on several occasions gave defense counsel full opportunity to elicit from his client whether or not he was saying the "Survivor" executives had agreed to pay his taxes and, if so, what it was he was told at the time. The failure of Hatch to present any evidence of such conversations when invited by the court strongly suggested that no actual promises were made, and no such "deal" actually existed. It was not the court's right, much less duty, to put words in Hatch's mouth.
The defendant repeatedly now invokes "context" as his argument for saying the court should have allowed Hatch to be examined about the producers', various alleged misdeeds. But without evidence that the producers had agreed to pay Hatch's taxes, the evidence that Hatch had caught those running the show cheating was of no contextual materiality to the revenue violations with which Hatch was charged. The court was well within its discretion to reject, further testimony of Hatch's complaints about "cheating" during the show until the defense furnished evidence of a tax payment promise that made such contextual evidence relevant.[4]
IV. Limits on Cross-Examination
Hatch argues that the district court improperly limited his cross-examination of three witnesseshis former accountants Plotkin and Wallis, and IRS Agent Jason Rameakaand thus violated his right to confrontation under the Sixth Amendment. We review these claims for abuse of discretion, United States v. Charles, 456 F.3d 249, 255 (1st Cir.2006), recognizing that limitations on cross-examination should be scrutinized "with the utmost caution and solicitude for the defendant's Sixth Amendment rights," United States v. Tracey, 675 F.2d 433, 437 (1st Cir.1982) (internal quotation and citation omitted). See United States v. Wilson, 798 F.2d 509, 518 (1st Cir.1986) (defendant is entitled to "broad latitude in questioning government witnesses"). But there is another *158 side to the coin, necessary to prevent trials from becoming mired in confusion and irrelevance. It is well-established that "the license to cross-examine is not absolute," id., and the district court "retains wide latitude to impose reasonable limits on cross-examination in order to avoid confusion of the issues or extended discussion of marginally relevant material." United States v. Gonzalez-Vazquez, 219 F.3d 37, 45 (1st Cir.2000) (internal quotations and citations omitted).
Here, the district court's limitations on cross-examination in this nine-day trial were thoughtful and far from being excessive. Most of the defense's numerous questions asked on cross-examination were uninterrupted. The relatively few exclusions were largely of questions that could reasonably be thought to be repetitive, improper, incoherent, or confusing to the jury, or else dealt with matters of seemingly scant relevance to the charges upon which Hatch was being tried. We address some of Hatch's contentions in greater detail as follows.
a. Wallis and Exhibit Three
Hatch contends that the court unfairly limited his cross-examination of Wallis on Exhibit Three, the unfiled 2000 tax return prepared by Wallis which reported the "Survivor" income but omitted the charity, rental and other sources of income. Instead of that return, Hatch subsequently filed with the IRS a different "hypothetical" tax return Wallis had prepared at his request for informational purposes only that omitted the "Survivor" income (Exhibit One).
In contending improper curtailment of his efforts to cross-examine Wallis regarding Exhibit Three, Hatch refers specifically to only two places in the record. In the first, the court sustained the government's objections when counsel asked how many amended tax returns Wallis had prepared that year and during her entire career. Hatch never, at the time, stated his reasons for the questions, nor did he object to the court's exclusionary ruling. The court's sustaining of the objections was well within its discretion given the questions' doubtful materiality to the criminal tax charges against Hatch.
The court also sustained an objection to a second question regarding the impact of the "alternative minimum tax" on Hatch's claimed deductions for the alleged $200,000 in commissions. Hatch says he pursued the line of questioning on the alternative minimum tax to indicate that he did not stand to gain from fabricating reference to the commissions. The court told Hatch's counsel, "If you want to get into this in your case, if it's relevant, that is only a small part of the question. You are confusing the jury. You're mixing up a lot of things and misleading the jury" (emphasis supplied). The court went on to assure defense counsel that he could pursue the issue of deductions Hatch might but did not take in order to demonstrate the tax loss was minimal, so long as he could show relevance. Hatch's counsel did not object further, nor provide any calculations indicating the possible materiality of the alternative minimum tax. The court did not abuse its discretion in concluding that the applicability of the alternative minimum tax in the context of the claimed deductions on Exhibit Three was more confusing than relevant and, accordingly, in limiting discussion of it at that time.
Hatch also argues, without record citation as to where the offending ruling occurred, that the court prevented him from inquiring into Wallis' "accounting practice." The government comes to his aid by offering the suggestion that defendant perhaps means the point in the trial record where defense counsel asked Wallis, *159 "[w]hy didn't you recommend to [Hatch] that he use your bookkeeping services, or somebody else's?" At this point, the court sua sponte called a sidebar to tell defense counsel that his "questions are seeming to get more and more out into the periphery." Defense counsel never gave a clear explanation of why the bookkeeping questions were relevant, and the court noted that counsel had stated "that there is no dispute that the returns that were filed on his behalf or that he filed were incorrect." The court went on, "What this case is about is whether he acted willfully. And none of these questions seem to bear on that issue at all. So why don't you think about it for a minute and see if we can sharpen up the focus a little bit." We see no error in the court's handling of the matter.
Hatch declares at some length that Wallis' testimony that she encouraged Hatch to file Exhibit Three to avoid further penalties was an admission that she had advised him to file a false tax return. This assertion in no way advances his argument that his cross-examination was limited on Exhibit Three, since he was allowed to develop, and did develop, this line of questioning, bringing the point to the jury's attention without interruption.[5]
*160 b. Wallis and Exhibit One
Hatch includes in his brief a subheading on "Cross-Examination on Exhibit 1," implying he has an argument that cross-examination was restricted regarding the return Wallis prepared, but did not intend Hatch to file. This section of Hatch's brief, however, does not identify any areas in which cross-examination was restricted. No discernible error exists.
c. Wallis and Exhibits Five and Seven
Hatch argues that the court unfairly restricted cross examination of Wallis regarding Exhibit Five, Hatch's 2001 individual return, and Exhibit Seven, Hatch's 2001 S-corporation return for Tri-Whale Enterprises.
Exhibit Seven falsely stated that Tri-Whale Enterprises received only $68,173 in income, omitting $321,139 that Entercom paid to Tri-Whale for Hatch's April-December appearances as a radio host. As the sole shareholder of Tri-Whale, Hatch should also have included the same $321,139 on his personal 2001 tax return, Exhibit Five, but he did not. This omitted income formed part of the basis for Count 2. Wallis had told Hatch he was required to report all Tri-Whale income on both returns, but he concealed the $321,139 from her and even denied he had created a bank account for Tri-Whale. Not only had Hatch opened an account for Tri-Whale, but he had transferred most of the Entercom payments in that account to his personal account.[6]
Wallis, Plotkin, and IRS Agent Rameaka testified that in the case of S-corporations, profits or losses flow through to the shareholders, who bear the tax consequences. Hatch now claims that Wallis' testimony on this point was "absurd" and that he was "not allowed to challenge" it on cross-examination, citing to a transcript page. The only blocked question on this page, however, was: "The S Corporation, it must pay a reasonable salary to its employees, must it not; isn't that legally required?" There is no explanation in Hatch's brief of the relevance of the question, and it did not relate to the tax consequences Hatch now claims he was trying to address. Hatch says his attempt to cross-examine Wallis on the "alternative minimum tax" concerned Exhibits 5 and 7, but in fact it related only to Exhibit Three, discussed supra. Hatch makes no effort to explain in what way any preparer's errors in the corporate tax return were relevant to whether he (1) deliberately concealed the $321,139 from Wallis, and (2) filed the return knowing it was false.
As the court emphasized elsewhere in the trial, unless the claimed imperfections could have had an effect on Hatch's intent, the fact that the returns prepared by Plotkin and Wallis may not have been "letter perfect" or "absolutely correct in every *161 single respect" was irrelevant. When the court made a similar point at a pretrial hearing ("What does whether [the returns] were properly prepared have to do with whether Mr. Hatch knew or didn't know that the return he filed was false and that he did so with an intention to evade substantial amount of tax?"), defense counsel conceded that the question of whether the tax returns were incorrect in other areas "may not go directly to the issue of willfulness in that sense, your Honor."
d. Cross-Examination of Wallis on Incompetence and Bias
Hatch concludes his argument that his counsel's cross-examination of Wallis was unfairly truncated by contending that the district court prevented him from exploring Wallis' alleged incompetence and bias, pointing to the court's sustaining of objections to four questions. We have reviewed the record as relates to each question. None of the court's rulings amounts to an abuse of discretion.
Regarding the first question, Hatch repeats his claim that he tried to ask Wallis about her "accounting expertise," but the cited question was actually "Why didn't you recommend to [Hatch] that he use your bookkeeping services, or somebody else's?" There was little apparent relevance to this question, and the court acted within its discretion in excluding it. We have already addressed Hatch's second question regarding payment of a reasonable salary to S-corporation employees: the question, on its face, lacked materiality. Third, Hatch claims that the court erred in preventing his counsel from asking Wallis about the difference between an employee and an independent contractor. Hatch never explained the point of his question, and, in ruling it irrelevant, the court acted within its discretion, stating it didn't matter whether Hatch was an employee. Finally, contrary to Hatch's interpretation, the court did not preclude his counsel from asking Wallis if she knew why Tri-Whale had received a loan from a "shareholder": rather the judge sustained an objection to this initial question in the series because of counsel's editorial comment. Counsel was thereafter allowed to ask further questions on this topic.[7]
e. Cross-examination of Plotkin
Plotkin was the first of two accountants who told Hatch that he was required to report the $1 million prize. Plotkin prepared a completed tax return for Hatch that reflected that income but omitted other income Hatch had not revealed to him. Hatch chose not to file that return and thereafter sought the services of Wallis. Hatch claims that on cross-examination, "[t]he thoroughness of Plotkin's interview with Hatch, a component of the defense, was cut off," citing Volume 3, page 136 of the trial transcript. That citation reveals one sustained objection to an argumentative and confusing question, "How do you explain that you're sent a client to deal with a million dollars and he set up a charitable foundation and you had no discussions with him on the charitable foundation whatsoever?" That objection aside, Hatch received many other opportunities to cover the thoroughness of Plotkin's work with Hatch, including asking a lengthy series of questions regarding the small amount of time Plotkin spent with Hatch's file, and entering into a back-and-forth about Plotkin's ignorance of the Horizon Bound charity. Hatch had founded.
*162 Hatch additionally claims that "Plotkin's statement that he had never talked to Rodrigues-Wallis, a statement that was highly suspect, could not be sufficiently tested." The record citation in his brief, however, demonstrates that Plotkin admitted he had spoken about Hatch with a female accountant (presumably Wallis) but merely could not recall her name, and counsel had the opportunity to push on that detail to demonstrate that Plotkin's memory was at best fuzzy on the point.
Hatch also complains that he could not ask Plotkin about the employee/contractor distinction, but in fact he was allowed to pursue the topic with Plotkin. The one question to which an objection was sustained called for an answer about what the IRS is "inclined" to say about the distinction between an employee and independent contractor. This inquiry into the inclination of the IRS was beyond anything Plotkin could meaningfully answer, and its materiality was less than plain.
Finally, Hatch claims that "Plotkin's understanding of Hatch's knowledge of subchapter S corporations was judicially determined, not fair game, in cross-examination," citing Volume 3, p. 124. The only blocked question, however, was, "Would it be fair to say that Mr. Hatch didn't even know what a subchapter S corporation was before he got this advice from you and the others?" (emphasis supplied). It was within the court's discretion to exclude a question asking someone to testify to another's knowledge.
f. Cross-Examination of Rameaka
Hatch argues that he was prevented from cross-examining IRS Agent Rameaka on the subject of how he obtained certain documents offered into evidence. He says the purpose of the excluded questions was to undermine Rameaka's effort to suggest that evidence was "hard to get" from Hatch and to give the jury the "impression that Hatch was sneaky, that he hid information."
The court restricted cross-examination on only two occasions. First, the court ruled irrelevant the question, "And you haven't told the jury that many records came as a result of Mr. Hatch obeying the law and handing them over to you, correct?" The court told counsel he could explain his position to the contrary at the morning recess. Immediately following the sustained objection to this question, counsel was permitted to establish that Tri-Whale produced one of the exhibits pursuant to a subpoena. This led to the next question that the court ruled irrelevant, "Is that always the case when you ask someone that's been accused of tax evasion, do they always obey the subpoena and give you the documents?" The court eventually explained its thinking as follows:
First of all . . . the fact that Mr. Hatch may have obeyed a Subpoena, doesn't reflect on any issue in this case. A Subpoena requires someone to produce whatever the Subpoena commands. Secondly, to the extent that Mr. Hatch voluntarily turned over records, again, is not really relevant unless we know the exact circumstances. But beyond that, it's now a moot question because Agent Rameaka later testified and acknowledged that Mr. Hatch had provided him with some documents. Third, the manner in which you asked some of these questions was a problem. You interjected into the question a lot of editorial comment. . . . Whether he obeyed the law in complying with a Subpoena, doesn't have any bearing on whether or not he wilfully evaded income taxes. His state of mind that he filed the returns, or whatever it is that the Government alleges he did, would be relevant. *163 But the fact that he may have complied with a Subpoena long after that doesn't shed any light on the issue. So for all those reasons, the Court stands by its ruling.
The court's ruling was within its discretion.
To sum up our disposition of Hatch's myriad contentions of overly-restricted cross-examination, the court acted within its discretion in sustaining the objections it did during the cross-examination of the three witnesses, We discern no basis for appellant's argument that the court's rulings contravened his Sixth Amendment right to cross-examine.
V. Expert Witness Testimony
Hatch argues that the district court wrongly admitted what he calls the "expert" testimony of Plotkin, Wallis, Rameaka and Agent Michael Pleshaw, who were never formally designated as experts by the government, and that it erred in excluding some expert testimony offered by defense witness Daniel Urso. Taking each witness in turn, we find no error. We review a court's decision to admit testimony for abuse of discretion. United States v. Cormier, 468 F.3d 63, 72 (1st Cir.2006). Where no objection was made below, as was often the case here, we review the decision for at most plain error. United States v. Diaz, 300 F.3d 66, 74-76 (1st Cir.2002).
a. Plotkin
Plotkin testified not as an expert witness but as a fact witness. There was no objection lodged to his testimony on the ground now argued, and hence therefore its admission can be reviewed only for plain error. Plotkin testified on direct examination without objection to (1) the mechanics of how he prepared the tax return which included the "Survivor" income but omitted the other income; (2) the significance of various dollar amounts which appeared on the return; (3) what a W-2 is; (4) the fact that some handwriting on Exhibit 125 was Hatch's and some was his assistant's; (5) the fact that Hatch never questioned the inclusion of the "Survivor" prize in the return and indeed discussed the possibility of a compromise with the IRS; (6) what an offer in compromise is; (7) that he and Hatch signed the return but that Hatch declined an offer for the firm to mail the return for him; (8) that he discussed with Hatch the advantages of receiving his radio station income as an independent contractor as opposed to an employee, and what those benefits were; and (9) that Tri-Whale was an S-corporation, that he explained to Hatch what an S-corporation is, and that he told Hatch that all S-corporation income would have to be reported on his individual return.
Plotkin subsequently testified on redirect, over one "leading" and "mischaracterization" objection, to three issues that had been raised by the defense on cross-examination: (1) his credentials as an accountant; (2) the significance of various items on the tax return he had prepared for Hatch; and (3) his memory about a call from the female accountant,
Hatch claims without record support that the "chief real reason" for the testimony was to "persuade the jury of Plotkin's professional expertise" and to demonize Hatch for being wealthy.[8] We see nothing in the record to suggest that Plotkin was being presented as an expert, nor does Hatch's appellate brief make any argument *164 beyond the mere assertion that he was an expert. To whatever extent his answers might be said to have included opinion testimony, they largely fell within the limits of admissible lay opinion testimony, see Fed.R.Evid. 701(b), and even were that not so in every respect, their unobjected-to admission could in no way be considered to be plain error.
b. Wallis
Wallis also testified as a fact witness to, among other things, the facts: (1) that Hatch gave her a 1099 reflecting the "Survivor" income and what a 1099 is; and (2) that Hatch discussed with her his unsupported theory that perhaps CBS might have paid his taxes, that she told him this was improbable, that he never produced any evidence that CBS might have paid his taxes, and that she warned him that if CBS had done so this itself would be a taxable item. Wallis subsequently testified without objection concerning the mechanics of how she prepared the 2000 tax return (which Hatch never filed), the significance of various dollar amounts on the return, and her interactions with Hatch during the process. Again, the bulk of Wallis' testimony fell within the ambit of Fed.R.Evid. 701. There was no objection to Wallis' testimony on the present ground, nor, any more than Plotkin's, was it expert testimony. It was certainly not plain error for the court to admit Wallis' unobjected-to testimony.
c. Rameaka
As with Plotkin and Wallis, Hatch made no objection to Rameaka as an expert witness but rather complained below that he should not be allowed to testify as a summary witness, a claim he does not pursue on appeal. His two-sentence statement that Rameaka was not a named expert and that he created several summary charts does not constitute an argument.
d. Pleshaw
Hatch objected on several occasions at trial that IRS Agent Pleshaw was improperly being asked to testify as an expert although not previously qualified as such by the court. We review the overruled objections for abuse of discretion. Cormier, 468 F.3d at 72. Hatch had sufficient advance notice of the substance of Pleshaw's testimony, and Pleshaw himself, as an experienced IRS agent, was clearly qualified to testify regarding the tax issues at stake in the case. The court did not abuse its discretion in admitting the testimony.
Pleshaw's testimony was introduced in order to establish whether, if the sums omitted from the tax returns had been included, substantial tax would be owed. United States v. Mikutowicz, 365 F.3d 65, 70 (1st Cir.2004) ("tax evasion requires government to prove that defendant owed substantially more federal income tax than declared"). Hatch had conceded before trial that the key omitted income charged in the indictment should have been included in the tax returns and that this would be undisputed at trial. In addition, Hatch acknowledged that the odds were slim that a jury would find there was no "substantial" tax owed if those sums had been included, and that consequently this would not be the focus of his defense. Hatch did not stipulate to this point, however, and the government introduced evidence on that element of the crime at trial using Pleshaw as its witness.
Pleshaw's forthcoming testimony was addressed at length in a pretrial hearing on December 22, 2005, a couple of weeks before trial began. The court did not rule expressly on whether Pleshaw would be considered an expert but observed that,

*165 even if this witness is classified as an expert, if the scope of his testimony is simply that he's going to explain how the tax would be calculated for the purpose of showing that a substantial tax is due and owing, if it's limited to simply doing the calculations, it's a very low bar, I guess, to establish that he has the qualifications to give that testimony.
The court then urged the parties to confer and discuss the potential testimony and expressly invited defense counsel to file a motion for a so-called Daubert hearing if he believed one was required so as to challenge Pleshaw's expert qualifications. The government provided Hatch with a resume establishing Pleshaw's credentials, but no request or motion for a Daubert hearing at which Pleshaw's expertise could be examined and challenged was ever filed by the defense.
Hatch suggests that Pleshaw's testimony was not properly noticed pursuant to Fed.R.Crim.P. 16(a)(1)(G), which requires the government "at the defendant's request" to give a written summary of any upcoming expert testimony.[9] Whatever the dispute about the precise nature of the notice given to Hatch concerning Pleshaw's qualifications, or, for that matter, whether Hatch expressly requested the kind of report addressed in the Rule, there is no doubt that Pleshaw's identity, qualifications, and the scope of his testimony were front and center at the pretrial hearing well in advance of the trial. There can be no argument that Hatch was caught off-guard by Pleshaw's appearance at trial or by the purpose and substance of Pleshaw's testimony. Hatch, moreover, had been told by the court prior to trial that if he desired a hearing on Pleshaw's qualifications, he could request one, which he never did. Given, therefore, the substantial degree of compliance with the purpose, whether or not in all respects the letter, of Rule 16(a)(1)(G), we think the court had ample discretion to overrule defendant's objections and allow Pleshaw's responses as it did. See also United States v. Cuellar, 478 F.3d 282, 293, cert. granted on another issue, ___ U.S. ___, 128 S.Ct. 436, 169 L.Ed.2d 304 (2007) (court has discretion whether to grant sanctions for a violation of Rule 16; new trial must be ordered based on alleged discovery violation only if such a violation prejudices the defendant's substantial rights).
To the extent that Hatch now challenges Pleshaw's qualifications to testify, we note that he concedes on this appeal that Pleshaw had "significant expert background." We have noted, in another case where this same agent, Pleshaw, testified, that "It is well-established in several circuits that `expert testimony by an IRS agent which expresses an opinion as to the proper tax consequences of a transaction is admissible evidence.'" Mikutowicz, 365 F.3d at 73 (quotation omitted). See also United States v. DeSimone, 488 F.3d 561, 577 (1st Cir.2007). Pleshaw was giving just such testimony here. Hatch has made no argument that Pleshaw's testimony was based on unreliable principles, inadequate data, or a flawed methodology. Finally, Pleshaw's testimony did not stray into a statement of opinion about Hatch's intent to evade income taxes. See Fed.R.Evid. 704(b) (expert may not testify to mental state of defendant where mental state is element of the offense); Mikutowicz, 365 F.3d at 72.[10] There was no abuse of discretion.
*166 e. Urso
After briefing and argument by the parties below, the district court granted in part and denied in part the government's motion in limine to preclude Daniel Urso, a CPA and witness for the defense, from testifying on certain topics.[11] The court nonetheless made clear that either side could request reconsideration at trial. Hatch now argues that there were four areas where his examination of Urso was improperly restricted. Contrary to Hatch's contentions, none of those areas would have gone to addressing the central issue of whether Hatch willfully withheld disclosure of income on his tax returns.
The court first sustained an objection to the question, "Can you tell the jury the basics about how a CPA starts to do business and the relationship that is required to do appropriate business with a new client?" Defense counsel later proffered that Urso would testify that "a normal business relationship with a CPA takes time to develop, that they to start [sic] look into these matters, and that there has been absolutely no due diligence with Mr. Plotkin at all, and that would give a normal taxpayer cause to be concerned about whether or not they had an accurate return." This proffer did not demonstrate how the question was relevant. It did not identify any specific instances of incompetence by Plotkin or Wallis and, more importantly, did not show how the alleged incompetence related to Hatch's intent.
The second area involved Hatch's attempt to introduce testimony from Urso to the effect that the 1099 Hatch received reflecting the $1,010,000 (Exhibit Twelve), was incorrectly filled out by SEG because the $1 million and $10,000 should have been treated separately and certain numbers should have been shown in different boxes in the form. The court noted, however, that "[u]nless there is some evidence that because of the way this form was filled out, Mr. Hatch was misled into believing this was not taxable income, this evidence would be totally irrelevant," When the court offered defense counsel another chance to make the connection, he responded "it is relevant because it shows that SEG got it wrong, and it was an extremely complicated tax issue." This was not responsive to the point the court had made, that the issue was not pertinent to whether Hatch believed this income was non-taxable.
The third area Hatch sought to explore with Urso was the effect of the "alternative minimum tax" on the $200,000 in alleged *167 commissions listed in the Exhibit Three return, to suggest Hatch would not have received any tax advantage from the false statements had the return been filed. The court rightly found the issue irrelevant. There was no indication Hatch was aware of the effect of the alternative minimum tax when he told Wallis falsely about commissions he paid on the prize. Additionally, since Hatch never filed Exhibit Three, discussion of the claimed commissions would not have gone to the issue of whether Hatch willfully failed to disclose income to the IRS. The return he did file, Exhibit One, the hypothetical return drawn up by Wallis, did not include any commissions at all because it made no reference to the "Survivor" prize itself.
The fourth area Hatch wanted to address with Urso was that the tax returns prepared by Plotkin and Wallis were "abysmally poorly prepared" and "incompetently prepared beyond imagination," and that Wallis had committed "ethics violations." The court rightly ruled that the proposed testimony was irrelevant to the issue of Hatch's intent. The court noted that Hatch was "not claiming that he didn't file any of [the returns that were never filed] because he thought there was some flaw in the return" and that "[o]n the contrary, the gist of [his] position is that he didn't understand enough about the tax laws to really know whether these returns were correct or not". As the court concluded, "So, therefore, any evidence that Mr. Urso might present as to whether he agrees with every entry in the return or whether he would have prepared the returns differently, is irrelevant."
Hatch relies on United States v. Lankford, 955 F.2d 1545, 1548 (11th Cir.1992), in which the Eleventh Circuit found that a district court had erred when it determined that the tax expert offered by the defense could not testify about the reasonableness of Lankford's conclusion that the money he received was a gift rather than taxable income. Id. at 1550. Here, however, Lankford does not help Hatch because there is no specific connection between the expert testimony and Hatch's intent. Id. at 1550-52. The minimal restrictions on Urso's testimony were not an abuse of the court's discretion.
VI. Sentencing
Lastly, Hatch challenges in the briefest of language his sentence on the grounds that the court erred in the loss finding and in applying a perjury enhancement. Both claims are undeveloped and fail in any event.
The loss calculation claim is waived, United States v. Barrow, 448 F.3d 37, 44 (1st Cir.), cert. denied, ___ U.S. ___, 127 S.Ct. 176, 166 L.Ed.2d 124 (2006) ("issues adverted to in a perfunctory manner, unaccompanied by some effort at development argumentation, are deemed waived" (citation omitted)). It is also meritless. Hatch claims that the district court wrongly accepted Pleshaw's testimony that Hatch evaded paying well over $400,000 in taxes (triggering a two-level sentencing enhancement) instead of multiplying the total of the alleged unpaid funds by 28 percent, as called for in the guidelines, for a total of $399,000. Hatch ignores the language of the guideline provision at issue, USSG § 2T1.1(c)(1) n.(A), which provides that the court may accept a "more accurate determination of the tax loss" in lieu of the guidelines' own recommended calculation. At sentencing, the government argued that Pleshaw's testimony had provided this more accurate determination (which was also subject to cross-examination by the defense), and the court adopted this approach. On appeal, Hatch makes no argument to undermine it.
*168 Secondly, Hatch, apparently invoking an acquitted conduct theory, glancingly argues that the court erred in applying an upward adjustment because it found Hatch had lied on the stand. The claim is waived because it is entirely underdeveloped. Moreover, it fails because, sharply contrary to Hatch's vague claim that "[m]uch of this finding was based on supposed perjury on the counts on which Hatch was acquitted," the court catalogued many instances in which Hatch had committed perjury, noting that the list was "a pretty long one" and included lying on the stand about his failure to disclose the income which formed the bases for the charges on which he was convicted and about his alleged failure to read the letter drafted by Wallis regarding the hypothetical Exhibit One which he then submitted for his tax return. The court further detailed false statements Hatch had made to the Probation Office concerning his assets. Hatch did not raise the acquitted conduct theory below and has an insurmountable hurdle here to show any error, never mind plain error. United States v. Donnelly, 370 F.3d 87, 91-92 (1st Cir.2004).
Affirmed.
NOTES
[1]  An S-corporation is a flow-through corporation, meaning that profits or losses flow through to the shareholders, who bear the tax consequences. As sole shareholder of Tri-Whale, Hatch was additionally obligated to report all of the ordinary income earned by Tri-Whale on his individual tax return.
[2]  Hatch was acquitted on the bank fraud count that was supported by the allegation of check altering.
[3]  Hatch disputes this fact on the grounds that Wallis testified she asked him about a checking account for Tri-Whale, not a general bank account, but her testimony also refers to her having asked him about the existence of a "business account." Further, it is clear from the testimony that Hatch provided her with information about Tri-Whale's income but omitted information about the relevant sums of money at issue in the indictment and also omitted any information about the existence of a bank account for Tri-Whale, which he did have.
[4]  Our conclusion that the district court did not abuse its discretion in excluding testimony about alleged cheating on "Survivor" negates any need for us to address Hatch's related claim, that what he calls the "Cheek error" prejudiced his case on Counts 2 and 3. Since the court did not err in its rulings, there could be no prejudice.
[5]  In discussion not clearly tied to his claims of truncated cross-examination, Hatch also accuses the government or Wallis of having intentionally doctored Exhibit 135A, which was a piece of accountants' graph paper in Wallis' handwriting, showing $101,000 in commissions paid to Hatch's agent and the same amount to his manager, along with another square of paper in Hatch's handwriting, apparently cut from a larger piece, stapled onto it and listing in Hatch's handwriting the commissions Hatch generally paid. The government had initially introduced Exhibit 135, a copy of the original document, because it was all Wallis' attorney had provided the government. When the government submitted the original later in the trial, it was admitted as Exhibit 135A. Hatch's argument about the introduction of this exhibit is at best tangential to the heart of the casewhether Hatch willfully withheld information about his income from the IRS. To whatever extent the dispute may be relevant on other grounds, Hatch has waived any such objection by failing to preserve it in the district court or even develop it on appeal. Briefly stated, there was no objection to the admission of Exhibit 135 nor, after a request for a limiting instruction which was given, to 135A.

To give a bit more detail, the government had initially introduced Exhibit 135 along with Exhibit 124, a piece of paper Hatch had given Plotkin which listed his 2000 earnings at the top with actual amounts deducted for commissions and other expenses. At the top of Exhibit 124, Hatch noted that he paid no commission to anyone on his "Survivor" winnings. Wallis testified that she never saw Exhibit 124 but received from Hatch only the square piece of paper listing the commissions, which she took to be referring to commissions for the "Survivor" prize.
As best we can discern from Hatch's appellate brief, Hatch alleges that the government intentionally introduced Exhibit 135, the copy, so that it would appear that Hatch's handwritten notes on the commissions were a stand-alone "sticky" attached to Wallis' notes, when in fact it appears to have been cut from the larger Exhibit 124, which allegedly demonstrated no commissions paid on the "Survivor" winnings. These allegations against the government were not presented to the district court in the first instance and are therefore waived. Furthermore, Exhibit 135 was admitted without objection, and Hatch's own testimony on direct seemed to support Wallis' testimony that he had given her the small square of paper. When the original document was found and introduced, there was a lengthy discussion at sidebar. Hatch's counsel requested a limiting instruction related to the government claim it had just discovered the original after submitting a photocopy. The government then introduced the original exhibit, saying that the defense had no objection to it. Defense responded, "Well, yes and no. I mean" and was cut off by the court, saying "If you want to object, you object, and I'll rule on the objections. I don't want to hear any more about it, the jury is on its way in." Subsequently, defense said, "We have no objection to its entry with strict limiting instructions, your Honor."
On appeal, Hatch claims he "repeatedly objected," and only stopped when the court said, "I don't want to hear any more about it." This ignores the fact that the court invited objection to occur when the evidence was offered, and that Hatch affirmatively stated "We have no objection to its entry with strict limiting instructions," which the court had already promised to provide and did. There was no objection preserved. Even if there had been a preserved objection, the court did not abuse its discretion in admitting the original exhibit for the sake of clarity.
[6]  Hatch makes much in his briefs of the fact that Tri-Whale did not have a checking account, ignoring the fundamentally unchallenged point that he did have a corporate account for Tri-Whale, the existence of which he concealed from Wallis, and from which he transferred funds to his own account. He misquotes the government's brief in order to create the appearance of a discrepancy where there is none, claiming that the government's brief referred to Tri-Whale's "corporate checking account," when in fact it referred only to "a bank account for Tri-Whale."
[7]  To the extent Hatch now claims that these four questions together might have exposed bias on the part of Wallis and concern for her own career, he never argued, and thus waived, this theory below,
[8]  In another example of misrepresentation in Hatch's brief, Hatch claims that government counsel "argued Plotkin's credentials as an expert in closing." The record transcript page he cites reflects no such argument.
[9]  Despite complaining generally about this issue at length in his primary brief on appeal, Hatch cites to the relevant rule only in his reply brief.
[10]  Hatch asserts that Pleshaw "opined that Hatch lied about $25,000 in charity money" and thus issued an opinion about Hatch's willfulness, but he overstates Pleshaw's testimony, which was that a $25,000 check for Horizon Bound "ended up in [Hatch's] personal account for personal use." Defense counsel objected that the testimony was "narrative speech, not just an answer," and the court sustained the objection, stating, "Yes, I think you have answered that question that it ended up in Mr. Hatch's personal account."
[11]  On the issues relevant to this appeal, the court ruled that Urso could not testify about the quality of Hatch's bookkeeping abilities, noting that "this case isn't about Mr. Hatch's bookkeeping abilities, it's about whether or not he willfully did not report certain items of income that were taxable and should have been reported." The court further ruled that proffered testimony that it's a common experience to have difficulty with taxes when trauma occurs was irrelevant because the question in the case was whether income was willfully omitted. It noted also that such an opinion about traumatic events is outside the expertise of an accountant. The court denied the government's motion with respect to testimony about efforts Hatch may have made to file amended returns, indicating that it was too early (pre-trial) to decide whether such evidence would be admissible. It ruled discussion about the alleged incompetence of the prepared tax returns to be irrelevant but noted that Hatch could pursue testimony on the issue of whether Hatch didn't claim deductions that would have reduced his tax liability.
