Full opinion text
WINTER, Circuit Judge: A jury convicted Leona M. Helmsley of one count of conspiracy, three counts of tax evasion, three counts of filing false personal tax returns, sixteen counts of assisting in the filing of false corporate and partnership tax returns, and ten counts of mail fraud. The convictions concerned a scheme to charge personal expenditures to various business enterprises that she and her husband owned or controlled. She was sentenced to four years in prison to be followed by three years of probation, fined over $7 million and ordered to pay restitution of nearly $2 million. The evidence demonstrating that Mrs. Helmsley, with her husband, charged personal expenditures to businesses through deceptive billings and tax returns was overwhelming, and no sufficiency claim is raised in that regard. Nevertheless, Mrs. Helmsley challenges her convictions and sentence on numerous other grounds. First, she argues that her convictions were obtained in violation of her right against self-incrimination because the prosecution resulted from immunized testimony she had previously given to a state grand jury. Next, she contends that, because evidence of overpayment of taxes offset the government’s proof of a tax deficiency, her convictions for tax evasion must be reversed. Mrs. Helmsley also claims that several of her convictions were for crimes not alleged in the indictment, that the mail fraud convictions were invalid, and that prosecutorial misconduct deprived her of a fair trial. Finally, she contests the legality of various aspects of her sentence. We affirm her convictions. However, her convictions on three counts of filing false personal tax returns and one count of aiding in the filing of a false partnership return must, as lesser-included offenses, be merged with her convictions for tax evasion. We therefore remand to the district court for resentencing on those counts. BACKGROUND Throughout the 1980’s, Harry B. Helms-ley and his wife, Leona M. Helmsley, presided over a network of real estate, hotel and insurance businesses. Based principally in New York City but with operations as far away as Florida and Ohio, these businesses were organized as a series of holding companies, subsidiary corporations, and partnerships directly or indirectly owned and controlled by Mr. and Mrs. Helmsley. The centerpiece of the organization was a holding company called Helmsley Enterprises, Inc. (“HEI”) of which Mr. Helmsley was President and sole shareholder. HEI operated a number of wholly owned subsidiary corporations. Helmsley-Spear, Inc. (“Helmsley-Spear”) engaged in real estate and insurance brokerage businesses and acted as managing agent for various commercial office buildings and residential apartment properties in New York City and elsewhere. Many of these properties were owned or leased by other entities in the Helmsley organization. Helmsley Hotels, Inc. (“Helmsley Hotels”), of which Mrs. Helmsley was President, operated several hotels in New York City. Helmsley Hotels also held an interest, usually controlling, in a number of separate partnerships that in turn owned individual hotel, apartment and office properties. These included 280 Park Avenue Associates, 166 East 61st Street Associates, Windsor Park Apartments Associates, and Graybar Building Company. Harley Hotels, Inc. (“Harley Hotels”), of which Mrs. Helmsley was also President, was a wholly owned HEI subsidiary based in Cleveland, Ohio that operated hotels and motels outside New York City. DECO Purchasing and Distributing Co., Inc. (“DECO”), another HEI subsidiary, was headquartered in Florida and acted as a centralized purchasing agent for the entire network of Helmsley businesses. Finally, HEI owned seventy-eight percent of the common stock of Realesco Equities Corp. (“Realesco”), which in turn operated a number of wholly owned subsidiaries engaged in New York City hotel and real estate brokerage businesses. The balance of Realesco’s stock was held by outside investors. In addition, Mr. Helmsley held partnership interests in a number of other businesses. These included Middletowne Associates and Garden Bay Manor Associates. Mrs. Helmsley held the balance of the partnership interest in Middletowne Associates, while a wholly owned subsidiary of HEI held the balance in Garden Bay Manor Associates. In June 1983, Mr. and Mrs. Helmsley purchased a twenty-one room mansion known as “Dunnellen Hall” located on approximately twenty-six acres in Greenwich, Connecticut. Soon thereafter, the Helms-leys undertook a major renovation and decoration of Dunnellen Hall. The aspects of the project pertinent to this action included a $2 million addition that enclosed one of two swimming pools and featured a rooftop marble dance floor, four jade art pieces costing $500,000, and an indoor/outdoor stereo system worth over $100,000. The Helmsleys also did extensive gardening and landscaping work at Dunnellen Hall. Beginning at the end of 1983 and continuing for two more years, the Helmsleys schemed to charge personal expenses associated with Dunnellen Hall and elsewhere to various Helmsley business entities. With the collaboration of Joseph V. Licari, Senior Vice President and Chief Financial Officer of HEI, and Frank J. Turco, Vice President and Chief of Financial Services for Helmsley Hotels, the Helmsleys arranged for hundreds of thousands of dollars of their personal expenses to be paid by companies they directly or indirectly owned and controlled and to be carried on the books of those companies as business expenditures. In this manner, Mr. and Mrs. Helmsley were able to reap two illegal tax benefits. First, by having the companies pay the expenses rather than distribute taxable income to the Helmsleys, the Helmsleys avoided personal income taxes. Second, because the various Helmsley companies involved treated the payment of these personal expenses as business expenditures, the companies enjoyed artificially inflated business expense deductions. The tax returns filed by the Helmsleys and by the various firms reflected the false billing. At the Helmsleys’ behest, Licari and Tur-co carried out the scheme through the preparation of phony invoices that characterized items for Dunnellen Hall as business-related goods and services. Turco kept careful records of the expense diversions and provided Mrs. Helmsley with monthly summaries of them. Initially, DECO served as the major purchasing vehicle for the Helmsleys’ personal expenses, including lamps, furniture, carpeting and fabric. After DECO’s outside accountants discovered irregularities, however, DECO became a conduit, making the purchases itself, but then billing other Helmsley-controlled businesses for reimbursement. Many of the expenses resulting from the Dunnellen Hall addition, the jade art pieces, and the stereo system were thus charged to the other Helmsley businesses. The construction of the addition was financed in part through invoices describing the work as done at various Helmsley Hotel properties. Each of the four jade pieces was purportedly purchased for a different Helmsley hotel, using invoices characterizing the pieces as antique furniture. Part of the cost of the stereo system was charged to the Helmsley Building, 230 Park Avenue in New York City, using phony invoices describing the installation of an electronic security system. at that site. In addition, Helmsley-Spear, Helms-ley Hotels, Harley Hotels, and subsidiaries of Realesco all were charged with personal purchases. Meanwhile, a series of events that would bring the Helmsleys’ misdeeds to the attention of the government had begun. A New York Post reporter, Ransdell Pierson, had at one time pursued a tip about the misuse of corporate funds by the Helmsleys but had abandoned the quest after finding little hard evidence. However, an investigation into a sales tax avoidance scheme by two jewelers had caused Mrs. Helmsley to make two appearances before state grand juries during which she gave immunized testimony. Some time later, a New York Times article implicated Mrs. Helmsley in the state sales tax avoidance scheme. Pier-son’s interest was renewed by the Times story, and, tipped by a disgruntled former Helmsley employee named Jeremiah McCarthy, Pierson published an article in the Post on December 2, 1986, stating that the Helmsleys had used false invoices to pay personal expenses with corporate funds. This article triggered investigations by both the United States Attorney for the Southern District of New York and the New York State Attorney General. Their investigations, later combined, resulted in the federal indictment that is the genesis of the instant case and in a separate state indictment, since withdrawn. The federal indictment contained forty-seven counts against Mr. and Mrs. Helms-ley, Licari and Turco. Count 1 alleged that the four defendants conspired in violation of 18 U.S.C. § 371 to commit offenses against the United States in the form of tax and mail fraud crimes and to defraud the Internal Revenue Service. Counts 2-4 charged that Mr. and Mrs. Helmsley attempted to evade personal income tax in the calendar years 1983, 1984 and 1985 in violation of 26 U.S.C. § 7201 by failing to report on their joint personal federal income tax returns the income represented by the payment of personal expenditures by Helmsley businesses. Counts 5-7 alleged that Licari and Turco violated 26 U.S.C. § 7201 and 18 U.S.C. § 2 by aiding and abetting the Helmsleys’ personal income tax evasion. Counts 8-10 charged Mr. and Mrs. Helmsley with filing fraudulent federal personal tax returns in 1983, 1984 and 1985 in violation of 26 U.S.C. § 7206(1). Counts 11-13 charged Licari and Turco with aiding and abetting the fraudulent filings, this time in violation of 26 U.S.C. § 7206(2). Counts 14-29 charged all four defendants with assisting in the filing of fraudulent federal corporate and partnership income tax returns for various Helmsley-con-trolled business entities in violation of 26 U.S.C. § 7206(2). Each count alleged a separate instance of a phony deduction claimed in the period 1983-1985. Counts 30-39 charged all defendants with mail fraud in violation of 18 U.S.C. § 1341 by using the mails to file false personal New York State income tax returns and false New York State Corporation Franchise Tax Reports. Counts 40-46 also charged mail fraud, alleging that all four defendants had defrauded the minority shareholders of Realesco by mailing financial statements that characterized the payment of personal expenses for Mr. and Mrs. Helmsley as business-related expenditures. Finally, Count 47 charged Mrs. Helmsley and Turco with conspiracy to commit extortion in violation of 18 U.S.C. § 1951 by demanding kickbacks from various contractors and vendors that did business with the Helms-ley companies. Before trial, Judge Walker found that poor health rendered Mr. Helmsley incompetent to stand trial. See United States v. Helmsley, 733 F.Supp. 600 (S.D.N.Y.1989). On August 30, 1989, after a ten-week trial, the jury returned guilty verdicts against the remaining defendants on thirty-nine counts. Mrs. Helmsley was found guilty on Counts 1, 2-4, 8-10, 14-29, and 30-39. Licari and Turco each were found guilty on Counts 1, 5-7, 11-13,14-29, and 30-39. All defendants were acquitted on Counts 40-46, the alleged Realesco fraud, and Mrs. Helmsley and Turco were acquitted on Count 47, the alleged extortion of kickbacks. On December 12, 1989, Judge Walker sentenced Mrs. Helmsley to four years’ imprisonment followed by three years’ probation and 250 hours of community service. Additionally, he imposed fines totalling $7,152,000 and mandatory special assessments totalling $1,350, directed Mrs. Helmsley to pay the entire cost of her prosecution, and ordered her to pay restitution for taxes owed to the United States in the amount of $1,221,900 and to New York State in the amount of $469,300, plus interest. Judge Walker sentenced Licari to thirty months’ imprisonment, three years’ probation, a $75,000 fine and $1,350 in mandatory special assessments. Turco received two years in prison, three years’ probation, a $50,000 fine, and $1,350 in mandatory special assessments. Licari and Turco did not appeal their convictions. On appeal, Mrs. Helmsley argues that all her convictions must be reversed because they were obtained in violation of her Fifth Amendment right against self-incrimination. In addition, she argues that her convictions on Counts 2-4 must be reversed for insufficiency of the evidence, or alternatively, vacated and remanded for a new trial because of erroneous jury instructions. Mrs. Helmsley further contends that her convictions on Counts 1, 8-10, and 14-29 must be vacated and remanded for a new trial because they were based on conduct not charged in the indictment. She also claims that her mail fraud convictions are invalid and that prosecutorial misconduct requires a new trial on all counts. Finally, Mrs. Helmsley challenges various aspects of her sentence. DISCUSSION A. The Self-Incrimination Claim Mrs. Helmsley claims that her investigation, prosecution and convictions were based on the unconstitutional use of immunized testimony that she had previously provided to a New York State grand jury. As noted above, reports of, or based on, this testimony aroused Pierson’s suspicions and led to his article that triggered the federal-state investigation and resulted in her indictment and convictions. She claims that the causal link between her prior testimony and subsequent convictions violates her Fifth Amendment right against self-incrimination. She asks that the convictions against her be reversed, or that the case be remanded for an evidentiary hearing as to whether the evidence against her was sufficiently independent of her prior immunized testimony to pass constitutional muster. We conclude, however, that, even if all of the potentially disputed facts are resolved in Mrs. Helmsley’s favor, her right against self-incrimination was not violated. Her claim arises as follows. On June 11, and November 7, 1985, Mrs. Helmsley was compelled to testify before New York State grand juries investigating sales tax fraud by two New York jewelers, Bulgari and Van Cleef & Arpéis. By testifying, she received an automatic statutory grant of transactional immunity. See N.Y.Crim. Proc.Law §§ 190.40, 50.10-.30 (McKinney 1981 & 1982). Mrs. Helmsley’s testimony concerned her alleged participation in a scheme to avoid New York State sales taxes by shipping empty boxes to out-of-state addresses that she provided. On November 6, 1986, the New York Times published a story that “Leona Helmsley ... failed to pay sales taxes in New York on hundreds of thousands of dollars of jewelry she purchased over several years from Van Cleef & Arpéis.” The story identified its sources as “court documents” filed by two senior officers of Van Cleef & Arpéis who were facing state charges that they helped customers avoid taxes, and “law-enforcement officials” who apparently confirmed that Mrs. Helmsley had purchased $485,000 worth of jewelry without paying the required tax. Similar stories by the New York Post and United Press International indicated that Mrs. Helmsley’s name had surfaced in filings made by the Manhattan district attorney in response to the Van Cleef & Arpéis defendants’ motion for dismissal. About a year before these stories appeared, Pierson, the Post reporter, had begun an investigation into possible misuse of corporate funds by the Helmsleys based on an uncorroborated tip. His research proved fruitless, however, and he discontinued the investigation a few months later. However, when he read about Mrs. Helms-ley’s involvement in the Van Cleef & Ar-péis sales tax fraud case, Pierson perceived a “morality connection” between the jewelry probe and his earlier project and reopened his investigation of the Helmsleys. This time, Pierson amassed sufficient evidence on which to base a story. Apparently, previously uncooperative or unknown witnesses now stepped forward to give Pierson information on the Helmsleys. In particular, Jeremiah McCarthy, a former Senior Vice President of Helmsley-Spear who had been fired by Mrs. Helmsley in September 1985, appears to have been Pier-son’s key informant. On December 2, 1986, Pierson published an article in the Post alleging that various expenses relating to the renovation of Dunnellen Hall were billed to Helmsley-owned companies. Assistant United States Attorney James R. DeVita, who had meanwhile commenced an investigation of Mr. Helmsley on an unrelated tax matter, widened his probe to include the new allegations in Pierson’s article. Leads turned up quickly. McCarthy provided the government with a substantial amount of information relating to the practice of charging Dunnellen Hall expenditures to Helmsley business entities. This information included names of employees familiar with the scheme and falsified invoices bearing the initials of Mr. and Mrs. Helmsley. DeVita also heard from Mark Arisohn, a lawyer who called the United States Attorney’s Office to explain that he was representing the Helmsleys and their companies with respect to matters discussed in the Post article. Arisohn purported to have an innocent explanation of the various charges to the business entities. In January 1987, documents were produced pursuant to grand jury subpoena that included two memos from Turco that Judge Walker later termed a “virtual road-map for further investigation of the Dun-nellen Hall expenditures.” United States v. Helmsley, 726 F.Supp. 929, 936 (S.D.N.Y.1989). They set forth on a cumulative basis the amounts expended on Dun-nellen Hall, identified the specific Helmsley business entity that made each expenditure and the vendor to whom each amount was paid, stated the purpose of each payment, and revealed Mr. and Mrs. Helmsley's personal knowledge of the scheme. Armed with this information, the federal investigation was combined with a parallel inquiry by the New York attorney general’s office. A federal grand jury thereafter indicted the Helmsleys. Prior to trial, Mrs. Helmsley moved for an evidentiary hearing on her claim that the prior immunized state grand jury testimony on the jewelry matter had tainted the federal prosecution leading to the instant indictment. Judge Walker postponed the question until the completion of trial, at which time he could determine with the benefit of trial evidence whether there was a sufficient nexus between the immunized testimony and the federal prosecution to warrant a hearing. After her conviction, Mrs. Helmsley renewed her motion for a hearing. After a limited hearing, Judge Walker determined that a full evidentiary hearing was not required. Before him were the transcripts of the two grand jury proceedings and several submissions, including an affidavit from DeVita. That affidavit stated that the income tax investigation was based on evidence independent of Mrs. Helmsley’s immunized testimony or leads derived therefrom and explained DeVita’s knowledge relating to the commencement and conduct of the investigation. Judge Walker also heard testimony from DeVita and from Diane Peress, a lawyer from the New York State attorney general’s office who had been present during one of Mrs. Helmsley’s state grand jury appearances, and had since been designated as a Special Assistant United States Attorney for the joint federal-state investigation. DeVita elaborated on his affidavit, and Peress testified that she made no use of Mrs. Helms-ley’s June 1985 testimony, directly or indirectly, in the subsequent joint income tax investigation. DeVita testified that he had arranged for a third member of his office, acting as a “Chinese Wall,” to review Mrs. Helmsley’s grand jury testimony and assure that the subject matters were sufficiently independent to remove the danger of taint by Peress’s involvement. Satisfied that the government had made a credible showing that it had an independent eviden-tiary basis for its prosecution and that no further hearing regarding the influence of the immunized testimony on the motives of Pierson, McCarthy or other witnesses was required, Judge Walker denied Mrs. Helms-ley’s motion for a full evidentiary hearing. See Helmsley, 726 F.Supp. at 939. On appeal, Mrs. Helmsley asserts that “[t]he Fifth Amendment imposes ‘a total prohibition on use’ of immunized testimony ‘in any respect’ in any subsequent prosecution of the witness.” Appellant’s Opening Brief at 14 (quoting Kastigar v. United States, 406 U.S. 441, 453, 460, 92 S.Ct. 1653, 1661, 1664, 32 L.Ed.2d 212 (1972)). Hypothesizing a direct “chain of taint” from her immunized testimony to the November 1986 newspaper stories to Pierson’s Post article to the federal investigation to her prosecution and convictions, she con-eludes that her prior immunized testimony was the “but for” cause of her instant convictions and hence that her right against self-incrimination has been violated. The Fifth Amendment provides that “[n]o person ... shall be compelled in any criminal case to be a witness against himself.” In Kastigar, the Supreme Court stated that this prohibition against compelled testimony is not absolute and upheld the constitutionality of the federal use immunity statute, 18 U.S.C. §§ 6002-03. The petitioners had been held in contempt for refusing to testify before a federal grand jury under a grant of immunity pursuant to Sections 6002 and 6003, which authorize the government to order a witness to testify, but prohibit use of that testimony against the witness in any criminal case. The Court affirmed the contempt order, finding that the statute sufficiently protected the right against self-incrimination. This total prohibition on use provides a comprehensive safeguard, barring the use of compelled testimony as an “investigatory lead,” and also barring the use of any evidence obtained by focusing investigation on a witness as a result of his compelled disclosures. 406 U.S. at 460, 92 S.Ct. at 1664-65 (footnote omitted). Before Kastigar, the Court held in Murphy v. Waterfront Commission, 378 U.S. 52, 84 S.Ct. 1594, 12 L.Ed.2d 678 (1964), that the Fifth Amendment bars the use in a subsequent federal prosecution of compelled testimony obtained in state proceedings. It declared, Once a defendant demonstrates that he has testified, under a state grant of immunity, to matters related to the federal prosecution, the federal authorities have the burden of showing that their evidence is not tainted by establishing that they had an independent, legitimate source for the disputed evidence. 378 U.S. at 79 n. 18, 84 S.Ct. at 1609 n. 18. Because the district court did not hold an evidentiary hearing, we accept ar-guendo Mrs. Helmsley’s hypothesis that the November 1986 news stories contained information based on Mrs. Helmsley’s immunized testimony; that these stories caused Pierson to renew his inquiry into the Helmsleys’ income tax practices and caused previously unavailable sources of incriminating information, such as McCarthy, to emerge; that Pierson’s Post article was the catalyst for the joint federal-state investigation; and that factual information derived from Pierson and his sources provided the basis of the subsequent prosecution and convictions of Mrs. Helmsley. Even if these assumptions are made, however, the causal links between Mrs. Helms-ley’s grand jury testimony and her convictions do not implicate the Fifth Amendment. Kastigar considered only the facial validity of the federal use immunity statute and did not address the intricacies of what constitutes an impermissible use of immunized testimony. While neither a witness’s immunized testimony nor information derived from that testimony may be offered as evidence against that witness in a subsequent criminal trial, courts interpreting Kastigar have struggled with more attenuated connections between immunized testimony and a witness’s conviction. See generally United States v. North, 910 F.2d 843, 853-73 (per curiam), cert. denied, — U.S. -, 111 S.Ct. 2235, 114 L.Ed.2d 477 (1991). Mrs. Helmsley argues that a cause-in-fact relationship between immunized testimony and a subsequent conviction, without more, triggers Fifth Amendment protection. That position, however, expands the right against self-incrimination far beyond any discernible policy served by the right. If a grand jury witness testifying under a grant of immunity were recognized by a grand juror as the perpetrator of a bank robbery committed the week before, an undeniable causal link between the immunized testimony and a conviction for bank robbery would exist, but a plausible Fifth Amendment argument could not be made. Similarly, if Pierson’s interest as sparked by the grand jury story had caused him to scrutinize Mrs. Helmsley’s future conduct and induced some of her employees to aid his ongoing investigation, she would certainly not be immune from prosecution for tax evasion occurring after the grand jury appearance although the causal connection to the immunized testimony would be as strong as in the instant matter. What is lacking in Mrs. Helmsley’s argument is a link between the chain of causation in her case, largely fortuitous, and policies underlying the Fifth Amendment. Under present caselaw, the Fifth Amendment prohibits the use of immunized testimony in two circumstances: (1) where the immunized testimony has some eviden-tiary effect in a prosecution against the witness, or (2) where there is a recognizable danger of official manipulation that may subject the immunized witness to a criminal prosecution arising out of the investigation in which the testimony is given. The cases concerning the evidentiary effect of immunized testimony in a prosecution against the witness arise, of course, directly from Kastigar. They are, however, of little relevance to the present case. There was no connection between the content of the evidence against Mrs. Helmsley in the instant matter and her immunized testimony apart from the attenuated chain of events that caused the federal authorities to learn of the existence of the evidence. Her case is thus much like the case of the bank robber recognized by the grand juror. In contrast, the most expansive reading of the Fifth Amendment to date regarding the evidentiary use of immunized testimony, United States v. North, supra, involved factual circumstances in which there was the possibility that the content of the testimony of the prosecution’s witnesses was affected by the defendant’s immunized testimony. No such claim can be made in the present case. Mrs. Helmsley thus relies most heavily upon United States v. Kurzer, 534 F.2d 511 (2d Cir.1976), a case in which the danger of official manipulation of immunized testimony existed. Kurzer involved a joint federal-state investigation of the meat industry in New York. Harry Kurzer, an accountant for several meat companies controlled by Moe Steinman, the original target of the investigation, testified against Steinman before a federal grand jury under a grant of immunity. Steinman eventually pleaded guilty to various charges. Pursuant to a cooperation agreement, Steinman thereafter informed investigators of a meat-packing industry scheme to generate cash income using false invoices, and of Kurzer’s involvement in the scheme. This information led to an indictment against Kurzer for tax fraud. We explicitly rejected the district court’s conclusion that Kur-zer’s right against self-incrimination was violated solely because his “testimony set in motion the train of events which ultimately resulted in his own indictment.” 534 F.2d at 515. However, we held that the Fifth Amendment would be violated if Kurzer’s testimony caused Steinman’s decision to provide evidence against Kurzer. See id. at 517; see also United States v. Biaggi, 909 F.2d 662, 689-90 (2d Cir.1990), cert. denied, — U.S.-, 111 S.Ct. 1102, 113 L.Ed.2d 213 (1991). Mrs. Helmsley argues that Kurzer requires us to reverse her convictions and remand for a hearing. She posits that her state grand jury testimony, as publicized in the November 1986 news stories, may have motivated certain witnesses, McCarthy in particular, to come forward with information against her. We do not interpret Kurzer so broadly, however. In Kurzer, the immunized testimony was given during the course of a single, integrated, official investigation that led to the revelation of crimes committed by the immunized witness. We held only that where the grant of immunity in the course of an investigation compels testimony that angers a target of the investigation and causes the target to implicate the immunized witness by testimony that would otherwise not have been given, a Fifth Amendment violation occurs. In contrast, the investigation into Mr. and Mrs. Helmsley’s federal income tax practices was factually, functionally and legally separate from the state sales tax matter. Moreover, the key link in the causal chain between Mrs. Helmsley’s grand jury testimony and her conviction was Pierson, a newspaper reporter who decided to reopen his earlier investigation because of his perception of a “morality connection” and who happened upon McCarthy as a result. Nothing in Kurzer suggests that the Fifth Amendment applies to situations in which publicity concerning immunized testimony triggers a purely private investigation into an entirely different matter solely because each matter involves dishonest conduct. In Kurzer, there existed a danger of manipulation by government investigators who might immunize a witness and then use the fact of the immunized testimony to anger a subject of the investigation and cause that subject in turn to incriminate the witness. Such a danger directly implicated Fifth Amendment policies, and thus testimony that might have resulted from such manipulation could not be used against the immunized witness. In the instant matter, the curiosity of a private party was fortuitously sparked a year after the grand jury appearances by publicity attending the sales tax prosecution of the jewelers. The matters investigated by the private party were factually and legally unrelated to the immunized testimony. Moreover, the federal investigation was initiated solely as a result of a newspaper story by the private party and before any cooperation with state authorities regarding income tax matters had begun. There was thus no evidentiary use of any kind of her immunized testimony and no serious danger of manipulative use of the fact of her testimony. The chain of events following her immunized testimony, although unlucky for her, did not, therefore, implicate Fifth Amendment policies. B. Tax Evasion Mrs. Helmsley challenges her tax evasion convictions (Counts 2-4) on the ground that the government failed to prove a tax deficiency, a necessary element of that crime. In addition to showing willfulness and an affirmative act constituting an evasion, the government must prove beyond a reasonable doubt the existence of a tax deficiency to establish tax evasion under 26 U.S.C. § 7201. See Sansone v. United States, 380 U.S. 343, 351, 85 S.Ct. 1004, 1010, 13 L.Ed.2d 882 (1965); Lawn v. United States, 355 U.S. 339, 361, 78 S.Ct. 311, 323, 2 L.Ed.2d 321 (1958); United States v. Koskerides, 877 F.2d 1129, 1137 (2d Cir.1989); United States v. Citron, 783 F.2d 307, 312 (2d Cir.1986). We have also required a showing that the deficiency was substantial. See Koskerides, 877 F.2d at 1137; Citron, 783 F.2d at 312. The evidence introduced by the government in its main case showed that by failing to report the value of personal goods and services charged to Helmsley-controlled businesses, the Helmsleys understated their taxable income on their joint personal federal income tax returns by $245,485 in 1983, $1,146,793 in 1984, and $1,197,454 in 1985. This resulted in income tax deficiencies of $49,770, $573,396, and $598,727, respectively. In response, Mrs. Helmsley offered evidence that she and her husband actually overpaid their personal income tax in 1983, 1984 and 1985 in amounts sufficient to offset the alleged deficiencies. This evidence, which is the basis for her claim of insufficiency as a matter of law, consisted of the testimony of two accountants who stated that the Helmsleys’ tax returns failed to comply with the accelerated cost recovery system (“ACRS”) of the Economic Recovery Tax Act of 1981, Pub.L. No. 97-34, § 201, 95 Stat. 172, 203, in effect during the years in question. In doing so, the accountants testified, the Helmsleys had deducted too little of the cost basis associated with buildings owned by partnerships in which Mr. or Mrs. Helmsley held an interest. Calculating that the overpayment in each tax year exceeded the amount of the deficiency shown by the government’s evidence, the experts opined that Mrs. Helmsley had in each year paid more income tax than she owed. Mrs. Helmsley’s overpayment defense rested on the amount of depreciation allowed with respect to certain buildings owned by partnerships in which the Helms-leys had an interest. On their tax filings for 1983 through 1985, the Helmsleys had recovered the cost basis of these buildings by depreciating them on a “straight-line” basis over their 15-year useful life — 6.67% per year. However, according to the accountant witnesses, ACRS mandated that the cost basis of buildings be segregated into “real” and “personal” property components and that the personal property component be depreciated over a shorter useful life of five years, at rates between 15% and 22% per year. See Pub.L. No. 97-34, § 201, 95 Stat. 172, 204-06. Mrs. Helmsley’s first expert witness, Robert Schweihs, appraised a sample of Helmsley partnership buildings and testified that 7.8% of their cost basis was attributable to personal property — carpeting, draperies, cabinetry and the like. The second defense expert, Gerald W. Padwe, testified that segregating real versus personal property was mandatory under ACRS and that Mrs. Helmsley had not done so on her tax filings. Padwe applied Schweihs’s 7.8% figure to the cost basis of buildings owned by three Helmsley partnerships — known as the Formula Properties — to derive personal property components. He then depreciated these components over a five-year period, and calculated the effect on the Helmsleys’ personal income tax returns. He testified that this adjustment gave Mrs. Helmsley additional depreciation deductions in the amounts of $519,983 for 1983, $1,000,028 for 1984, and $1,942,212 for 1985. In addition, Padwe testified that the Helmsleys had made a second depreciation error. Although they had depreciated the real property component of the partnership buildings at a rate of 6.67% per year (because they depreciated the entire cost basis of buildings at that rate), Padwe stated that ACRS regulations required a rate of 7% for the first ten years and 6% for the remaining five years. Applying the .33% differential to the Formula Properties and buildings owned by eleven other Helmsley partnerships, Padwe testified, gave Mrs. Helmsley additional depreciation deductions in 1983 through 1985 that she had not taken. The combined effect of the unused deductions, he further testified, was that the Helmsleys overpaid their joint personal income taxes by approximately $93,000 in 1983, $21,000 in 1984, and $477,000 in 1985, even if the unreported taxable income claimed by the government existed. In other words, the defense’s evidence suggested that, in each year, the tax overpayment resulting from underdepreciation of personal property — fifteen years rather than five years as explained supra — and real property — 6.67% rather than 7% — exceeded the tax deficiency resulting from the underreporting of income. The government then sought through cross-examination to show that Schweihs’s and Padwe’s conclusions were based on a selective application of the ACRS that ignored tax-increasing ramifications of depreciating personal property at a faster rate than real property. Most significantly, Padwe admitted that he had not taken into account the “recapture” provision of Internal Revenue Code Section 1245, which requires that any gain from the sale of personal property be taxed as ordinary income (as opposed to a capital gain) in the year of the sale to the extent that any depreciation was taken on the property. See 26 U.S.C. § 1245 (1982). Hence, while segregating personal property might afford extra depreciation in the years following purchase, it could also lead to higher taxes when sold. Padwe admitted on cross-examination that he had not calculated the effect of recapture resulting from the separation of real and personal property for depreciation purposes on the millions of dollars of capital gains from the sales of Helmsley partnership property in 1983, 1984 and 1985. Mrs. Helmsley’s insufficiency claim fails on two grounds. First, Padwe’s testimony was at odds with applicable law, and it would not have been error to exclude it completely. Having selected a particular depreciation method — whether or not it was a method authorized under the law— Mrs. Helmsley was not free to recalculate her taxes by resorting to one of the four depreciation methods in ACRS solely to defend an evasion charge. If her original selection of a depreciation period was made for strategic tax-saving purposes, the doctrine of election would prevent her from abandoning that choice. If her original selection was a good faith error, then an exception to that doctrine would allow her, with the permission of the Commissioner, to elect a new depreciation method. The depreciation method used by Padwe was one of four options, all of which would be available for late election in the case of a good faith mistake and at least two of which would entail a deficiency rather than overpayment. Because Padwe’s method was not mandatory, therefore, it cannot be used to establish an overpayment in an evasion case. Second, even if Padwe’s depreciation method was available and mandatory, his testimony was undermined by the government’s cross-examination, and a reasonable trier might choose to reject it, as did the jury in the instant matter. ACRS, since repealed, was mandatory for property “placed in service” after December 31, 1980. See Economic Recovery Tax Act of 1981, Pub.L. No. 97-34, § 201, 95 Stat. 172, 203-04. Within ACRS, formerly Section 168 of the Internal Revenue Code, a taxpayer did have options. That section designated real property as “15-year real property” and personal property as “5-year property.” The general depreciation provision, Section 168(b)(1), the one selected by Padwe, provided that the basis of 5-year property could be recovered over five years in percentages of 15, 22, 21, 21 and 21, respectively. Section 168(b)(2) stated that 15-year real property was to be depreciated according to a schedule to be promulgated by the Secretary. However, Section 168(b)(3) allowed a taxpayer to elect one of three additional options. Five-year property could be depreciated on a straight-line basis over 5, 12 or 25 years, and 15-year real property could be depreciated on a straight-line basis over 15, 35 or 45 years. Mrs. Helmsley argues that by not segregating her real and personal property she made no election with respect to personal property, and that therefore the ACRS provisions of Section 168(b)(1) applied by Padwe — five-year depreciation in percentages of 15, 22, 21, 21 and 21, respectively— applied to the personal property component of her partnerships by default. It is true that Section 168(b)(3) does not provide straight-line depreciation of 5-year property over fifteen years, the option used on the Helmsleys’ returns. However, Mrs. Helmsley had four depreciation options available for personal property: (1) over five years in percentages of 15, 22, 21, 21 and 21 respectively (the method used in Padwe’s testimony), (2) over five years on a straight-line basis, (3) over twelve years on a straight-line basis, and (4) over twenty-five years on a straight-line basis. The fact that a fifteen-year depreciation schedule for (unsegregated real and) personal property was selected is not grounds for allowing her now to convert the depreciation of personal property to the accelerated five-year schedule of Section 168(b)(1) that Padwe used — rather than five, twelve or twenty-five years on a straight-line basis— solely to avoid a tax evasion charge for an entirely separate aspect of her tax returns. This is so whether or not Mrs. Helmsley’s original selection was for strategic tax-savings reasons or was a good faith error. Under the doctrine of election, a taxpayer who makes a conscious election may not, without the consent of the Commissioner, revoke or amend it merely because events do not unfold as planned. See, e.g., J.E. Riley Investment Co. v. Commissioner, 311 U.S. 55, 61 S.Ct. 95, 85 L.Ed. 36 (1940); Pacific National Co. v. Welch, 304 U.S. 191, 58 S.Ct. 857, 82 L.Ed. 1282 (1938). “Once the taxpayer makes an elective choice, he is stuck with it.” Roy H. Park Broadcasting, Inc. v. Commissioner, 78 T.C. 1093, 1134 (1982). There is ample evidence in the record— although the issue is not dispositive — to regard Mrs. Helmsley’s original selection of a depreciation method as a strategically motivated, conscious decision. Padwe’s testimony itself would support an inference that her failure to segregate her personal property and depreciate it over a permissible period was a calculated decision intended to obtain substantial tax benefits. As he testified, at the time of the pertinent tax returns, gains from the sale of real property were taxed as capital gains, whereas gains from the sale of personal property were taxed as ordinary income. The capital gains tax rate was approximately forty percent of the top marginal income tax rate. Padwe acknowledged that a taxpayer planning to sell personal property would not want to depreciate it because upon sale of the property he would owe income tax on the depreciated amount. Moreover, he testified that: (i) there were tax advantages to misclassifying personal property as real property; and (ii) chief among these advantages was avoiding recapture as income of depreciated amounts. In addition, Padwe admitted that Mrs. Helmsley had segregated and depreciated personal property elsewhere on her return, acts wholly at odds with an inference of inadvertence. Based on Padwe’s own testimony, therefore, there is ample reason to believe that Mrs. Helmsley deliberately chose not to segregate personal property because she hoped to conceal the personal property components of her holdings, thereby reaping the benefit of real property depreciation without running the risk of subsequent recapture. Absent the Commissioner’s consent, a taxpayer who has used a particular depreciation method may not defend an evasion charge on the ground that, under an alternative method, additional depreciation could have been claimed. See Fowler v. United States, 352 F.2d 100 (8th Cir.1965), cert. denied, 383 U.S. 907, 86 S.Ct. 887, 15 L.Ed.2d 663 (1966). In Fowler, appellants were convicted of tax evasion and argued that the district court erred in excluding expert testimony that appellants could have taken greater depreciation on certain assets had the useful life of the assets been calculated under a different method. The Eighth Circuit disagreed, explaining that the exclusion of expert testimony was proper because appellants had “elected one method of determining depreciation and that election binds them for purposes of this action.” Id. at 106. The law could hardly be otherwise. If it were, evaders with complicated returns would be allowed to evade taxes on one portion of their return while using a depreciation period that would be the most profitable in the long run if the evasion went undetected. If the evasion were uncovered, then they would need only to recalculate under a shorter depreciation period that would increase deductions for the years in which evasion is charged. This is precisely the defense raised by Padwe’s testimony. Mrs. Helmsley seeks to distinguish Fowler on the sole ground that Fowler involved an original selection of a valid depreciation period whereas she wishes to recalculate after selecting an invalid depreciation period. Common sense dictates that, if recalculation is denied to tax cheats who have selected valid depreciation periods, it must a fortiori be denied to tax cheats like Mrs. Helmsley who further enhanced tax benefits by selecting impermissible periods. In any event, Mrs. Helmsley’s failure to segregate personal property was equivalent in scope and effect to the selection of an accounting method for personal property, and it is axiomatic that a taxpayer may not change accounting methods without first obtaining the Commissioner’s consent. See 26 U.S.C. § 446(e) (1988); Treas.Reg. § 1.446-l(e)(2)(ii)(a) (1957) (defining accounting method change as “a change in the treatment of any material item”). See also Witte v. Commissioner, 513 F.2d 391 (D.C.Cir.1975); Standard Oil Co. (Indiana) v. Commissioner, 77 T.C. 349 (1981). Moreover, Treasury Regulation Section 1.167(e)-l(a) requires that “[a]ny change in the method of computing the depreciation allowances with respect to a particular account ... is a change in method of accounting, and such a change will be permitted only with the consent of the Commissioner.” Treas.Reg. § 1.167(e)-l(a) (as amended in 1972). This rule applies whether or not the original accounting method was permissible. See Witte, 513 F.2d at 394 (consent requirement applies “regardless of whether the change in method is from one proper method to another or from an improper method to a proper one”); United States v. Kleifgen, 557 F.2d 1293, 1297 n. 9 (9th Cir.1977) (same). Finally, even if Mrs. Helmsley made a good faith mistake when she failed to segregate her personal property, her sufficiency defense fails as a matter of law. The government’s showing of a deficiency can be rebutted by a recalculation showing an overpayment that is, under applicable law, mandatory. A showing of a deficiency cannot be rebutted by a recalculation based on the selection of the most favorable option, where other equally available options result in a deficiency. Padwe’s testimony merely selected the most favorable option. If the original depreciation method selected by Mrs. Helmsley was a good faith mistake, she may still make a late election of depreciation periods under Section 168(b)(3) as well as under Section 168(b)(1). Resort to Section 168(b)(1) is, therefore, not mandatory. Under an exception to the doctrine of election, a taxpayer who makes a good faith mistake may make a late election. See, e.g., Dougherty v. Commissioner, 60 T.C. 917 (1973) (permitting late election under Section 962 where taxpayers mistakenly believed that they had no Section 951(a) gross income for taxable year at issue); Reaver v. Commissioner, 42 T.C. 72 (1964) (late installment sale election allowed where taxpayers erroneously but in good faith characterized payments received as gross receipts rather than proceeds from a sale of property); Bayley v. Commissioner, 35 T.C. 288 (1960) (permitting late installment sale election where taxpayer made good faith error on original return). It is a matter of public record that, for the reasons stated supra, the Internal Revenue Service applies this exception to Section 168 and allows taxpayers who have originally made a good faith mistake to make a late election of one of the options available under Section 168(b)(3) as well as under Section 168(b)(1). IRS Tech. Mem. 1986-46010 (July 21, 1986). If Mrs. Helmsley had made a good faith mistake, therefore, she would be allowed to make a late election among four recovery periods for 5-year personal property. (Two of the periods were for five years but differed in the percentage to be depreciated annually.) Padwe’s testimony, however, recalculated depreciation on the basis of only one of the four recovery periods. In particular, he made no recalculation based on the two permissible longer periods available under Section 168(b)(3), each of which would have resulted in a deficiency. His recalculations within ACRS, rather than his application of ACRS, were thus elective rather than mandatory. Moreover, Padwe’s adjustment of the depreciation rate on real property from 6.67% to 7.0% was based on a proposed, but never adopted, Treasury Regulation. Hence this adjustment was not mandatory either. We thus conclude that Padwe’s testimony regarding an overpayment could have been excluded because it was based on assumptions at odds with relevant tax law. Even if Padwe’s testimony was admissible, it was not of sufficient weight to rebut as a matter of law the government’s showing of a deficiency. As noted, Padwe’s testimony was seriously undermined on cross-examination. Adjusting her sufficiency claim in light of the undermining of her expert’s testimony, Mrs. Helms-ley relies on an unusual burden-shifting argument. She claims that once she produced evidence of unclaimed deductions negating the government’s prima facie case of tax deficiency, the government “bore the new burden of proving beyond a reasonable doubt that the untaken depreciation was not available or, if available, was not sufficient to offset the unreported income.” Appellant’s Reply Brief at 26. She further contends that the government could not carry this burden merely by providing the jury with a basis for discrediting Padwe. Id. at 29. This' argument misstates the government’s burden, however. Under traditional principles, the government bears the burden throughout the trial of proving beyond a reasonable doubt all elements of tax evasion. See In re Winskip, 397 U.S. 358, 364, 90 S.Ct. 1068, 1072, 25 L.Ed.2d 368 (1970); Davis v. United States, 160 U.S. 469, 487, 16 S.Ct. 353, 358, 40 L.Ed. 499 (1895). So long as, after viewing the evidence in the light most favorable to the prosecution, a rational trier of fact could find the essential elements of the crime beyond a reasonable doubt, the trial judge must submit the question to the jury. See Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979); United States v. Taylor, 464 F.2d 240, 242-43 (2d Cir.1972). In the instant matter, the government established a prima facie case of tax evasion. We know of no reason to apply to tax evasion cases, and to proof of a deficiency in particular, unique and cumbersome notions of burden-shifting that appear to be justified solely by their usefulness to this appellant. It would belie common sense to hold that evidence of overpayment that has been undermined by cross-examination somehow creates a new burden upon the government. Like any evidence, evidence of overpayment ought simply to be weighed against evidence of underpayment, and the existence or nonexistence of a tax deficiency determined by the trier’s balancing of the evidence. If the totality of the evidence was such that a rational juror could find the existence of a tax deficiency beyond a reasonable doubt, the jury’s verdict must stand. We find that the evidence of a deficiency was sufficient in this case. The government’s cross-examination provided ample reason for a rational juror to reject Mrs. Helmsley’s evidence of overpayment. In applying ACRS, Padwe calculated the reduced tax liability that would result from increased depreciation on buildings purchased during or shortly before 1983 through 1985 but did not calculate the increased tax liability that would result from the recapture of depreciation for buildings sold in those years. Moreover, Padwe did not examine the tax records of the more than one hundred Helmsley partnerships but rather only a sample given him by defense counsel. He thus testified that he was instructed by counsel to perform the ACRS adjustments for only fourteen specified partnerships, the selection of which he knew nothing about. After an evidentiary hearing on the admissibility of his testimony at which both the government and Judge Walker questioned him about the representativeness of his sample, Padwe “flipped through” the tax documents of about seventy more-partnerships, focusing exclusively on partnerships that acquired property after 1981, the effective date of ACRS. The remaining Helmsley partnerships were not examined. There was thus ample reason for the jury to discount Padwe’s conclusions as based on a wholly inadequate, and perhaps thoroughly biased, sample of partnerships that had acquired but not sold property in the relevant years. Mrs. Helmsley’s sufficiency claim as to the existence of a tax deficiency thus fails. C. Constructive Amendment of the Indictment Mrs. Helmsley challenges her convictions on Count 1, Counts 8-10, and Counts 14-29 on the ground that the jury instructions unconstitutionally amended and expanded the offense alleged in the indictment. Under the Fifth Amendment, a criminal defendant has the right to be tried only on the charges contained in the indictment returned by a grand jury. See Stirone v. United States, 361 U.S. 212, 216-17, 80 S.Ct. 270, 272-73, 4 L.Ed.2d 252 (1960); Ex Parte Bain, 121 U.S. 1, 7 S.Ct. 781, 30 L.Ed. 849 (1887). An unconstitutional amendment of the indictment occurs when the charging terms are altered, either literally or constructively, such as when the trial judge instructs the jury. In contrast, a variance occurs when the charging terms are unaltered, but the evidence offered at trial proves facts materially different from those alleged in the indictment. See United States v. Zingaro, 858 F.2d 94, 98-99 (2d Cir.1988). Variances are subject to the harmless error rule and thus are not grounds for reversal without a showing of prejudice to the defendant. Constructive amendments, however, are per se violative of the Fifth Amendment. See id. at 98; United States v. Weiss, 752 F.2d 777, 787 (2d Cir.), cert. denied, 474 U.S. 944, 106 S.Ct. 308, 88 L.Ed.2d 285 (1985). A defendant is deprived of his right to be tried only on the charges returned by a grand jury when an essential element of those charges has been altered. See Zingaro, 858 F.2d at 98; Weiss, 752 F.2d at 787. Nevertheless, even an amendment or variance that does not alter an essential element may still deprive a defendant of an opportunity to meet the prosecutor’s case. See Weiss, 752 F.2d at 789 (citing Berger v. United States, 295 U.S. 78, 55 S.Ct. 629, 79 L.Ed. 1314 (1935)). However, the indictment and the jury charge in the instant matter comported with one another in all essential respects, and Mrs. Helmsley had adequate notice of the conduct she was called upon to defend. 1. Count 1: Conspiracy Count 1 charged defendants with conspiracy in violation of 18 U.S.C. § 371. Judge Walker instructed the jury that it could return a guilty verdict if they found that a conspiracy existed either to defraud the United States or to violate one of four specific federal statutes set forth in the indictment. These statutes were 26 U.S.C. § 7201 (income tax evasion), 26 U.S.C. § 7206(1) (filing false returns), 26 U.S.C. § 7206(2) (assisting in the filing of false returns), and 18 U.S.C. § 1341 (mail fraud). Mrs. Helmsley argues that the indictment alleged only the four specific statutory violations as objects of the conspiracy, and did not allege defrauding the United States as a fifth object. The general federal conspiracy statute, 18 U.S.C. § 371 (1988), reads in pertinent part: If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined not more than $10,000 or imprisoned not more than five years, or both. Section 371 thus defines two ways in which its provisions are violated: (1) conspiring to commit “offenses” that are specifically defined in other federal statutes, and (2) conspiring to “defraud the United States.” These offenses overlap when the object of a conspiracy is a fraud on the United States that also violates a specific federal statute. See United States v. Rosenblatt, 554 F.2d 36, 40 (2d Cir.1977). The instant indictment unambiguously charged Mrs. Helmsley under both the offense clause and the defraud clause. In plain terms, paragraph 25 alleged: [Defendants] did unlawfully, wilfully and knowingly combine, conspire, confederate and agree together ... to commit offenses against the United States, to wit, violations of Title 26, United States Code, Sections 7201 and 7206, and Title 18, United States Code, Section[s] 1341, and to defraud the United States and an agency thereof, to wit, the Internal Revenue Service of the United States Department of Treasury. (emphasis added). This statement, along with paragraphs 30-45, which detailed the particulars of the conspiracy, were sufficient to charge a defraud clause violation and to put Mrs. Helmsley on notice with respect to that violation. See United States v. Lane, 765 F.2d 1376, 1380 (9th Cir.1985). • Mrs. Helmsley argues that because her indictment did not employ the language of the indictment in United States v. Klein, 247 F.2d 908, 915 (2d Cir.1957), cert. denied, 355 U.S. 924, 78 S.Ct. 365, 2 L.Ed.2d 354 (1958) — “impeding, impairing, obstructing and defeating the lawful functions of the Department of the Treasury in the collection of the revenue; to wit, income taxes” — it did not sufficiently charge her with violating the defraud clause of Section 371. Although the Klein language may have become customary boilerplate in defraud clause indictments, it is not legally required. What is required is only that an indictment charging a defraud clause conspiracy set forth with precision “the essential nature of the alleged fraud.” Rosenblatt, 554 F.2d at 42; see Dennis v. United States, 384 U.S. 855, 860, 86 S.Ct. 1840, 1843, 16 L.Ed.2d 973 (1966); Russell v. United States, 369 U.S. 749, 765, 82 S.Ct. 1038, 1047, 8 L.Ed.2d 240 (1962). Paragraphs 30-45, which particularize the alleged scheme to charge personal expenditures for Dunnellen Hall to Helmsley-con-trolled business entities, were more than sufficient to hone the broad language of Paragraph 25 into a pointed allegation of a specific fraud. Nor does the absence of defraud clause allegations in the section of Count 1 entitled “Objects of the Conspiracy” render the indictment defective. That section contained four paragraphs (numbers 26-29), reciting the language of each of the four federal statutes that the defendants allegedly conspired to violate. By definition there is no specific statutory language to recite in conjunction with the fifth object— defrauding the United States. As discussed, paragraphs 30-45 sufficiently detail that object to create a proper indictment. Thus, because Count 1 of the indictment alleged the same five objects as contained in the jury charge on that count, there is no chance that the jury convicted Mrs. Helmsley of something other than that for which she was indicted. See United States v. Mollica, 849 F.2d 723, 729 (2d Cir.1988); Weiss, 752 F.2d at 788-89. Alternatively, Mrs. Helmsley contends that, if Count 1 sufficiently alleged both offense clause and defraud clause violations of Section 371, then that count is invalidly duplicitous because of the possibility of a non-unanimous jury verdict. See United States v. Gordon, 844 F.2d 1397, 1401 (9th Cir.1988). She posits that some jurors may have convicted for offense clause violations and other jurors for a defraud clause violation. However, any possibility of a duplicitous verdict was removed by Judge Walker’s careful charge regarding unanimity on Count 1: In this case, the defendants are charged with conspiring to accomplish five different illegal objectives. T