COX, Circuit Judge:
Robert J. (“Jack”) Mills and his wife, Margie B. Mills,1 appeal their convictions and sentences for false statements, mail .fraud, Medicare fraud, and witness tampering. We affirm their convictions and vacate their sentences. The Government cross-appeals the district court’s post-trial judgment of acquittal on several mail fraud counts against Jack. We reverse.
I. Facts-
The Millses were officers and majority shareholders of a Medicare services provider, ABC Home Health Services, Inc., which later became First American Health Care of Georgia, Inc.2 Over sevéral years they used their positions to cheat the Medicare program out of millions of dollars. A reasonable jury could have'found the following facts true based on the evidence. Some detail Is necessary because of the harmless-error and sufficiency-of-the-evidence issues that are presented.
A. Background
The Medicare home-health care system has three players. First, care providers such as First American care for patients in exchange for reimbursement of their reasonable patient care-related expenses. The second player, the fiscal intermediary, holds the purse strings to reimbursement funds under contract with the third player, the Health Care Financing Administration, a government agency. Fiscal intermediaries, like providers, are entitled only to return of their costs in exchange for their services. Aetna Life Insurance Company was First American’s intermediary during most of the time period relevant here.
Providers generally receive biweekly payments in an amount based on quarterly figures of how many patients the provider has visited and how much each visit cost. At year end, providers submit an annual “cost report” for a true-up with the sum of these interim payments. If the total interim payments exceed-the provider’s actual allowable expenses as determined by the cost report, the provider owes the intermediary money. If, on the other hand, the provider’s actual allowable expenses surpass the total periodic payments, the intermediary pays the provider. In practice, Aetna subjected First American’s cost reports to a detailed audit, and this true-up for years as far back as 1990 was incomplete at the time of trial.
Jack brought a businessman’s outlook to this cost-based system. He dreamt of making First American profitable, a goal impossible in ■ the current program. Jack also enjoyed the perquisites, such as corporate airplanes and golf retreats, that First American’s growth brought, and according to every witness but him, he ran First American as an autocratic founder. Jack naturally bridled at Aetna’s audits and intrusion, believing that Aetna. was “telling him how to. run his business.” (R.31 at 236.). He judged the auditors to be “more dangerous than a punk with a gun.” (R.37 at 281.)3 When Aetna obtained potentially damaging information from First American, which had to keep its books open for audit, Jack, memoed employees that when he “f[ou]nd out which person or persons are involved in passing out First American confidential information, they better give their heart and soul to God because I will sure own every part that is left.” (R.32 at 68.) At a leadership conference speech to First American employees, shown at trial on videotape, he boasted of “challenging” “the feds” and breaking the rules. (R.41 at 480.)
Not surprisingly, First American and Jack had a history of disputes with fiscal intermediary auditors. In the mid-1980s, disputes arose between Blue Cross and Blue Shield of Georgia, then First American’s auditor, over Jack’s use of airplanes to get around; Jack took the position that his family life warranted the substantial additional expense [931]*931to Medicare. In 1988, First American fought its assignment to Aetna as its intermediary, going so far as to petition Congressmen. In 1989, Aetna threatened to withhold interim payments because First American had denied access to records. In 1990, Aetna reported First American to the Office of the Inspector General because of perceived irregularities and withheld interim payments because of a sudden and unexplained increase in costs. In 1991, Aetna disallowed salaries paid to former Georgia senator Bill English and Atlanta City Council member Ira Jackson because they related not to patient care, but to marketing and agency acquisition costs. Jack’s attitude, these conflicts with Aetna, and chronic cash-flow problems perhaps led Jack and First American to develop sophisticated schemes to disguise questionably reimbursable expenses as reimbursable. The schemes involved five categories of expenses.
B. The Schemes
1. Personal Use of Medicare-Reimbursed, Airplanes
First American owned, leased, or borrowed several airplanes, including a $2.8 million King Air jet, that its executives used for business travel. Aetna policies did not prohibit reimbursement of the corporate airplane costs. Aetna was skeptical, however, that corporate planes were a fiscally prudent way to fill First American’s travel needs. In 1990, following the purchase of the King Air, Aetna agreed nonetheless to reimburse First American for its plane installment payments, provided that at least 90% of the plane’s flight time was reimbursable, patient care-related travel. Aetna also consented to reimburse expenses such as maintenance and pilot salaries prorated to the percentage of time spent on business travel. In 1991, Aet-na demanded and First American agreed to provide further documentation of the planes’ use so that Aetna could measure the reimbursable use of the planes. That documentation included records of the purpose, passengers, length, and destination of every flight.
During and after these discussions with Aetna, Jack and Margie took First American planes on dozens of personal trips — twelve round trips alleged in the indictment, 72 total found by investigators — that included visiting their mothers, sunning in Cozumel, viewing prefab columns in llallas that they wished to incorporate into their new mansion, and attending their high school reunions and sports events like Auburn University football games.4 They also transported non-First American-related passengers, including their children, both Millses’ mothers, then-Governor of Alabama Jim Folsom, Georgia Speaker of the House Tom Murphy, and University of Georgia football coach Vince Dooley.
The costs allocable to this personal use would not have been reimbursable, of course, under the arrangement with Aetna. If this use rose over 10% of total flying time, moreover, it threatened reimbursement for the King Air payments. First American, at Jack’s direction and with the cooperation of the chief pilot, Jim McManus, therefore undertook to disguise and conceal personal use. They used several methods. First, passengers with no business purpose for traveling would not appear on passenger manifests— so-called “ghost passengers.” Second, pilots would pull a circuit breaker to prevent the planes’ hour meter .from adding the flight time during personal flights to the planes’ total flight time; thus, these “breaker” or “ghost” flights would not lower the percentage of patient care-related flight time. Many breaker flights left no trace in company records, although First American employees would schedule the flights on Post-Its, some of which were in evidence, inserted in the airplane schedule book. Other breaker flights were listed in the company flight log with false or omitted destinations. Yet another method for concealment had pilots pad their Medicare-reimbursable expense reports with extra meals to recover expenses incurred during these “breaker flights.” First American rounded out the scheme in 1991 meetings with Aetna auditors about documentation; there, Jack and First American’s counsel, Wayne Phears, denied knowing of [932]*932“breaker flights”5 and indeed berated Aetna for not trusting First American’s records.
2. Kickbacks on Aviation Fuel Purchases
First American purchased most of its fuel and leased hangar and office space from Golden Isles Aviation, Inc., on St. Simons Island. For some time, Golden Isles had discounted the fuel sold to First American because of the volume purchased. When First American leased new hangar and office space, however, the companies struck a new deal. Golden Isles would continue to charge less'for the fuel First American purchased according to a volume-based stepped percentage. But the difference between retail and First American’s price would go into a rebate account with Golden Isles. Golden Isles initially applied the rebate account to renovation costs for First American’s hangar, but later the rebates went to pay other maintenance expenses. Jim McManus would typically present invoices to Golden Isles to be paid out of the rebate account, or he would charge bills on a credit card paid by Golden Isles out of the rebate account. Checks from this account also reimbursed Jack for fuel he bought for some personal flights; thus, although it would appear that. Medicare was not fueling the flights, through the rebate mechanism it was.
First American and Jack never disclosed this arrangement to Aetna. Rather, First American reported the full fuel cost as part of its travel expenses. Thus, First American had the advantage of using the rebate money without having to justify the relation between the expenditures and patient care.
3. Lobbying Expenses
Medicare reimburses providers only their actual costs for patient care. Thus, Medicare providers cannot make a profit. A legislative proposal exists, however, that would change this system. Under the proposal, called the “prospective payment system,” or “PPS,” providers would receive a flat fee for patient care. Hence, an efficient provider — or one that successfully inflated the baseline costs on which the flat fee rested — could realize a profit. As Jack explained in a speech to First American employees, with PPS First American could go public and make lots of money.
For this reason, Jack hired lobbyists to promote PPS. Some were politicians, such as former Georgia senator Mack Mattingly, whom First American hired as a “consultant” to introduce Jack to influential lawmakers and to exploit his connections for First American’s benefit. Others were full-time, professional. lobbyists. One of these was Paul Berry, a former roommate of President Clinton’s. First American hired Berry, a federally registered lobbyist, in 1992 and 1993. Although nominally a “consultant,” Berry in fact lobbied for First American. For example, he memoed Jack a recitation of his progress in persuading lawmakers of PPS’s advantages. And Jack himself described Berry’s job as help with the “project” of “get[ting] prospective pay” so that First American could go public. (R.41 at 483.) Furthermore, Berry’s functions included introducing the Millses to Capitol Hill staffers and members of President Clinton’s newly formed health care task force. Another lobbyist was Steve Clark, a former attorney general of Arkansas and friend of President Clinton’s, who was hired as a “vice president of managed care.” Clark was well connected and' succeeded in getting Jack into a foursome with Donna Shalala, Secretary of Health and Human Services, at a charity golf tournament in Texarkana.
In addition to exploiting their networks, Clark and Berry worked hand-in-glove with two Washington lobbying firms — one Democrat. and one Republican — Global USA and the Borden Group. Together, they orchestrated a large First American campaign focused on changing certain proposed legislation. This campaign included television advertisements that were facially for nurse recruitment, but were in fact intended to influence congressmen at home during recess. The drive also involved a mass distribution of a pro-PPS position paper to First American employees with the instruction for them to retype it and send it as a “letter to the editor” to their local papers. [933]*933Some of this lobbying activity was nominally for the American Federation of Home Health Agencies, an organization that Jack claimed to control.
Lobbying costs are not reimbursable. First American’s lobbying expenses were therefore reported on First American’s cost reports as consulting expenses, which are reimbursable. There was no mistake here: Borden Group bills were indeed originally taken off First American’s cost report by First American’s reimbursement department. At Jack’s direction, however, the bills were claimed on the report. And these misrepresentations were backed up by well-engineered paperwork. For instance, the check request generated to pay Mattingly’s fee for introducing Jack to important politicians showed the purpose of the cheek as “consulting fee for matters relating to existing regulations” — an arguably reimbursable cost. All the contracts with the Other lobbyists were couched in “consulting agreement” terms; Berry’s contract in fact forbade him from lobbying.
4. Political Contributions
In June 1991, during a Georgia gubernatorial campaign, Jack pressured seven First American executives to atténd a Zell Miller fundraiser. In fact, one executive, William Edwards, was called from vacation in the midst of home-moving and asked to attend the function. All seven executives made $500 contributions, which were then reimbursed by way of “bonuses” that were reported to Aetna as reimbursable salary expense. Jack testified that the contributions, were purely coincidental to the bonuses, but there was no evidence that any executive who had not made a contribution received a $500 bonus at this time. When a similar scheme led to a federal indictment against another Medicare company, Jack told the worried executives that Georgia Attorney General Michael Bowers had provided First American immunity from prosecution for its actions. Bowers, who testified at trial, denied ever granting immunity to any First American-related person.
On two prior occasions, attempts to force lower-level employees to make campaign contributions were defeated by First American executives. In one, Jack sought to have First American’s Florida employees contribute $100 apiece to the Lawton Chiles campaign, to be reimbursed by adding mileage to expense reports. Jack ultimately withdrew this request, persuaded by a Florida manager that it would get the company in trouble. Jack’s demand of an Alabama manager to make, campaign contributions, again to be reimbursed by padding expense reports, failed because First American’s accounting department refused to approve the expense reports.
5. “Salaries” to Former Owners of Acquired Agencies
First'American was growing rapidly during the late eighties and early nineties; in 1985, it operated only in Georgia, and by 1994 it was in 23 states. The company achieved this rapid expansion by acquiring local home health care providers, often those that were in financial difficulty. First American’s cash-flow predicament, however, made it difficult for it to pay for even these ailing agencies. Medicare would not pay for First American’s acquisition of other agencies’ goodwill.
Jack solved this problem in a few cases by inducing the owners of acquired agencies to sell by putting them on First American’s payroll to be “community relations” specialists or, as one was told, “vice president of smiles.” (R. 36 at 98-99.) Although the detáils differed from owner to owner, a common thread was that the jobs were sinecures that required a few hours of marketing work a week with no patient care-related responsibilities. Those who sought to do more were rebuffed. Many of these owners in fact pursued other enterprises, such as private health care work or real estate management.' For instance, Catherine Brown, former owner of an agency in San Antonio, received $60,000 a year for five years as “salary.” After an initial transition period, however, she performed almost no work for First American, working instead on her separate private-care business. Brown’s secretary also received a First American salary while performing virtually no work for First American. In all [934]*934these instances, First American was careful to maintain an appearance of employment, firing the former owners when — as in the ease of one Michigan former owner who was imprisoned — they were patently unable to work. Time sheets, often signed in blank by the owners, were also kept.
Another aspect of some of the agency acquisitions suggests that a purchase scheme motivated the sinecures’ creation. ' First American avoided paying out of pocket more than a few thousand dollars for any agency, enough to cover the tangible assets such as furniture. Many of the owners had substantial liabilities, however, that they had guaranteed personally. Jack’s solution to this problem was to encourage the agencies to delay reporting the purchase to the fiscal intermediary and to continue receiving periodic interim payments, which the owners would use as they pleaded. Although the agency would owe those payments back to the government, the agency’s sale of its assets to First American would prevent the government from ever collecting the money. Meanwhile, the liabilities would be paid, and the owner would walk away with a handsome employment contract.
The importance of this trick to First American’s acquisition scheme is illustrated by two instances when owners balked at delaying report of the sale. In the case of one California agency, .First American refused to honor the owner’s employment contract, which prompted litigation that ended in a judgment in the owner’s favor. A New Mexico agency owner refunded the interim payments rather than use them to pay off debts; First American then refused to a honor a contingent note intended to cover the agency’s debts left over after the interim payments. Although several former owners independently testified to the existence of this strategy, Jack and current First American employees denied they ever proposed it.
6. Margie’s Misrepresentations
The jury convicted Margie of only two acts of falsification. Both related to one trip in a First American plane. Margie filled out and signed two Aetna-mandated passenger manifests to report that she traveled in August 1992 from St. Simons, Georgia to San Antonio and back in connection with First American’s acquisition of a home health care provider in Texas. In fact, Margie went to Mobile, Alabama, where the plane stopped en route, to attend her high school reunion. She did not return on the flight back from San Antonio.
7: Jack’s Witness Tampering
During the grand jury investigation that led to the indictment in this case, a First American executive, William Edwards, was subpoenaed to testify concerning the campaign contributions that Jack had. asked First American executives to make to the Zell Miller gubernatorial campaign and that were reimbursed as bogus bonuses. Edwards at that time had decided to resign from First American. Having obtained a copy of the subpoena, however, Jack offered Edwards about $100,000 to remain in First American’s employ until after he had testified before the grand jury. Jack was concerned about the impression it would create for Edwards to resign so soon before testifying. Jack informed Edwards of the company line: that the bonuses were real bonuses, and that the use of the bonuses to make campaign contributions was merely encouraged, not coerced. Edwards refused the offer and resigned.
II. Procedural History
A grand jury indicted Jack and Margie with First American, a First American accountant, and James McManus. The 82-count indictment included, against various defendants, one count of conspiracy in violation of 18 U.S.C. § 371; multiple counts of mail fraud in violation of 18 U.S.C. § 1341; receipt of Medicare kickbacks in violation of 42 U.S.C. § 1320; falsification of documents submitted to the government, in violation of 18 U.S.C. § 1001; money laundering in violation of 18 U.S.C. § 1957;- filing false tax returns in violation of 26 U.S.C. § 7206; and one count of witness tampering in violation of 18 U.S.C. § 1512. McManus pleaded guilty to the conspiracy charge and testified against the other defendants.
[935]*935Following trial, Jack was convicted of all counts except those for tax evasion. Margie was convicted on only two counts of false statements, both related to the high school reunion flight to Mobile. First American was convicted on all counts against it, and the accountant was acquitted. Following the verdict, the district court granted Jack a judgment of acquittal for mail fraud counts predicated on the mailing of payments for one of First American’s planes.
Jack and Margie have appealed. Of the many issues they raise, only three merit discussion. We reject their other challenges, which are set out in the margin, without further discussion. See 11th Cir. R. 36-1.6 The Government has cross-appealed, asserting that the district court improperly granted pretrial judgments of acquittal on several mail fraud counts. We address each of these four issues in turn.
III. Discussion
A. Prior-Act Evidence Admitted Under Fed.R.Evid. U0k(b)
Margie asks for reversal of her convictions because the district court admitted evidence that in 1993, when she returned from a trip to Europe, she concealed from customs inspectors a purchase of jewelry subject to duty.7 The district court concluded that the evidence was admissible under Federal Rule of Evidence 404(b) because it showed Margie’s “propensity” to conceal facts and was thus relevant to Margie’s intent. (R.19-462 at 28.) This court reviews the district court’s evidentiary rulings for abuse of discretion. United States v. Diaz-Lizaraza, 981 F.2d 1216, 1224 (11th Cir. 1993). Admitting the evidence was an abuse of discretion, but the error is not reversible.
Rule 404(b) provides that evidence of offenses other than those charged is admissible only for purposes other than showing character. The Rule has been construed to require a three-part test for admissibility of such “other offenses” evidence. First, the evidence must be relevant to an issue other than the defendant’s character. Second, there must be sufficient proof that the defendant committed the extrinsic, act. Third, the evidence must survive the balancing test prescribed by Federal Rule of Evidence 403. United States v. Miller, 959 F.2d 1535, 1538 (11th Cir.1992) (en banc); United States v. Utter, 97 F.3d 509, 513 (11th Cir.1996). The proponent.of the evidence can satisfy the first prong by showing that the evidence is probative of the defendant’s “motive, opportunity, intent, preparation, plan, knowledge, or absence of mistake or accident,” if any of these are in dispute. Fed.R.Evid. 404(b); see United States v. Diaz-Lizaraza, 981 F.2d 1216, 1224 (11th Cir.1993).
The issue here turns on the first prong; the evidence is ample to satisfy the second prong, and we need not reach the third prong. The Government contends that the first prong is satisfied because the customs incident is relevant to Margie’s intent. Margie was charged with violating 18 U.S.C. § 1001, and its intent element requires the Government to prove that Margie wrote the false information on the manifests knowing it was false and intending to make the falsé statement. See Arthur Pew Const. Co. v. Lipscomb, 965 F.2d 1559, 1576 (11th Cir. 1992); United States v. Lange, 528 F.2d 1280, 1288 (5th Cir.1976). According to the [936]*936Government, the misrepresentation to customs is relevant to this .required knowledge and intent because it shows Margie’s “willingness to engage in intentional deception of government agents ... for personal financial gain.” (Gov’t Br. at 37.) Restated, the Government’s asserted relevant inference is that we can gather from the customs incident that Margie is disposed to lie to the government; therefore, being a liar, she must have intended to lie on the passenger manifests. This inference is precisely the one that Rule 404(b) prohibits: it makes an element'of the crime (intent to lie) more probable because of the defendant’s character (liar). Cf. United States v. Utter, 97 F.3d 509, 513-14 (11th Cir.1996).
Furthermore, the differences between Margie’s falsification of the customs declaration and the falsification of the passenger manifests are simply too great to make the customs incident relevant to Margie’s intent in any other way. Cf. United States v. Young, 39 F.3d 1561, 1573 (11th Cir.1994) (evidence of moonshining is not relevant to intent to distribute marijuana because the acts are not sufficiently similar). The key dispute at trial relating to intent was whether Margie knew enough about Aetna’s reporting requirements, or even about the meaning of the passenger manifests themselves, to know if what she was writing was false. The customs incident makes Margie’s knowledge about the passenger manifests neither more nor less likely. The concealment of the jewelry was unrelated to the Medicare fraud scheme, so it does not imply that Margie participated in Jack’s scheme and is therefore more likely to have willfully lied about her destination and travel purposes. The customs declaration form was different from the passenger manifests, and Margie’s interpretation of the customs form accordingly casts no light on her understanding of the passenger manifest. This failure of relevance to any issue other than Margie’s character makes the admission of the customs incident evidence an abuse of discretion.
The error does not, however, compel reversal because we conclude that it had n,o substantial influence on the jury’s guilty verdict on the two § 1001 counts. Cf. Young, 39 F.3d at 1573 (11th Cir.1994) (refusing to reverse a judgment for improper admission of 404(b) testimony, because evidence did not prejudice the defendant’s substantial rights). There was overwhelming evidence that Margie intentionally falsified the passenger manifests. The manifests themselves were in evidence, and First American’s general counsel, who was on the flight, testified that contrary to the manifest representations Margie did not travel on those flights to San Antonio for business purposes. The organizer of the high school reunion the Millses attended testified to their presence, and a videotape of the reunion showing them was introduced in evidence. Margie’s counsel did not cross-examine these witnesses and offered no contradictory evidence. There was copious evidence, moreover, about Margie’s other personal use of First American’s planes, including testimony that Margie had herself directed “ghosting” of passengers. Furthermore, the passenger manifest that she falsified listed each of several passengers on the plane with a separate entry, making it implausible that she would have misunderstood the “from” and “to” lines to refer to the plane’s destination and not to hers.8 Finally, the jury’s not-guilty verdict on most of the falsification counts against Margie implies that the jury’s consideration was not tainted by evidence of the customs incident, or any inference from the incident that Margie was a liar.
B. Denial of the Opportunity to Cross-Examine
Jack contends that the district court denied him his Sixth Amendment right [937]*937to confront witnesses against him by totally denying him the opportunity- to cross-examine one witness. During the trial, the district judge became impatient with the cross-examinations conducted by First American’s and Jack’s counsel. The judge objected to .the “jam-up honey deal” the judge perceived between Jack and his majority-held corporation that led their lawyers to conduct “tag team” cross-examinations representing the same interest. (R.33 at 435; R.34 at 44.) Ultimately, the judge forbade Jack’s counsel from examining a Government summary witness, Patricia Terris, at all. The court demanded rather that Jack share First American’s counsel for the cross-examination. Jack objected9 and now contends that the ruling compromised his Sixth Amendment confrontation rights. We consider de novo the legal question of the scope of Jack’s constitutional rights, see Kennedy v. Herring, 54 F.3d 678, 682 (11th Cir.1995), and we agree with Jack. The error, however, is harmless beyond a reasonable doubt.
The Sixth Amendment’s Confrontation Clause provides that “[i]n all criminal prosecutions, the accused shall enjoy the right ... to be confronted with the witnesses against him.” “The central concern of the Confrontation Clause is to ensure the reliability of the evidence against a criminal defendant by subjecting it to rigorous testing, in the context of an adversary proceeding before the trier of fact.” Maryland v. Craig, 497 U.S. 836, 845, 110 S.Ct. 3157, 3163, 111 L.Ed.2d 666 (1990). This concern has prompted the recognition of several different rights guaranteeing adversarial testing of evidence. Accused persons enjoy a qualified right to see witnesses against them in person. See id.; Coy v. Iowa, 487 U.S. 1012, 108 S.Ct. 2798, 101 L.Ed.2d 857 (1988). A variety of out-of-court statements may not be used against the criminal defendant. See, e.g., Lee v. Illinois, 476 U.S. 530, 547, 106 S.Ct. 2056, 2065, 90 L.Ed.2d 514 (1986) (admission of one defendant’s out-of-court confession incriminating his codefendant forbidden in a joint bench trial); Bruton v. United States, 391 U.S. 123, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968) (admission of one defendant’s out-of-court confession incriminating his codefendant forbidden in a joint jury trial); Pointer v. Texas, 380 U.S. 400, 85 S.Ct. 1065, 13 L.Ed.2d 923 (1965) (forbidding admission of transcript of testimony from pretrial hearing in which defendant had no opportunity to cross-examine the witness). .A third protection, which originated with Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974), ensures more than perfunctory adversarial testing by limiting the trial judge’s discretion to restrict the scope of cross-examination. See, e.g., Kentucky v. Stincer, 482 U.S. 730, 737, 107 S.Ct. 2658, 2663, 96 L.Ed.2d 631 (1987); Delaware v. Van Arsdall, 475 U.S. 673, 680, 106 S.Ct. 1431, 1436, 89 L.Ed.2d 674 (1986) (defendant not allowed to cross-examine prosecution witness on key source of bias).
The Government asserts that the judge at worst reached the edge of the discretion permitted under this third protection. Ter-ris was fully cross-examined for all sources of bias, according to the Government, and thus was amply confronted. The Government further points out that Jack cannot point to a single piece of impeaching evidence that the jury did not hear. Thus, the Government concludes, his confrontation-clause rights have not’ been compromised. Cf. e.g., United States v. Baptista-Rodriguez, 17 F.3d 1354, 1370-71 (11th Cir.1994); United States v. Bennett, 928 F.2d 1548, 1554 (11th-Cir. 1996); United States v. Haimomtz, 706 F.2d 1549, 1559 (11th Cir.1983).
The Government’s analysis overlooks what happened here: Jack did not get to cross-examine the witness at all. A trial judge may limit the scope of cross-examination after the defendant has had some opportunity to cross-examine. See, e.g., Haimowitz, 706 F.2d at 1559; United States v. Tolliver, 665 F.2d 1005, 1008 (11th Cir.1982). But because the district judge permitted Jack no cross-examination, the judge was not operating within any discretion to control the progress of the trial. The district judge’s action here differed in quality from [938]*938the error in the Davis line of cases and cannot be judged by their standard.
The judge’s action rather merits its own Sixth Amendment rule in accord with other rules based on the Amendment: A trial judge may not totally deny a defendant the opportunity to cross-examine a witness against him, whatever the time constraints, number of defendants being tried, or relationship between the defendants. See Ferguson v. United States, 329 F.2d 923, 924 (10th Cir.1964). In developing other Sixth Amendment rules, the Supreme Court has repeatedly reminded us that the right to cross-examination lies at the root of the Clause’s guarantees. See, e.g., Delaware v. Fensterer, 474 U.S. 15, 19-20, 106 S.Ct. 292, 294, 88 L.Ed.2d 15 (1985) (“The main and essential purpose of confrontation is to secure for the opponent the opportunity of cross-examination.” (quoting Davis v. Alaska, 415 U.S. 308, 315-16, 94 S.Ct. 1105, 1109-10, 39 L.Ed.2d 347 (1974)) (emphasis in Fen-sterer))-, Chambers v. Mississippi, 410 U.S. 284, 294-95, 93 S.Ct. 1038, 1045, 35 L.Ed.2d 297 (1973) (“The right[] to cross-examine witnesses ha[s] long been recognized as es sential to due process.”); Douglas v. Alabama, 380 U.S. 415, 418, 85 S.Ct. 1074, 1076, 13 L.Ed.2d 934 (1965) (“Our cases construing the [confrontation] clause hold that a primary interest secured by it is the right of cross-examination.”); In re Oliver, 333 U.S. 257, 273, 68 S.Ct. 499, 507, 92 L.Ed. 682 (1948) (among the minimum standards of a fair trial is the defendant’s “right to examine the witnesses against him”); Mattox v. United States, 156 U.S. 237, 242-43, 15 S.Ct. 337, 339, 39 L.Ed. 409 (1895) (“The primary object of the constitutional provision ... was to prevent depositions or ex parte affidavits from being used against the prisoner in lieu of a personal examination and cross-examination of the witness.”). The district judge’s denial of cross-examination was therefore error.
A thornier question is whether the district judge’s error requires reversal. Jack insists that the prohibition on cross-examination amounts to a “structural defect” that is never subject to review for prejudice. . See Arizona v. Fulminante, 499 U.S. 279, 310, 111 S.Ct. 1246, 1264, 113 L.Ed.2d 302 (1991) (describing distinction between “trial errors,” which are subject to harmless-error review, and “structural defects,” which are not). The Government, on the other hand, views the error as one involving the conduct of trial — in other words, a classic trial error that is not ground for disturbing the verdict if the error is “harmless beyond a reasonable doubt.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967); see Fulminante, 499 U.S. at 307-08, 111 S.Ct. at 1264 (trial error is “error which occurred during the presentation of the case to the jury, and which may therefore be quantitatively assessed in the context of other evidence presented in order to determine whether its admission was harmless beyond a reasonable doubt”).
The Government’s argument comports with precedent. While no one could deny the value of the constitutional right to cross-examination, Fulminante’s definitions of “trial error” and “structural defects” make clear that the dividing line is not determined by the importance of the constitutional right. See id. at 306-07, 111 S.Ct. at 1263 (listing examples of appropriate instances for harmless-error analysis and noting that “most constitutional errors can be harmless”). After all, the “harmless beyond a reasonable doubt, standard” already respects the constitutional origin of the right and elevates it over mere statutory or evidence-rule rights. The trial error/substantive defect distinction, rather, rests on how the error affected the trial. On one hand, there are errors that infect the whole proceeding, such as a biased judge or an absence of counsel. In those cases, there is no way of imagining how the trial would have looked to the jury without the constitutional error. See Brecht v. Abrar hamson, 507 U.S. 619, 629-30, 113 S.Ct. 1710, 1717, 123 L.Ed.2d 353 (1993) (structural defects “infect the entire trial process” (emphasis added)); Fulminante, 499 U.S. at 309-10, 111 S.Ct. at 1265. For such errors, it is thus impossible to gauge the error’s effect. On the other hand, trial errors typically relate only to admission or exclusion of a single piece of evidence. Such errors therefore leave enough of a constitutionally acceptable [939]*939trial for the reviewing court to assess the effect of the error on the jury’s verdict. See id. at 310, 111 S.Ct. at 1265. '
This error lands squarely in the trial-error category. What has gone awry is that the jury has heard one witness’s testimony that is tainted by a lack of cross-examination. Put differently, the jury has heard a piece of evidence — Terris’s testimony — that it should not have. In that sense, the error is materially similar to all other Confrontation Clause error. As in the case of Bruton or Davis error, for instance, the jury has heard evidence — in Bruton, an out-of-court statement, here and in Davis, in-court testimony — that has not undergone constitutionally sufficient adversarial testing. And as far as we know, no kind of Confrontation Clause error since Chapman, including Bruton and Davis violations, has escaped harmless-error analysis under the “harmless beyond A reasonable doubt” standard.10 See, e.g., Delaware v. Van Arsdall, 475 U.S. 673, 681-82, 106 S.Ct. 1431, 1436, 89 L.Ed.2d 674 (1986) (restricted cross-examination in violation of Davis); Schneble v. Florida, 405 U.S. 427, 430, 92 S.Ct. 1056, 1059, 31 L.Ed.2d 340 (1972) (Bruton error); see also Coy v. Iowa, 487 U.S. 1012, 1021-22, 108 S.Ct. 2798, 2803, 101 L.Ed.2d 857 (1988) (denial of face-to-face confrontation). In all of these cases, most of the trial was unaffected, and there is therefore a basis on which, to assess prejudice. It is true that we cannot know what the cross-examination would have revealed. But if the impossibility of knowing what weaknesses cross-examination would have exposed does not bar harmless-error analysis- of Bruton,' Davis, or Coy error, it should not do so here.
The effect of the error in this case is so closely analogous to that of restricted cross-examination that we can readily look to the harmless-error analysis conducted in such cases for guidance. The Supreme Court has noted five factors to consider in such harmless-error analysis: (1) how important the witness’s testimony was to the prosecution’s case; (2) whether the testimony was cumulative; (3) the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points; (4) the extent of cross-examination otherwise permitted; and (5) the overall strength of the prosecution’s case. Van Arsdall,. 475 U.S. at 684, 106 S.Ct. at 1438. In the present circumstances, there is one variation. For the fourth element we look to the cross-examination conducted by other defendants, rather than the complaining defendant’s, to gauge the ultimate effect of Terris’s testimony on the jury.
The denial of cross-examination is not reversible error in light of these factors. First, Terris was not a vital witness for the prosecution. An auditor, she testified merely as the author of a series of summary charts that depicted the Government’s calculation of the total loss to Medicare from Jack’s fraud. She knew nothing of the offense conduct; the key evidence of Jack’s scheme came from other witnesses and' the underlying documents. The auditors from Aetna and First American’s later fiscal intermediary, Blue Cross and Blue Shield of Iowa, and witnesses with personal knowledge, such as the pilots, former employees, executives, and lobbyists, all testified as to the actual misrepresentations in the cost reports and the extent of the mail-fraud scheme. Terris’s name was mentioned only twice in the Government’s closing argument, and then only'in passing. While Terris’s testimony may have inclined the jury more to convict because it exposed the magnitude of Jack’s crime, the documentary and testimonial evidence of guilt was so great that this additional piece would not have changed the jury’s verdict.
Second, as a summary witness, Terris provided testimony that was by definition cumulative. She testified only as to her analysis of First American’s financial records and reports that were in evidence. She had no personal knowledge of any of the information behind the financial reporting and so testified. The third factor yields the same result: Terris’s testimony was corroborated and ver[940]*940ifiable by inspecting the financial documents on which she based it.
Fourth, cross-examination by other lawyers provided a basis to argue Terris’s lack of reliability. First American’s lawyer pointed out a typographical error in Terris’s financial calculations. Other counsel pointed out that Terris may not have reviewed all relevant documents. Jack therefore had a basis on which to argue at closing that Terris’s calculation of the loss was untrustworthy. In fact, Jack tellingly identifies not a single additional area of impeachment he intended to explore. That suggests that a retrial would simply involve a different jury’s hearing exactly the same evidence.
Finally, the prosecution’s case was strong. The Government presented testimony from several of the pilots about ghost flights and ghost passengers, personal logs from the pilots showing the ghost flights, and even Post-Its with notes from Jack requesting ghost flights. The secretary, the pilot, and the fuel seller who arranged and then operated the kickback scheme all testified to Jack’s involvement, and checks written to Jack were offered to corroborate their testimony. Several i non-nurse agency owners, including some who did not sell, independently and consistently testified about First American’s employment-based acquisition scheme. First American’s lobbyists, whose expenses were claimed as consulting fees, testified to their lobbying activities; memoranda describing those activities were in evidence. Finally, executives who participated in the campaign contributions testified to the pressure they were under to contribute in exchange for a refund, and the circumstances — one executive was called in the middle of house-moving to attend the fundraiser, and another had never contributed to a campaign before giving this $500 — corroborate their testimony. And Jack admitted that the bonuses (although described as being for superior performance) were in fact intended to be used for campaign contributions.
The defense did not meet this assault. With witness after witness, the defense was limited to diverting attention. For example, it tried to show that the executives who made political contributions at Jack’s instance might have made the contributions anyway. With the lobbyists, the defense focused on the merits of PPS and the innoeuousness of lobbying per se. The defense impeached some former owners with criminal histories and lawsuits against First American; from others, it elicited testimony about their respect for First American’s professional standards; for others, it showed that some work had been done; and the defense offered evidence of other, lawftd acquisitions. But apart from eonelusory testimony of current First American employees, the defense offered no evidence that any of the former agency owners at issue worked full-time. As to the airplane-related scheme, the defense contended that the falsified and omitted records were not required and that Jim Mc-Manus had a scheme of his own that happened to benefit the Millses, not him. Throughout, the defense emphasized that Medicare regulations are complex, that Aet-na was evil, and that the true economic losses to Medicare were minimal,11 but it did not offer evidence suggesting that the various falsifications and misrepresentations were good-faith attempts to seek reimbursement in grey areas. In essence, the overarching defense was that the alleged frauds were legitimate self-defense against intrusive bureaucracy. As Jack vividly put it, “[t]he moment you put [a cost] on there and protest it, you might as well put bells and whistles on it because you know it’s coming out.” (R.48 at 95.) The absence of Terris’s summary testimony would neither have weakened the Government’s case nor enhanced the defense strategy.
[941]*941All factors point to the error’s harmlessness. We conclude that the total denial of an opportunity to cross-examine, while constitutional error, was harmless beyond a reasonable doubt.
C. Enhancing Sentences for Breach of Trust.
Both Margie and'Jack challenge the district court’s two-level increase, under U.S.S.G. § 3B1.3, of their offense levels for abuse of a position of trust. They argue that the victim was the United States, and that because they owed only contractual, and not fiduciary, duties to the United States, they have breached no cognizable trust. We review the district court’s fact findings for clear error, but its determination whether the facts justify an abuse-of-trust enhancement we review de novo. United States v. Rummer, 89 F.3d 1536, 1546 (11th Cir.1996).
After submission of this case, another panel of this court resolved this issue in the Millses’ favor. A breach-of-trust enhancement under § 3B1.3 is not appropriate unless the victim of the breach itself conferred the trust. United States v. Garrison, 133 F.3d 831, 844-46 (11th Cir.1998). And a Medicare-funded care provider, as a matter of law, does not occupy a position of trust visa-vis Medicare. Id. at 852-53. The Millses’ sentences could therefore not be enhanced because of any breach of public trust by lying to Medicare.
The • Millses’ presentence reports, however, also found that they abused their positions of private trust as officers of First American. Arguably, First American was a victim of the Millses’ crime; because of their actions, it incurred extensive criminal liability and the burden of increased government oversight. But Garrison apparently requires us to hold that the United States is, as a matter of law, the only possible victim of a Medicare-fraud crime and that therefore this private position of trust is irrelevant. See id. at 848 (noting that Garrison was CEO of a health care provider). Section 3B1.3 does not therefore apply to the Millses, and they are entitled to resentencing without the enhancement.
D.. Judgment of Acquittal on Mail Fraud Counts
The Government cross-appeals the district court’s judgment of acquittal for Jack on counts 2-5 and 7 after the jury found him guilty on those counts. These mail fraud counts were predicated on the mailing of checks to Beech Aircraft Acceptance Corporation as payment' for the First American-owned King Air jet. The district court accepted Jack’s argument that there was insufficient evidence to support conviction on these counts because the checks followed the achievement of the fraud’s object (receiving interim payments from Aetna), and that they were thus not necessary to the scheme. We review, the grant of the judgment of acquittal de novo, drawing all reasonable factual inferences in favor of the jury’s guilty verdict. See United States v. Massey, 89 F.3d 1433, 1439 (11th Cir.1996), cert. denied, — U.S. -, 117 S.Ct. 983, 136 L.Ed.2d 865 (1997); United States v. Garcia, 13 F-3d 1464, 1473 (11th Cir.1994). We reverse.
A mailing is of course one element of mail fraud. See United States v. Brown, 40 F.3d 1218, 1221 (11th Cir.1994), cert. denied, 514 U.S. 1092, 115 S.Ct. 1815, 131 L.Ed.2d 738, and cert. denied, 514 U.S. 1121, 115 S.Ct. 1985, 131 L.Ed.2d 872 (1995). The mailing may be perfectly innocent as long as it is “incidental to an essential part of the scheme” to defraud or a “step in the plot.” Schmuck v. United States, 489 U.S. 705, 714, 109 S.Ct. 1443, 1449, 103 L.Ed.2d 734 (1989). The mailing can, therefore, follow the achievement of the object of the fraud, since it may be. essential, for example, to avoid detection or to lull the victim into complacency. United States v. Allen, 76 F.3d 1348, 1363 (5th Cir.1996), cert. denied, - U.S. -, 117 S.Ct. 121, 136 L.Ed.2d 71 (1997).
The evidence at trial was sufficient to convict Jack of the plane payment-based counts. The jury could reasonably have disagreed with the district judge that the fraud was complete before the payment checks were mailed. The evidence supports the inference that the fraudulent scheme was not one to obtain a single interim Medicare payment, as [942]*942the district judge concluded, but an ongoing one to enjoy private airplane travel at Medicare expense. Under this view of the evidence, the necessity of the payments is evident: No payments, no plane. No plane, no Medicare-funded junkets to Cozumel. That the Millses could have made the same junket in a leased plane, as the district judge observed, is beside the point; that is not our case, and if it were, the mailing of the lease payments would play the same essential role.
This case is indeed analogous to Schmuck Schmuck allegedly engaged in a long-running scheme to buy used cars, roll back their odometers, and sell the cars to dealers at inflated prices. Mail fraud charges against Schmuck rested on the dealers’ mailing of title applications to state authorities after the purchase. The Supreme Court rejected the argument that these mailings were not a proper basis because they followed the achievement of the scheme’s object. The evidence showed, the Court reasoned, a scheme that extended beyond the sale of a single car. Therefore, even if the mailing were unnecessary to the fraudulent sale just completed, it was essential to future sales because without it the scheme could not survive. See Schmuck, 489 U.S. at 714, 109 S.Ct. at 1449-50. Likewise, here the payments were not essential to any portion of the fraud just completed, whether the object is a particular personal plane trip or a bloated Medicare check. But they were essential to the ongoing fraud, since without the possession of the plane the fraud would have collapsed.
We therefore conclude that the evidence was sufficient to convict Jack of mail fraud on counts 2-5 and 7.
IV. Conclusion
For the foregoing reasons, we affirm the Millses’ convictions. We reverse, however, the judgment óf acquittal as to counts 2-5 and 7 against Jack. We also vacate the Mills-es’ sentences and remand for a resentencing that accounts for the convictions on counts 2-5 and 7 and does not include any § 3B1.3 enhancement.
Affirmed in part; reversed in part; and VACATED AND REMANDED IN PART.