United States v. Bernard Greenspan

BIBAS, Circuit Judge. Sometimes, the only plausible explanation for a lab's stream of payments to a doctor is cash for blood. Over seven years, Dr. Bernard Greenspan referred more than 100,000 blood tests to Biodiagnostic Laboratory Services. The Lab made more than $3 million off these tests. In exchange, the Lab gave Greenspan and his associates more than $200,000 in cash, gifts, and other benefits. A jury convicted Greenspan of fraud and of taking bribes and kickbacks. He raises four claims of error. But none warrants reversal, particularly because the evidence of his guilt was overwhelming. First, the District Court suggested at one point that Greenspan bore the burden of proof on his advice-of-counsel defense. And it improperly excluded and limited evidence on this defense. But the unpreserved jury-instruction error did not prejudice him. And the Court's errors in excluding and limiting related evidence were harmless. Second, the Court properly excluded evidence that the blood tests were medically necessary. That evidence was only marginally relevant and risked misleading the jury. Third, we need not decide whether the prosecution constructively amended the indictment to broaden the potential bases for conviction. Even if it did, Greenspan's trial counsel never objected to any amendment. And any error would not have seriously affected the proceedings' fairness, integrity, or public reputation because the evidence was overwhelming and essentially uncontroverted. Fourth, the Court erred in asking only Greenspan's counsel, not Greenspan personally, whether he wished to speak at sentencing. As his counsel explained, Greenspan chose not to allocute and used other ways to plead for leniency. But this was a deliberate tactical choice, and we will not reward this litigation strategy. So we will affirm. I. BACKGROUND Greenspan was a long-time family doctor who ran a solo medical practice. The Lab tests blood samples so doctors, including Greenspan, can diagnose and treat their patients. For years, the Lab made a series of payments to Greenspan and his practice. Most of the Lab's payments are undisputed. The key dispute at trial was whether Greenspan took these payments as bribes or kickbacks in exchange for referring blood tests to the Lab. The prosecution's three cooperating witnesses insisted that Greenspan did, but Greenspan consistently denied it. A. The alleged bribery and kickback scheme Health-insurance companies negotiate low rates for blood tests with labs that are in their network. But they sometimes let out-of-network labs test blood samples and charge higher rates. That creates a lucrative business opportunity for out-of network labs if they can persuade doctors to send blood samples to them. Brothers David and Scott Nicoll bought the Lab and ran it with their cousin, Craig Nordman. All three men eventually pleaded guilty to bribing roughly a hundred doctors for referrals, and testified against Greenspan as cooperating witnesses. In early 2006, David visited Greenspan and persuaded him to start referring blood tests to the Lab. His visit came at an opportune time: Greenspan's medical practice was bleeding cash. As Greenspan's long-time office manager testified, sometimes Greenspan and his staff could not draw a salary. And the doctor complained to his staff weekly that he needed more money. Over the next seven years, Greenspan, his medical practice, his staff, his son, and even his mistress received a variety of benefits from the Lab, David and Scott Nicoll, Nordman, and Nordman's shell company, Advantech. Everyone agreed that Greenspan tried to steer blood to the Lab. On cross-examination, Greenspan admitted that "yes, [he] would try. Yes, [he] would try" to "send the blood to [David's] laboratory" and that "David Nicoll knew [Greenspan] would try to send [David] blood." App. 2523; accord App. 2525. David testified that, right after Greenspan agreed to send blood to the Lab, Greenspan called in his office manager and told her that the office would "do whatever [it] could to help support [David]." App. 1083. The office manager corroborated that Greenspan told that to her: "If you can use [the Lab], use [the Lab]." App. 1614. Greenspan then began sending blood to the Lab. The heart of the case at trial was whether Greenspan was steering blood tests to the Lab in exchange for payments and other benefits. Here are the payments and benefits: 1. Rent payments . Federal bribery, kickback, and fraud laws forbid any quid pro quo for blood-test referrals. But until 2010, New Jersey allowed blood labs to put a phlebotomist (a professional trained to draw blood) in a doctor's office in exchange for rental payments. So David offered Greenspan an on-site phlebotomist plus $2000 per month in rent to accommodate her. Greenspan asked his lawyer, the late Barry Cohen, to review the contract. According to David, Greenspan asked Cohen: "How do we make this contract look legitimate and how do we get it to pass the smell test"? App. 1064. Cohen allegedly reviewed the contract in front of them and advised against using a round number. So the Lab lowered the rent from $2000 to $1992.50 per month and began paying that amount. Greenspan denied that David was present at the meeting and disputed David's account of what was said. In the contract, the Lab promised to pay monthly rent in exchange for the phlebotomist's using 50% of Greenspan's 2000-square-foot office. But those numbers were dubious in several respects. Greenspan's office was only about 1658 square feet, not 2000. And even though the phlebotomist shared access to bathrooms, waiting areas, and other rooms, she occupied only one room that took up less than 5% of the office, not 50%. Though the Lab used very little space, its rent payments began at more than 50% of the rent Greenspan paid for the entire office. And the Lab's rent increased over time. By 2010, the Lab paid more than 66% of Greenspan's rent. And that is not all: Greenspan was also collecting $1750 per month in rent from two other companies that shared some of the rooms supposedly used by the phlebotomist. So Greenspan made a substantial profit from renting his office space. 2. Service fees . On top of its rent, the Lab paid Greenspan service fees for the costs associated with drawing blood. It did so even though it was also providing the phlebotomist and paying her salary to do just that. By 2010, these fees were $1748 per month. 3. Consulting fees . In July 2010, New Jersey banned labs from renting space from and entering into service agreements with doctors. N.J. Admin. Code § 8:44-2.14 (a)(2) (2010). So the Lab ended its rental agreement with Greenspan. Instead, it engaged him as a consultant. David testified that he met with Greenspan in November 2010 to discuss an alternative payment plan. He said that he first offered Greenspan cash payments, but the doctor worried about depositing large amounts of cash each month. So they agreed to pay him consulting fees indirectly through a shell company called Advantech. They also agreed that David's cousin Nordman, Advantech's sole employee, would visit Greenspan once a month for consulting advice. In return, Advantech sent Greenspan $1500 per month, which the Lab reimbursed. Greenspan admitted meeting with Nordman every month for two-and-a-half years and receiving the payments from Advantech. And he admitted knowing that Nordman also worked for the Lab. But he denied meeting with David about the consulting arrangement and denied knowing that the payments came from the Lab. Greenspan claimed that the consulting sessions were legitimate. But just as with the rental agreement, the details were suspect. The unscheduled sessions sometimes lasted for only ten or fifteen minutes. And Nordman and Greenspan's staff testified that the doctor worked during the sessions, seeing patients, filling out charts, taking calls, or dealing with the office staff. Nordman's notes from the consulting sessions corroborate this story. They show that Greenspan asked him questions about the Lab as its sales representative. And they show Greenspan assigning Nordman work, such as picking up his favorite iced tea. Nordman testified that he asked almost no medical questions and that Greenspan never told him anything that was useful to Advantech. Finally, the consulting fee was unusually high. According to his own testimony and records, Greenspan consulted with others for much less; he received between $10 and $175 in fees for up to an hour, and on one occasion $500 for two-and-a-half hours. No one else paid anywhere near $1500 for sessions ranging from ten minutes to an hour. 4. Fee-per-test payments . The one set of payments that Greenspan denied receiving was a series of envelopes of cash. Certain tests were especially profitable for the Lab. So the Lab paid doctors a modest cash bonus for each one they referred to the Lab. Scott testified that he hand-delivered cash payments to Greenspan, and Nordman testified that he left them in Greenspan's desk drawer. The cash payments were not large: at $10 per test, the envelopes often contained little more than $100. And though Greenspan denied receiving these payments, Advantech's careful recordkeeping confirmed them. 5. Christmas parties . Greenspan asked Nordman to pay for two Christmas parties for Greenspan and his staff, in 2011 and 2012. The first cost just under $1000; the second, about $2000. Greenspan admitted asking Nordman for the parties. But he denied knowing that the Lab paid for them. Yet he charged each party to one of the Lab's corporate credit cards. And Scott signed one of the event agreements. So Greenspan's denial was dubious. And his explanation was even more so: Greenspan testified that the expensive parties were Nordman's way of thanking the staff for access to the office and for the occasional snack or "cup of coffee." App. 2549-50. 6. Hiring Greenspan's mistress and son . Next, Greenspan asked David to hire his mistress, whom he had been supporting financially. So the Lab hired her to process data. But she was a bad employee, so the Lab fired her after a year. To make up for her lost income, the Lab increased its service fees to Greenspan by $1000 per month. Greenspan also got the Lab to hire his son. The Lab did not need him, but hired him anyway to enter data. In sum, Greenspan contended that he did nothing wrong. He argued that, at first, New Jersey law let doctors accept rent payments from blood labs. And an on-site phlebotomist was helpful to ensure that patients would complete their blood work. But the prosecution argued that, whatever legitimate reasons Greenspan may have had for the payments, he also took many creative streams of money from the Lab in exchange for his blood-test referrals. B. Procedural history A grand jury charged Greenspan with accepting kickbacks, in violation of 42 U.S.C. § 1320a-7(b)(1)(A) ; using interstate facilities with the intent to commit commercial bribery, in violation of 18 U.S.C. § 1952 (a)(1), (3) ; committing honest-services wire fraud, in violation of 18 U.S.C. §§ 1343 , 1346 ; and conspiracy to do all of the above. The trial lasted sixteen days. The District Court struggled to decide whether to admit testimony about whether the blood tests were medically necessary. In the end, Greenspan himself got to testify that he had ordered blood tests because they were necessary to diagnose and treat his patients' maladies. But the Court excluded expert and other testimony to the same effect. The Court also wrestled with whether Greenspan could testify about his conversations with his lawyer. It concluded that he could, but only about five of the eight agreements his lawyer had reviewed and not about anything that his lawyer had told him. And at one point, the Court appeared to shift the burden of proof to him. The jury deliberated for only a few hours before convicting Greenspan on all counts. Greenspan hired separate counsel just for sentencing. Before sentencing, Greenspan's sentencing counsel submitted a thorough letter brief pleading for leniency. His counsel also submitted two videos explaining why Greenspan deserved a lower sentence: one from two former prison wardens and a clinical and forensic psychologist; the other prominently featuring Greenspan as well as his family and former patients. Greenspan also made a written acceptance-of-responsibility statement, addressing the Court directly and offering a heartfelt apology. But at sentencing, the Court asked only Greenspan's counsel, not Greenspan himself, if he wanted to speak. Greenspan's sentencing-guidelines range was 63 to 78 months. But the District Court gave Greenspan a four-level downward departure from that range. It cited as reasons his advanced age, his health, and his distinguished career. And the Court sentenced Greenspan to 41 months' imprisonment, which was at the bottom of the new range. That is nearly two years below the bottom of the original recommended guideline range. Greenspan now appeals, raising four claims: (1) on Greenspan's advice-of-counsel defense, the District Court (a) should not have implied that Greenspan bore any burden of proof; (b) should have let Greenspan testify about what his lawyer told him, and (c) should not have limited the defense to five particular agreements; (2) on medical necessity, the Court should have let him introduce an expert witness and cross-examine the prosecution's witnesses; (3) in its closing argument, the prosecution should not have constructively amended the indictment, by suggesting that the jury could convict based on acts different from those listed in Counts Three and Four of the indictment; and (4) at sentencing, the Court should have addressed Greenspan directly and asked him if he wanted to allocute. All four claims fail. II. THOUGH THE DISTRICT COURT ERRED IN LIMITING THE ADVICE-OF-COUNSEL DEFENSE, THOSE ERRORS WERE HARMLESS First, Greenspan argues that the District Court erred by limiting his advice-of-counsel defense. Here is how that defense works: Imagine that you are thinking about doing something and want to know if it is legal. So you go to your lawyer and tell him all the material facts about it. He responds that the action is legal as long as you do it the way he tells you to. You follow that advice to the letter. But your lawyer was mistaken-you broke the law. So you get charged with a crime. And it is a specific-intent crime, so it requires proof that you acted willfully or with an unlawful intent. But because you relied on that legal advice in good faith, you did not willfully violate the law. United States v. Traitz , 871 F.2d 368 , 382 (3d Cir. 1989). Advice of counsel is thus a species of good-faith defense. It negates the mental state required for the crime. See id. Because it goes to whether the defendant had the requisite mental state, it is not an affirmative defense. United States v. Scully , 877 F.3d 464 , 476 (2d Cir. 2017). The advice-of-counsel issue does not arise unless there are enough facts in the record to support the defense's prerequisites. Id. Only after the defendant satisfies his burden of producing enough facts must the prosecution rebut this defense. Id. at 476-77 . And the trial court decides whether the defendant has met his burden. Id. at 477 n.5. The defendant bears the initial burden of production. But he bears no burden of persuasion. The prosecution is always responsible for proving the defendant's guilty state of mind. So at all times, the burden of persuasion remains with the prosecution. Id. at 476 . Greenspan contends that the District Court erred in three ways: (1) instructing the jury that he had to "demonstrate" the prerequisites for the defense; (2) excluding as hearsay some of his testimony about Cohen's legal advice; and (3) limiting the scope of the defense to five particular agreements rather than all eight. We agree that the jury instruction erroneously suggested that Greenspan bore the burden of proving his mental state. But this unpreserved error did not prejudice him. The latter two rulings were also errors, but they were harmless. A. The jury instruction erroneously suggested that Greenspan bore the burden of persuasion Greenspan argues that the jury instruction on the advice-of-counsel defense wrongly shifted the burden of proof to him. He never objected to this instruction, so we review for plain error. Fed. R. Crim. P. 52(b). Under Olano 's four-part framework, we reverse only if (1) there was an "error"; (2) the error was "plain"; (3) the error prejudiced or "affect[ed] substantial rights"; and (4) not correcting the error would " 'seriously affect[ ] the fairness, integrity or public reputation of judicial proceedings.' " United States v. Olano , 507 U.S. 725 , 732, 734-36, 113 S.Ct. 1770 , 123 L.Ed.2d 508 (1993) (quoting United States v. Young , 470 U.S. 1 , 15, 105 S.Ct. 1038 , 84 L.Ed.2d 1 (1985) ). Olano 's fourth prong is discretionary. Even if an error satisfies the first three prongs, we may correct the error but need not do so. 507 U.S. at 735 , 113 S.Ct. 1770 . When reviewing jury instructions, we look at the instructions as a whole, not piecemeal. United States v. Shaw , 891 F.3d 441 , 450 (3d Cir. 2018). Greenspan challenges both the beginning and the end of the instruction. The end was proper. Greenspan claims that the Court erred by telling the jury "that to return an acquittal [it] has to find that ' the defendant lacked the requisite intent to violate the law .' " Appellant's Br. 37 (emphasis added to the portion quoting the jury instruction at App. 2887). But the instruction did not tell the jury that it had to find anything to acquit. That is counsel's gloss. The actual instruction simply explained: "Rather, the basis for the defense is that relying upon counsel's advice, the defendant lacked the requisite intent to violate the law." App. 2887. It accurately quoted our governing precedent. See Traitz , 871 F.2d at 382 . So that part of the instruction was proper. But the beginning of the instruction was erroneous: "To avail himself of the advice of counsel defense, the defendant has to demonstrate from the evidence each of the" prerequisites of the defense. App. 2887 (emphases added). The District Court was likely trying to explain that Greenspan bore the burden of producing enough facts to put the defense in issue. But mentioning the defendant's burden of production in jury instructions risks confusing the jury about who bears the burden of persuasion throughout the trial. See Scully , 877 F.3d at 477 n.5. And the words "avail himself" and "demonstrate" erroneously suggested that Greenspan bore the burden of disproving his mental state. But the burden of proving that element, and every other, always remains on the prosecution. See Patterson v. New York , 432 U.S. 197 , 204-05, 97 S.Ct. 2319 , 53 L.Ed.2d 281 (1977) ; In re Winship , 397 U.S. 358 , 364, 90 S.Ct. 1068 , 25 L.Ed.2d 368 (1970). So this phrasing was improper. We need not decide whether this error was plain because it was not prejudicial. Instructional errors that shift the burden of proof are not structural errors that "automatically require reversal of an otherwise valid conviction." Rose v. Clark , 478 U.S. 570 , 579, 106 S.Ct. 3101 , 92 L.Ed.2d 460 (1986). We will affirm a guilty verdict despite a jury-instruction error on criminal intent if the prosecution's evidence "conclusively establish[ed] [criminal] intent, so that no rational jury could find that the defendant committed the relevant criminal act but did not intend to cause injury." Id. at 580-81 , 106 S.Ct. 3101 . As we explain below, this is such a case. This error did not prejudice Greenspan. One final note: The District Court appears to have crafted its advice-of-counsel instruction by piecing together language from Traitz and United States v. Al-Shahin , 474 F.3d 941 (7th Cir. 2007). For instance, it followed Traitz in warning the jury that this defense "is not designed to insulate illegal conduct." App. 2887 (quoting 871 F.2d at 382 ). That statement of law is technically correct, but it risks confusing a jury. Appellate decisions are not always phrased well to explain complex concepts to juries. Scully , 877 F.3d at 477 . To avert confusion and litigation, we suggest that trial courts draw on better alternatives. See id. at 477-78 (quoting 1 Leonard B. Sand et al., Modern Federal Jury Instructions: Criminal , Instruction 8-4, at 8-19 (2017) and Seventh Circuit Pattern Criminal Jury Instructions § 6.12 (2012)). B. The Court erred in limiting Greenspan's testimony about his lawyer's advice Greenspan sought to convince the jury that, in dealing with David and the Lab, he had relied on the advice of Cohen, his lawyer. Cohen had died before trial, so Greenspan tried to testify about what exactly Cohen had told him. The Court let him testify about what he had said to Cohen and did after their meetings, but not about what Cohen had said to him. It reasoned that Cohen's out-of-court statements were hearsay. Greenspan challenges that ruling. Greenspan promptly objected at trial, so we review for harmless error. Fed. R. Crim. P. 52(a). The hearsay ruling rests on a question of law, so we review it de novo. United States v. Vosburgh , 602 F.3d 512 , 538 (3d Cir. 2010). The District Court erred. A statement is not hearsay unless a party "offers [it] in evidence to prove the truth of the matter asserted." Fed. R. Evid. 801(c)(2). Cohen may have said the agreements were lawful. But Greenspan was not using the statements to show that the agreements were in fact lawful. He wanted to use them to prove their effect on his state of mind-to explain why he believed that they were lawful. So the lawyer's advice was admissible non-hearsay. See also United States v. McLennan , 563 F.2d 943 , 946 (9th Cir. 1977). Greenspan's counsel did enough to preserve this error. At first, he cited the wrong hearsay rule numbers, suggesting that the statements fell within a hearsay exception rather than not being hearsay at all. And he did not use the magic words "not hearsay," "truth of the matter asserted," "state of mind," or " Rule 801(c)." But he made that point in substance: at the key moment, he twice explained that he wanted to introduce Cohen's advice to explain "why [Greenspan] thought that [signing the agreement] was okay to do." App. 2577. That objection was specific enough to give the District Court notice of its basis. See United States v. Russell , 134 F.3d 171 , 179 (3d Cir. 1998). C. The Court erred in limiting the scope of the defense to five agreements Greenspan also appeals the District Court's instruction limiting the scope of his advice-of-counsel defense to five specific agreements, rather than all eight. Its instruction covered neither two years' rental agreements nor the consulting agreement. He preserved the issue by objecting at trial. We review whether the instruction stated the law correctly de novo, but review its particular wording for abuse of discretion. Shaw , 891 F.3d at 449-50 . Here too, the Court erred. A district court may refuse to instruct the jury on a defense if there is insufficient evidence, as a matter of law, to support that defense. United States v. Taylor , 686 F.3d 182 , 194 (3d Cir. 2012). But if the evidence at trial could have supported a jury finding that the defense applied to the remaining three agreements, then the District Court should not have excluded them from its instruction. That is a question for the jury. See Mathews v. United States , 485 U.S. 58 , 63, 108 S.Ct. 883 , 99 L.Ed.2d 54 (1988). Greenspan testified that he had run all agreements by Cohen before signing them: "[A]ny contract I entered into would have to be looked at by Mr. Cohen to make sure it's legal." App. 2413. He reiterated that point more concretely: "Each new contract was reviewed by [his office manager] and by Barry Cohen." App. 2528. True, in places he qualified or contradicted those blanket assertions. He later said he believed that he had asked Cohen to review the Advantech consulting agreement, and also believed that Cohen had not reviewed the 2008 rental agreement. The District Court latched on to the contradiction to exclude the latter agreement. But that contradiction was for the jury to resolve, not the Court. And there was no basis for excluding the Advantech consulting agreement or the 2009 rental agreement. Greenspan's repeated testimony that Cohen had reviewed all agreements sufficed to include them all. So the Court should have instructed the jury on the advice-of-counsel defense for all the agreements. D. The jury-instruction error was not prejudicial, and the hearsay and scope errors were harmless As mentioned above, the jury-instruction error was not preserved. So we review it for plain error and ask whether it prejudiced Greenspan. The hearsay and scope-of-defense errors were preserved, so we review them for harmless error. Fed. R. Crim. P. 52(a). We need not reverse these latter, nonconstitutional errors if they had no "substantial and injurious effect or influence in determining the jury's verdict." United States v. Toliver , 330 F.3d 607 , 612 (3d Cir. 2003) (quoting Kotteakos v. United States , 328 U.S. 750 , 776, 66 S.Ct. 1239 , 90 L.Ed. 1557 (1946) ); accord Brecht v. Abrahamson , 507 U.S. 619 , 623, 629-31, 113 S.Ct. 1710 , 123 L.Ed.2d 353 (1993). To meet that standard, the government must show that it is "highly probable that the error did not contribute to the judgment," but it need not "disprov[e] every reasonable possibility of prejudice." United States v. Mathis , 264 F.3d 321 , 342 (3d Cir. 2001) (internal quotation marks omitted). In other words, "we [must] have a sure conviction that the error[s] did not prejudice" Greenspan. Id. We have that sure conviction here about all three errors for three reasons. 1. Greenspan presented significant evidence on his advice-of-counsel de fense . Greenspan succeeded in getting almost all of his advice-of-counsel defense before the jury. He repeatedly testified that he had brought each agreement to Cohen to review. He said that Cohen had told him that the first rental agreement "was a good contract and I could sign it." App. 2417. He explained that he had "[a]bsolutely" relied on that advice in signing the agreements with the Lab. App. 2579. And he "[a]bsolutely [would] not" have signed them if Cohen had advised against it. Id. Short of parroting Cohen's exact words, we do not see what more Greenspan could have said even if the District Court had allowed it. And his testimony explained his innocent state of mind for all eight agreements. 2. The prosecution did not challenge Cohen's involvement in all the agreements . Next, the prosecution never argued that Greenspan had not consulted Cohen, or that he had not consulted Cohen about the three agreements omitted from the advice-of-counsel instruction. Instead, the prosecution's theory was that Greenspan had used Cohen only to make the bribery agreements appear legitimate. David testified that when he had first offered to rent space from him, Greenspan took him upstairs to see Cohen and said to Cohen: "[T]hese guys want to pay me $2000, you know, to do blood in my office. I want to do it. How do we make this contract look legitimate and how do we get it to pass the smell test[?]" App. 1064. Cohen had advised that it would look bad to use a round number. So they lowered the initial rent from $2000 to $1992.50. Thus, there was no dispute about Cohen's involvement in any of the agreements. Instead, the issue was whether Greenspan had sought legal advice in good faith or rather to facilitate bribery or kickbacks. All eight agreements stood or fell together as part of a single scheme. The jury believed David's version, not Greenspan's: the lawyer was there to help Greenspan "pass the smell test," not to help him follow the law. Letting Greenspan elaborate more would not have changed that. Nor would mentioning the other three agreements in the advice-of-counsel instruction. 3. The evidence as a whole reeked of corruption . Finally, Greenspan was right to worry about "the smell test." The entire scheme reeked. Greenspan admitted that he had steered blood to the Lab and that David knew that he would do so. He admitted that the Lab had paid him "rent" out of all proportion to his own rent and the size of the phlebotomist's tiny office. He admitted that the Lab had paid him large service fees even though it was also paying the phlebotomist's salary. He admitted that Nordman had paid him consulting fees out of all proportion to the other consulting fees that he had earned. He admitted that he had asked Nordman for, and received, two expensive Christmas parties for his staff. He never denied that the Lab had hired his son and his mistress. And neither he nor his trial lawyer plausibly explained this cornucopia of cash. The only reasonable explanation was cash for blood. In the face of this mountain of evidence, the jury found that Greenspan's self-serving advice-of-counsel claims rang hollow. The advice-of-counsel instruction, testimony, and hearsay ruling made no difference. In any event, there is no reasonable possibility that the jury would have changed its mind about the defense. So the unpreserved jury-instruction error was not prejudicial, and the preserved errors were harmless. III. THE DISTRICT COURT PROPERLY LIMITED GREENSPAN'S MEDICAL-NECESSITY EVIDENCE Greenspan also claims that the District Court should have let him introduce expert testimony and conduct cross-examination of a government witness to show that the blood tests he ordered were medically necessary. That evidence, he argues, was relevant to disproving his criminal mental state. So, he contends, the District Court abused its discretion by barring the extra evidence. But medical necessity was only marginally relevant. Rather, the prosecution argued that Greenspan had steered medically necessary tests to the Lab, instead of other facilities, in exchange for bribes or kickbacks. The limited probative value of medical-necessity evidence was thus substantially outweighed by the risk of misleading or confusing the jury. So the District Court properly excluded it. Regardless, any error would have been harmless. A. The Rule 403 balancing is properly before us We review a district court's exclusion of evidence for abuse of discretion. United States v. Starnes , 583 F.3d 196 , 213-14 (3d Cir. 2009). Under Rule 403, a district court has broad discretion to "exclude relevant evidence if its probative value is substantially outweighed by a danger of ... confusing the issues, [or] misleading the jury." Fed. R. Evid. 403 ; Vosburgh , 602 F.3d at 537 . We "strongly prefer" that a district court do that balancing test explicitly. Egan v. Del. River Port Auth. , 851 F.3d 263 , 277 (3d Cir. 2017). But if it does not, we either "decide the trial court implicitly performed the required balance; or, if we decide the trial court did not, we undertake to perform the balance ourself." United States v. Eufrasio , 935 F.2d 553 , 572 (3d Cir. 1991). We have declined to balance those factors de novo only where a district court said nothing about particular evidence's probative value or prejudicial effect. United States v. Finley , 726 F.3d 483 , 491 (3d Cir. 2013). That is not the case here. To be sure, the District Court never explicitly balanced the Rule 403 factors. It discussed the excluded evidence's probative value at length, but not its potential to mislead the jury. And it vacillated, ruling inconsistently on this evidence's admissibility both before and during trial. But the prosecution explicitly invoked Rule 403 before trial, arguing that the medical-necessity evidence was not only logically irrelevant but also likely to mislead the jury. And the District Court accepted that argument, excluding the evidence because it "is not relevant and is likely to mislead the jury." App. 13. The latter half of that phrase is almost a verbatim quotation of Rule 403 's "danger of ... misleading the jury." Fed. R. Evid. 403. So the District Court appears to have done the balancing implicitly. Even if it did not, we can do it and we will. B. The danger of misleading or confusing the jury substantially outweighed the medical-necessity evidence's limited probative value 1. Limited probative value . The medical-necessity evidence had little probative value. Even if the tests were necessary, that explains only why Greenspan ordered the tests, not why he referred them to the Lab instead of to other labs. So medical necessity was at most marginally relevant. 2. Misleading or confusing the jury . That scant probative value was substantially outweighed by the risk of confusing or misleading the jury. As the prosecution argued before trial, the medical-necessity argument would have been "calculated to invite the jury to acquit [Greenspan] because he performed many good works and somehow deserved a break." App. 94. It would have served "only to confuse and distract the jury from the actual issues they must consider at trial." App. 111. We agree. To be clear, medical-necessity evidence could be relevant in future bribery or kickback cases. But given the government's blood-diversion theory, the District Court did not abuse its discretion by limiting this evidence. C. Even if there were error, it would have been harmless Even if the government opened the door to medical-necessity evidence at trial by introducing evidence of cash payments for ordering more lucrative tests, any error in excluding medical-necessity evidence would have been harmless. As discussed in the harmless-error section above, the prosecution's case was overwhelming. Greenspan's office manager, a long-time employee with no incentive to lie, testified that Greenspan had told her to send blood to the Lab when patients' insurance would allow it. Over the next seven years, Greenspan, his staff, his son, his mistress, and his struggling medical practice received more than $200,000 in payments and benefits. Most were undisputed, and all were suspect. Greenspan never plausibly explained the many large, frequent cash infusions and benefits. So even if the medical-necessity expert and cross-examination on medical necessity should have been allowed, they would not have mattered. And both the government and the defense ultimately made clear in closing remarks that medical necessity was not at issue. In his closing argument, Greenspan's counsel underscored that point: "There's been no allegation whatsoever that his decision on what blood work was necessary, was anything but necessary." App. 3063. The government, in its closing rebuttal, likewise emphasized that "at no point did the government say [Greenspan] was adding tests. It was just that he was sending them to [the Lab] as opposed to another lab." App. 3101-02. And just in case "[the jury] thought this was an issue," the government clarified that "there is no requirement, nothing in the jury charge, nothing" about proving that Greenspan added unnecessary tests. App. 3101. Any error would have been harmless. IV. EVEN IF THE PROSECUTION CONSTRUCTIVELY AMENDED THE INDICTMENT IN ITS CLOSING, IT DID NOT SERIOUSLY AFFECT THE PROCEEDINGS' FAIRNESS, INTEGRITY, OR PUBLIC REPUTATION Greenspan also argues that the prosecution constructively amended Counts Three and Four of the indictment. Those counts, he claims, were limited to his receiving Christmas parties as kickbacks. But the prosecution's closing argument, he argues, improperly broadened them to include receiving consulting fees a week or two before each party. Greenspan never raised this argument in the District Court, so we again review for plain error. United States v. Syme , 276 F.3d 131 , 148 (3d Cir. 2002). Here, we need not decide whether there was an error or whether it was plain or prejudicial. Even if the government constructively amended the two counts and plainly did so, the evidence of the payments and parties was overwhelming and basically undisputed. So at Olano 's fourth prong, failing to reverse this error would not impair the proceedings' fairness, integrity, or reputation. Thus, there was no reversible error. A. No need to address whether there was a constructive amendment and whether any error was plain or prejudicial The Grand Jury Clause of the Fifth Amendment guarantees federal defendants the "right to be tried only on charges presented in [the grand jury's] indictment." Stirone v. UnitedStates , 361 U.S. 212 , 217, 80 S.Ct. 270 , 4 L.Ed.2d 252 (1960). The court or prosecution constructively amends the indictment when the arguments, evidence, or jury instructions create "a substantial likelihood that the jury may ... convict[ ] the defendant for an offense" different from the one in the indictment. United States v. Daraio , 445 F.3d 253 , 259-60 (3d Cir. 2006). Greenspan argues that the prosecution constructively amended Counts Three and Four of the indictment. Those two counts charged Greenspan with receiving a bribe or kickback "[o]n or about ... [a]pproximate[ly]" December 14, 2011, and December 12, 2012. App. 62. Neither count mentioned a specific overt act or a type of payment. But the two dates corresponded to the two Christmas parties paid for by the Lab. In its closing argument, the prosecution did not limit these two counts to receiving Christmas parties. Rather, it argued that the jury could convict Greenspan for receiving either each Christmas party or the consulting fee that came a week or two before each party. And the Court did not instruct the jury that it had to find any specific acts to convict on these counts. It said only that Greenspan was guilty of those counts if he "solicited or received kickbacks and bribes" from the Lab "on certain specific dates ." App. 2905 (emphasis added). It also told the jury that the prosecution need not prove "the exact date of the alleged offense." Instead, it need prove only that the crime was committed "on or about a certain date" or "on a date reasonably near the date alleged." App. 2873-74. Greenspan argues that all this was error because it let the jury convict him on overt acts different from those charged. We need not decide whether the government constructively amended the indictment, whether it did so plainly, or whether any error prejudiced Greenspan. Even if Olano 's first three prongs are all met, we find that its fourth prong is not. So we need not analyze the others. B. We decline to reverse a conviction that is based on overwhelming and essentially uncontroverted evidence and closely linked to the charged crimes Following the Supreme Court's guidance, some of our sister circuits decline to exercise their discretion to reverse constructive-amendment errors if (1) the charged and uncharged crimes were "closely linked" and (2) the evidence of guilt on the "closely linked" but uncharged crime is " 'overwhelming' " and " 'essentially uncontroverted.' " United States v. Gonzalez Edeza , 359 F.3d 1246 , 1251 (10th Cir. 2004) (quoting United States v. Cotton , 535 U.S. 625 , 633-34, 122 S.Ct. 1781 , 152 L.Ed.2d 860 (2002) and Johnson v. United States , 520 U.S. 461 , 470, 117 S.Ct. 1544 , 137 L.Ed.2d 718 (1997) ); see also United States v. Daniels , 252 F.3d 411 , 414 (5th Cir. 2001). So should we. Here, the consulting fees and Christmas parties both came from the Lab through Nordman. They were both kickbacks in the same bribery scheme. They were even discussed in the same voicemail. And the evidence was overwhelming and essentially uncontroverted that the consulting fees served as bribes or kickbacks. At trial, the prosecution presented records of each consulting fee from the Lab to Greenspan. Greenspan admitted knowing that Nordman worked for the Lab. And the prosecution presented overwhelming evidence detailing the sham consulting sessions between Greenspan and Nordman. The same is true of the Christmas parties. No one disputes that Nordman paid for both Christmas parties using the Lab's corporate credit card. Greenspan admitted that he asked Nordman for them. And there is no legitimate explanation for why he or Nordman did so. The only reasonable conclusion was that Greenspan had taken the Christmas parties as bribes or kickbacks. In short, the consulting fees and parties were undoubtedly closely linked. The entire scheme stood or fell together, and the jury found that it fell afoul of the law. Even though Greenspan had plenty of notice of these allegations, he could not adduce any plausible innocent explanation for these repeated payments. So we decline to exercise our discretion to notice any error. V. THE CUMULATIVE ERRORS DID NOT PREJUDICE GREENSPAN Where there are multiple trial errors, a defendant can ask us to consider them together. Under this cumulative-error analysis, we grant a new trial only if "the[ ] errors, when combined, so infected the jury's deliberations that they had a substantial influence on the outcome of the trial." United States v. Thornton , 1 F.3d 149 , 156 (3d Cir. 1993) (quoting United States v. Hill , 976 F.2d 132 , 145 (3d Cir. 1992) ). Like our sister circuits, we do not "simply count[ ] up the number of errors discovered." Grant v. Trammell , 727 F.3d 1006 , 1025 (10th Cir. 2013). There are two ways that errors that are not individually reversible can become so cumulatively. First, related errors can have "an inherent synergistic effect," in which "they amplify each other in relation to a key contested issue in the case." Cargle v. Mullin , 317 F.3d 1196 , 1221 (10th Cir. 2003) ; Ybarra v. McDaniel , 656 F.3d 984 , 1001 (9th Cir. 2011). Second, even if there is no synergy, "accumulating unrelated errors" can still warrant reversal "if their probabilistic sum sufficiently undermines confidence in the outcome of the trial." Grant , 727 F.3d at 1026 (emphasis added). In other words, even if the errors do not multiply, they can still add up to prejudice. We have not found that cumulative errors warranted reversal, however, where the remaining evidence of guilt was "overwhelming." See United States v. Copple , 24 F.3d 535 , 547 n.17 (3d Cir. 1994) (finding harmless the admission of prejudicial victim-impact testimony on top of six other alleged trial errors). Greenspan never raised a standalone cumulative-error claim either at trial or on appeal. At best, he raised this claim on appeal only about the advice-of-counsel errors. On direct appeal, we review a defendant's failure to raise a cumulative-error claim at trial for plain error. United States v. Fulton , 837 F.3d 281 , 312 (3d Cir. 2016). And at least on habeas, we and many of our sister circuits treat cumulative error as a discrete claim that defendants must affirmatively raise or else forfeit. See, e.g. , Collins v. Sec'y of Pa. Dep't of Corr. , 742 F.3d 528 , 541 (3d Cir. 2014) ; Keith v. Mitchell , 455 F.3d 662 , 679 (6th Cir. 2006) ; Gonzales v. McKune , 279 F.3d 922 , 925 (10th Cir. 2002) (en banc). We need not decide whether the same preservation requirement holds true on direct appeal. Even if we overlook his forfeiture at trial and any forfeiture on appeal, the combined errors do not warrant reversal. A. The cumulative errors on the advice-of-counsel defense were not prejudicial Greenspan never expressly asked us to consider any of the errors cumulatively. When read charitably, his brief hinted at this claim by grouping the advice-of-counsel errors together and explaining how each warranted reversal. But as then-Judge Gorsuch explained, "a perfunctory assertion falls well short of what's needed to overturn a judgment." Grant , 727 F.3d at 1025 (finding insufficient a request to "consider the synergistic effect of all the errors and grant [the defendant] relief"). And we have already explained why the advice-of-counsel errors, standing alone or together, do not warrant reversal. Greenspan pleaded his case to the jury with few limits: he testified throughout his trial that he relied on his lawyer's advice about the leases and agreements and that he thought they were legitimate. And the prosecution never challenged his lawyer's involvement in them all. So the only issue was whether Greenspan sought legal advice in good faith or to mask his corrupt intent. But the payments were out of all proportion to any legitimate purpose. He admitted receiving them. And he offered no plausible explanation for them. The evidence of corrupt intent was thus overwhelming. B. The cumulative trial errors and potential errors in the aggregate were not prejudicial Greenspan never raised a cumulative-error claim aggregating the advice-of-counsel, medical-necessity, and constructive-amendment alleged errors. Even if we overlook that forfeiture, the errors and potential errors were too unrelated to have any synergies. And the cumulative effect of these unrelated errors fell far short of undermining confidence in the outcome of the trial. 1. The errors did not compound one another. Medical necessity had little to do with the other claims of error. It bore only on the alleged fee-for-test payments as envelopes of cash. We have already explained why there was no error in excluding medical-necessity evidence. But even if there were error, these payments were not charged in the indictment. The payments were modest and revealed only a glimpse of the massive bribery or kickback scheme. And Greenspan denied receiving these payments, so he could not have claimed that he had relied on his lawyer's advice to sanitize them. Constructive amendment also had little to do with the other two claimed types of error. A constructive amendment of an indictment is a grand-jury error, not a trial error. Stirone , 361 U.S. at 217-18 , 80 S.Ct. 270 . Unlike a variance, which occurs when the evidence at trial is materially different from the facts alleged in the indictment, a constructive amendment does not affect the fairness of the trial and what evidence is presented to the petit jury. See United States v. McKee , 506 F.3d 225 , 231 n.7 (3d Cir. 2007). So even if this were error, it did not bear on Greenspan's criminal intent. And it was unrelated to the other two types of alleged error. Nor did any constructive amendment prejudice the trial. Greenspan had notice that the government was alleging that he had taken consulting payments as bribes or kickbacks. Those payments were among the many overt acts listed in Count One of the indictment. And he defended himself at trial against those allegations, unsuccessfully claiming that his consulting arrangement was legitimate and denying knowledge of who was funding those payments. So all the alleged trial errors were unrelated. 2. The unrelated errors did not add up to prejudice . And the unrelated errors did nothing to undermine the outcome of the trial. The evidence of guilt was overwhelming. The jury had no reasonable choice but to convict. Again, the modest fee-per-test payments were not charged and had negligible effect on his criminal intent. Greenspan never disputed receiving the rest of the payments and benefits. Yet he offered no plausible explanation for why he was being paid so much, out of all proportion to the space the Lab used, the time he spent consulting, or the work his mistress did for the Lab. The explanations he did offer were implausible, only highlighting the problems with Greenspan's story. "Adding [modest errors] together undoubtedly leads to a somewhat less modest sum." Grant , 727 F.3d at 1026 . Even so, "they do not collectively call into question the compelling case the government put on" here. Id. At trial, the jury heard one fishy statement after another. Each statement only made the stench of corruption more pungent. Even considered together, the alleged trial errors could not have substantially influenced the trial. So no new trial is warranted. VI. EVEN THOUGH THE DISTRICT COURT FAILED TO ADDRESS GREENSPAN DIRECTLY AT SENTENCING, WE NEED NOT REVERSE BECAUSE GREENSPAN MADE A STRATEGIC CHOICE NOT TO ALLOCUTE Finally, Greenspan challenges the District Court's failure to ask him personally if he wanted to speak at sentencing. The Court asked sentencing counsel if Greenspan wanted to say anything, but counsel said no. It asked again, and counsel responded: "No. We are taking an appeal so I have advised him we waive allocution." App. 3174. The judge never asked Greenspan himself whether he wanted to speak. Greenspan argues that the District Court should have asked him personally if he wanted to say anything at sentencing. Because he did not object at sentencing, we review for plain error. Fed. R. Crim. P. 52(b) ; United States v. Adams , 252 F.3d 276 , 278-79 (3d Cir. 2001). We again apply Olano 's four-part framework for plain-error review. A. There was error and it was plain The allocution error satisfies Olano 's first and second prongs. A sentencing judge must "unambiguously address" the defendant himself, not just his counsel, and "leave no room for doubt that the defendant has been issued a personal invitation to speak prior to sentencing." Green v. United States , 365 U.S. 301 , 305, 81 S.Ct. 653 , 5 L.Ed.2d 670 (1961) ; accord Fed. R. Crim. P. 32(i)(4)(A)(ii). Here, the District Court failed to do so. That was error. And the error was obvious on the face of the record, so it was plain. Adams , 252 F.3d at 286. The government does not dispute this. B. No need to decide whether the government has rebutted the presumption of prejudice At Olano 's third prong, under our precedent, allocution errors trigger a presumption of prejudice. Id. at 287. We apply that presumption whenever the allocution error could have influenced the sentence. Id. at 289. Although the District Court lowered Greenspan's sentence and sentenced him to the bottom of the new, lowered range, an opportunity existed for an even lower sentence under the advisory Sentencing Guidelines. So the presumption of prejudice applies here. The government contests the validity and strength of this presumption, citing many precedents from the Supreme Court. We have never held that this presumption is irrebuttable. "Unless flagged as irrebuttable, presumptions are rebuttable." Binderup v. Att'y Gen. , 836 F.3d 336 , 350 (3d Cir. 2016) (en banc) (opinion of Ambro, J.). And the government argues that it can rebut and has rebutted the presumption here: Greenspan allocuted indirectly through his statements on video and in the presentence report. But because we resolve this case at Olano 's fourth prong, we need not decide whether the Supreme Court has abrogated this presumption or whether the government has rebutted it here. C. We will not reverse an error that was part of Greenspan's strategy Even if the first three prongs are satisfied, we need not reverse at Olano 's fourth prong "unless the error 'seriously affect[ed] the fairness, integrity, or public reputation of judicial proceedings.' " 507 U.S. at 732, 113 S.Ct. 1770 (quoting Young , 470 U.S. at 15 , 105 S.Ct. 1038 ). Here, the error fit into Greenspan's counsel's strategy. So we will not exercise our discretion to reverse. Reversing a plain error "is permissive, not mandatory": we may correct the error but need not do so. 507 U.S. at 735 , 113 S.Ct. 1770 . Even before Olano , the Supreme Court limited courts to "correct[ing] only 'particularly egregious errors.' " Young , 470 U.S. at 15 , 105 S.Ct. 1038 (quoting United States v. Frady , 456 U.S. 152 , 163, 102 S.Ct. 1584 , 71 L.Ed.2d 816 (1982) ). And it later instructed courts to exercise their discretion to correct errors at Olano 's fourth prong rarely and "sparingly." Jones v. United States , 527 U.S. 373 , 389, 119 S.Ct. 2090 , 144 L.Ed.2d 370 (1999). Since Olano , the Supreme Court has rejected per se approaches that unduly restrict our discretion. Rather, we must apply Olano 's fourth prong case by case, delving into each case's particular facts. Puckett v. United States , 556 U.S. 129 , 142, 129 S.Ct. 1423 , 173 L.Ed.2d 266 (2009) ; e.g. , United States v. Marcus , 560 U.S. 258 , 266, 130 S.Ct. 2159 , 176 L.Ed.2d 1012 (2010) (rejecting per se rule of reversal whenever there is "any possibility, no matter how unlikely," that a defendant was convicted based on pre-enactment conduct). And Adams , our controlling precedent, does not eliminate our discretion. On the contrary, Adams found it appropriate to use our discretion to correct the particular error in that case. 252 F.3d at 288-89. To make that judgment call, Adams tells us to look at "the seriousness of the error in the context of the entire case ." 252 F.3d at 285 (emphasis added). Here, the context is that Greenspan strategically skipped allocution while expressing remorse on video and in writing to get a much lower sentence. That is precisely the type of "sand-bagging strategy" that makes appellate courts "particularly reluctant to notice a[n error] as plain error." Syme , 276 F.3d at 154-55 n.9 (constructive amendment). Courts must not create incentives for defendants to ignore errors at trial "to keep an issue for appeal as insurance in the event they are convicted." Id. at 154 n.9. So declining to fix the allocution error here would not work an injustice. But rewarding counsel's strategy with reversal would do just that. At times, we have overread Adams as adopting a per se approach to the denial of a defendant's right of allocution. See, e.g. , United States v. Plotts , 359 F.3d 247 , 250 n.6 (3d Cir. 2004) (reading Adams as setting out an unqualified rule for Olano 's fourth prong); United States v. Paladino , 769 F.3d 197 , 201-02 (3d Cir. 2014) (quoting Plotts 's footnote). But these footnote dicta create no special across-the-board rule just for allocution errors. Adams , the controlling precedent, never pronounced a blanket rule. Nor did the Supreme Court. See Hill v. United States , 368 U.S. 424 , 428, 82 S.Ct. 468 , 7 L.Ed.2d 417 (1962) (holding that an allocution error is neither a constitutional error nor "a fundamental defect"). And we are careful not to read our precedents to gainsay those of the Supreme Court. Unsurprisingly, our sister courts of appeals deny relief at Olano 's fourth prong when the error, or the failure to object to it, was part of defense counsel's strategy. E.g. , United States v.Rivera Rangel , 466 F.3d 158 , 165 (1st Cir. 2006) ; United States v. Bayless , 201 F.3d 116 , 128-29 (2d Cir. 2000). And at least one other court of appeals has refused to reverse an allocution error in similar circumstances. In United States v. Noel , the trial judge failed to address the defendant personally, but twice mentioned his right to allocution. 581 F.3d 490 , 504 (7th Cir. 2009). The defendant wrote a letter, which "was structured much as an allocution would have been" and was read aloud at sentencing. Id. And the defendant was sentenced below the applicable guidelines range. Id. The Noel court thus chose at Olano 's fourth prong not to reverse the error. Id. We will do the same. Here, allocuting would have put Greenspan on the horns of a dilemma: If he had allocuted and admitted guilt, that admission could have doomed his appeal. If he had allocuted without admitting guilt, he could have seemed unrepentant and unworthy of leniency. He had to walk a tightrope between the two. But if he did so in open court, he could have easily erred in either direction. And he would not have been able to edit his live remarks. Instead, Greenspan sandbagged. At sentencing, the judge twice asked whether Greenspan wanted to allocute. On Greenspan's behalf, counsel twice declined because Greenspan intended to appeal. Like Noel, Greenspan found other ways to plead for leniency. He wrote a sincere, four-paragraph-long apology to the District Court. Without admitting guilt, he accepted responsibility for his association with the Lab and Advantech. He also highlighted several mitigating circumstances: his old age; his long, crime-free career; and remorse for his family's pain. And he submitted two videos that drove these mitigating circumstances home. In the first, a psychologist and two former prison wardens relied on these same mitigating circumstances to recommend leniency. In the second, Greenspan himself spoke at length. While his family, patients, and close friends pleaded for leniency, he showcased his personal life and long medical career. Both the written statement and the videos were carefully crafted, avoiding the risks of live remarks. Greenspan's strategy worked. As in Noel , the sentencing judge lowered Greenspan's final offense level by four levels. He sentenced him at the bottom of the lowered range, to 41 months' imprisonment, 37 months lower than the guidelines' maximum. To explain the sentence reduction, the judge mentioned Greenspan's age, health, and distinguished career. So declining to reverse would not seriously affect the judicial proceedings' fairness, integrity, or public reputation. Defense counsel must zealously advocate for their clients. But we refuse to reward this strategic decision. Reversing this allocution error would work an injustice. So we will exercise our discretion to affirm Greenspan's sentence. * * * * * On appeal, Greenspan's counsel thoroughly examined the extensive record and skillfully highlighted the errors and potential errors below. We are grateful for their expert assistance in doing so. But we correct errors only when justice warrants doing so, not when the evidence is overwhelming and essentially undisputed, and certainly not when a litigant sandbags. So we will affirm.