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Opinion for the Court filed PER CURIAM. PER CURIAM: Defendants in this action, cigarette manufacturers and trade organizations, appeal from the district court’s judgment finding them liable for conducting the affairs of their joint enterprise through a pattern of mail and wire fraud in a scheme to deceive American consumers. They also appeal from the district court’s remedial order, which imposes numerous negative and affirmative duties on Defendants. The government and intervenors cross-appeal from the district court’s denial of additional requested remedies. After considering all of the parties’ arguments, we affirm in large part the finding of liability, remanding only for dismissal of the trade organizations. We also largely affirm the remedial order, including the denial of additional remedies, but vacate the order with regard to four discrete issues, remanding for further proceedings as directed in this opinion. I. Background The United States initiated this civil action under the Racketeer Influenced and Corrupt Organizations Act (“RICO”), 18 U.S.C. §§ 1961-1968, in 1999. The government alleged that nine cigarette manufacturers and two tobacco-related trade organizations violated section 1962(c) and (d) of the Act. Those subsections make it unlawful for “any person employed by or associated with any enterprise engaged in, or the activities of which affect, interstate or foreign commerce, to conduct or participate, directly or indirectly, in the conduct of such enterprise’s affairs through a pattern of racketeering activity” or to conspire to do so. 18 U.S.C. § 1962(c), (d). The eleven Defendants were Philip Morris, Inc., now Philip Morris USA, Inc. (“Philip Morris”); R.J. Reynolds Tobacco Company, now Reynolds American (“Reynolds”); Brown & Williamson Tobacco Company, now part of Reynolds (“Brown & Williamson”); Lorillard Tobacco Company (“Lorillard”); The Liggett Group, Inc. (“Liggett”); American Tobacco Company, which merged with Brown & Williamson and is now part of Reynolds (“American”); Philip Morris Companies, now Altria (“Altria”); British American Tobacco (Investments) Ltd. (“BATCo”); B.A.T. Industries p.l.c., now part of BATCo (“BAT Industries”); The Council for Tobacco Research — USA, Inc. (“CTR”); and The Tobacco Institute, Inc. (“TI”). The last two entities are trade organizations the cigarette manufacturers created; they do not manufacture or sell tobacco products. The district court dismissed BAT Industries from the case for lack of personal jurisdiction. ■ The government alleged that Defendants violated and continued to violate RICO by joining together in a decades-long conspiracy to deceive the American public about the health effects and addictiveness of smoking cigarettes. Specifically, the government alleged that Defendants fraudulently denied that smoking causes cancer and emphysema, that secondhand smoke causes lung cancer and endangers children’s respiratory and auditory systems, that nicotine is an addictive drug and Defendants manipulated it to sustain addiction, that light arid low tar cigarettes are not less harmful than full flavor cigarettes, and that Defendants intentionally marketed to youth. United States v. Philip Morris USA, Inc., 449 F.Supp.2d 1, 27 (D.D.C.2006). In addition, the government alleged that Defendants concealed evidence and destroyed documents to hide the dangers of smoking and protect themselves in litigation. Id. The government identified 148 racketeering acts of mail and wire fraud Defendants allegedly committed in furtherance of their scheme. Although the district court did not allow the government to prove 650 additional racketeering acts due to their late disclosure, the court did permit the government to introduce evidence supporting those acts to prove other RICO elements, such as the continuity and pattern of racketeering activity, the RICO enterprise and conspiracy, and Defendants’ participation in the enterprise. After years of pretrial proceedings and discovery, the case went to trial in September 2004. The bench trial lasted nine months and included live testimony from 84 witnesses, written testimony from 162 witnesses, and almost 14,000 exhibits in evidence. The government presented evidence that the presidents of Philip Morris, Reynolds, Brown & Williamson, Lorillard, and American assembled together in 1953 to strategize a response to growing public concern about the health risks of smoking and jointly retained a public relations firm to assist in the endeavor. Id. at 37. From the beginning they agreed that no cigarette manufacturer would “seek a competitive advantage by inferring to its public that its product is less risky than others”; they would make no “claims that special filters or toasting, or expert selection of tobacco, or extra length in the butt, or anything else, makes a given brand less likely to cause you-know-what.” Id. (quoting public relations firm’s Planning Committee Memorandum). Acting on this agreement, the cigarette manufacturers jointly issued “A Frank Statement to Cigarette Smokers,” published as a full-page advertisement in newspapers across the country on January 4, 1954. Id. at 39. “The Frank Statement set forth the industry’s ‘open question’ position that it would maintain for more than forty years — that cigarette smoking was not a proven cause of lung cancer; that cigarettes were not injurious to health; and that more research on smoking and health issues was needed.” Id. All of the Defendant manufacturers eventually joined this collective effort. The government presented evidence from the 1950s and continuing through the following decades demonstrating that the Defendant manufacturers were aware — increasingly so as they conducted more research — that smoking causes disease, including lung cancer. Evidence at trial revealed that at the same time Defendants were disseminating advertisements, publications, and public statements denying any adverse health effects of smoking and promoting their “open question” strategy of sowing doubt, they internally acknowledged as fact that smoking causes disease and other health hazards. Id. at 146, 164, 168-69. Although the manufacturers conducted their own research and public' relations regarding health and other issues, they also relied in part on a series of jointly-created entities. Among these entities were' Defendants TI and CTR (formerly the Tobacco Industry Research Committee). The Defendant manufacturers created TI and CTR, composed their membership, staffed their boards of directors with executives from the manufacturers, and maintained frequent communication between high-level manufacturer and joint-entity officials. Id. at 48-44, 63. Evidence at trial showed that TI and CTR conducted the manufacturers’ joint public relations through false and misleading press releases and publications, trained representatives from the manufacturers regarding their coordinated industry message, conducted some cigarette testing for the manufacturers, and funded “special projects” to produce favorable research results and witnesses specifically for use in litigation and for support of industry public statements. Id. at 66, 82, 86, 87, 91. In addition to the health hazards of smoking, the government presented evidence that Defendants intimately understood the addictiveness of nicotine and manipulated nicotine delivery in cigarettes to create and sustain addiction. Evidence showed that Defendants undertook extensive research into the physiological impact of nicotine, how it operates within the hm man body, and how the physical and chemical design parameters of cigarettes influence the delivery of nicotine to smokers. Id. at 208, 308-09. As a result of this research, they recognized and internally acknowledged that smoking and nicotine are addictive and they engineered their products around creating and sustaining this addiction. Evidence at trial suggested that despite this internal knowledge, for decades Defendants publicly denied and distorted the truth about the addictive nature of their products, suppressed research revealing the addictiveness of nicotine, and denied their efforts to control nicotine levels and delivery. Id. at 209, 309. The government also presented evidence tending to show that Defendants marketed and promoted their low tar brands to smokers — who were concerned about the health hazards of smoking or considering quitting — as less harmful than full flavor cigarettes despite either lacking evidence to substantiate their claims or knowing them to be false. Id. at 430. Internal industry documents introduced at trial revealed -that • by the late 1960s and early 1970s, Defendants were aware that lower tar cigarettes are unlikely to' provide health benefits because they do not actually deliver the low levels of tar and nicotine advertised. Id. at 430-31. Defendants researched and understood the phenomenon whereby smokers of low tar cigarettes, to satisfy their addiction, modify their smoking behavior to compensate for the reduced nicotine yields by “taking more frequent puffs, inhaling smoke more deeply, holding smoke in their lungs longer, covering cigarette ventilation holes with fingers or lips, and/or smoking more cigarettes.” Id. at 431. As a result of this nicotine-driven behavior, smokers of low tar cigarettes boost their intake of tar, so that lower tar cigarettes do not result in lower tar intake and therefore do not yield the touted health benefits or serve as a step toward quitting smoking. Id. Evidence at trial suggested that Defendants understood this concept — for some time, better than the public health community or government regulators — while they promoted lower tar cigarettes as “health reassurance” brands. Regarding secondhand smoke, the government presented evidence suggesting that Defendants became aware that secondhand smoke poses a health risk to nonsmokers but made misleading public statements and advertisements about secondhand smoke in an attempt to cause the public to doubt the evidence of its harmfulness. Id. at 692. At trial, internal industry documents revealed that Defendants believed the public perception of secondhand smoke could determine the industry’s survival and that secondhand smoke research by the cigarette manufacturers was a sensitive issue due to the absence of “objective science” supporting their position and the risk that their own research would lead to unfavorable results. Id. at 733. As a result, the manufacturers jointly created the- Center for Indoor Air Research (“CIAR”) to coordinate and fund their secondhand smoke research with the appearance of independence. Id. at 119, 735. The evidence also showed that they “created, controlled, used, or participated in” a vast array of foreign or international entities to conduct their sensitive secondhand smoke research, generate “marketable science” to use for public relations purposes, and coordinate their shared objectives and message. Id. at 119-20, 759. In addition to these topics, the government also presented evidence to the district court regarding Defendants’ targeted marketing to youth under twenty-one years of age and their denials of such marketing, id. at 561, 672, as well as evidence concerning Defendants’ employees and attorneys destroying documents relevant to their public and litigation positions and suppressing or concealing scientific research, id. at 801, 832. During the trial, this court rendered a decision on Defendants’ interlocutory appeal from the denial of summary judgment on the government’s claim for a disgorgement remedy under RICO section 1964(a). We reversed the district court and held that disgorgement is not an available remedy in civil RICO cases. United States v. Philip Morris USA, Inc. (“Disgorgement Opinion”), 396 F.3d 1190 (D.C.Cir.2005). In response, the district court granted the government leave to reformulate its proposed remedies. After the liability phase of the trial, the district court held a fourteen-day remedies trial. At the close of the remedies phase, several organizations moved to intervene in the litigation to assert their interests in the proposed remedies. The district court granted the American Cancer Society, the American Heart Association, the American Lung Association, Americans for Nonsmokers’ Rights, the National African American Tobacco Prevention Network, and the Tobacco-Free Kids Action Fund leave to intervene solely on .the subject of remedies. The district court entered final judgment against Defendants on August 17, 2006, finding that they maintained an illegal racketeering enterprise and each Defendant participated in the conduct, management, and operation of the enterprise in violation of section 1962(c), and that they explicitly and implicitly agreed to do so, in violation of section 1962(d). Philip Morris, 449 F.Supp.2d at 851, 901. The court found that Defendants engaged in a scheme to defraud smokers and potential smokers by (1) falsely denying the adverse health effects of smoking, id. at 854; (2) falsely denying that nicotine and smoking are addictive, id. at 856; (3) falsely denying that they manipulated cigarette design and composition so as to assure nicotine delivery levels that create and sustain addiction, id. at 858; (4) falsely representing that light and low tar cigarettes deliver less nicotine and tar and therefore present fewer 'health risks than full flavor cigarettes, id. at 859; (5) falsely denying that they market to youth, id. at 861; (6) falsely denying that secondhand smoke causes disease, id. at 864; and (7) suppressing documents, information, and research to prevent the public from learning the truth about these subjects and to avoid or limit liability in litigation, id. at 866. The court concluded' that the government failed to prove that Defendants deliberately chose not to utilize or market feasible designs or product features that could produce less hazardous cigarettes. Id. at 384. Before granting injunctive relief against Defendants the district court assessed whether they presented a “reasonable likelihood of further violation(s) in the future.” Id. at 909 (quoting SEC v. Savoy Indus., Inc., 587 F.2d 1149, 1168 (D.C.Cir. 1978)). The court concluded that Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, Altria, and BATCo were reasonably likely to commit future RICO violations unless enjoined because they continued to make false and misleading statements at the time of trial, their businesses presented continuing opportunities to commit RICO violations, and their corporate leadership continued to consist of veteran employees with longstanding ties to the companies. Id. at 910-13. Defendants argued that no injunction was necessary because their Master Settlement Agreement with forty-six states and the District of Columbia and their individual settlements with four states already sufficiently restrained them. The district court rejected this argument, concluding that the Master Settlement Agreement did not obviate the need for injunctive relief because Defendants had not fully complied with the agreement, parts of the agreement began expiring in 2006, the states could not vigorously enforce all aspects of the agreement, and BATCo and Altria were not subject to the settlement agreement. Id. at 913-15. The district court found that three Defendants — CTR, TI, and Liggett — did not present a reasonable likelihood of future RICO violations, therefore the court did not order injunctive remedies against them. CTR and TI, the court found, now exist solely for the limited purpose of winding up their activities and each retains only one adviser to support its litigation defense and handle any remaining administrative matters. Id. at 915-18. The court found that Liggett withdrew from the RICO conspiracy by admitting that smoking causes cancer and is addictive, by voluntarily restricting its advertising and including disclosures on its packages, and by cooperating with the United States and state attorneys general in ■ their claims against other tobacco companies. Id. at 906-07, 918-19. The district court concluded that Liggett was not reasonably likely to commit future RICO violations based on this withdrawal, its continued independence from the other Defendants, and its limited opportunity for future violations by virtue of its discount cigarette market and lack of traditional consumer advertising. Id. at 918-19. Pursuant to section 1964, the district court imposed injunctive remedies against the other seven manufacturer Defendants. Specifically, the court ordered Defendants (1) to refrain from any acts of racketeering relating to the manufacturing, marketing, promotion, health consequences, or sale of cigarettes in the United States; (2) not to participate in the management or control of CTR, TI, or CIAR, and not to reconstitute the form or function of those entities; (3) to refrain from making any material false, misleading, or deceptive representation concerning cigarettes that is disseminated to the United States public; (4) to cease using any express or implied health message or health descriptor for any cigarette brand, such as light or low tar; (5) to make corrective disclosures about addiction, the adverse health effects of smoking and secondhand smoke, their manipulation of cigarette design and composition, and light and low tar cigarettes; (6) to create document depositories providing the government and the public access to all industry documents disclosed in litigation; and (7) to provide their disaggregated marketing data to the government according to the schedule on which they provide it to the Federal Trade Commission. Id. at 938-45. The court also limited the sale and transfer of Defendants’ brands, product formulas, and businesses to entities that either are subject to the injunctive order or will sell the brand, use the formula, or conduct the business exclusively outside the United States. Id. at 945. The district court denied the remainder of the government’s requested injunctive relief, including its proposed national smoking cessation program, public education and counter-marketing campaign, and youth smoking reduction plan. Id. at 933-34, 936-37. The court also denied the government’s requests that it appoint a monitor to investigate and restructure the Defendant companies,, id at 935, and that it order Defendants to make public all “health and safety risk information” about their products in their own files, id. at 929. All Defendants except Liggett appealed, raising numerous challenges to the finding of liability and the remedies imposed. The government and the intervenors filed a cross-appeal regarding the remedies that the district court denied. On Defendants’ motion we stayed the remedial injunction pending appeal. We review the district court’s conclusions of law de novo. SEC v. Wash. Inv. Network, 475 F.3d 392, 399 (D.C.Cir.2007). To the extent it is not based on legal error, we review the district court’s decision to issue an injunction for abuse of discretion. Id. We may not set aside the district court’s findings of fact unless they are clearly erroneous, giving due regard to the court’s opportunity to judge the witnesses’ credibility. Id. (citing Fed. R. Civ. P. 52(a)(6)). This standard applies even when the district court adopts a party’s proposed findings verbatim. Anderson v. City of Bessemer City, 470 U.S. 564, 572, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). To establish RICO liability, the government had to prove the necessary elements of RICO itself — including the existence of an enterprise and a pattern of racketeering activity, 18 U.S.C. § 1962(c) — as well as the elements of the underlying conduct constituting the racketeering acts, here, numerous instances of mail and wire fraud under 18 U.S.C. §§ 1341 and 1343. Defendants challenge the district court’s findings regarding both RICO and the underlying fraud, as well as the remedies the court imposed. We address Defendants’ challenges to RICO liability in Part II, their general challenges to fraud liability in Part III, their challenges to specific aspects of the fraudulent scheme and the liability of specific Defendants in Part TV, their challenges to the finding that they are likely to commit future violations and therefore should be enjoined in Part V, and their challenges to particular remedies the court imposed in Part VI. II. Challenges to RICO Liability A. RICO Enterprise RICO makes it unlawful for “any person ... associated with any enterprise ... to conduct or participate, directly or indirectly, in the conduct of such enterprise’s affairs through a pattern of racketeering activity.” 18 U.S.C. § 1962(e). Thus, in a section 1962(c) suit, the defendants are the “persons” who conduct the “enterprise’s” affairs through racketeering activity. Because RICO defines “person” as including “any individual or entity capable of holding a legal or beneficial interest in property,” id. § 1961(3), corporations as well as individuals can be liable if they conduct an enterprise’s affairs through a pattern of racketeering activity. In language central to the issue before us, section 1961(4) states: “enterprise” includes any individual, partnership, corporation, association, or other legal entity, and any union or group of individuals associated in fact although not a legal entity. Id. § 1961(4). The enterprise as such generally faces no section 1962(c) RICO liability; indeed it may be the innocent vehicle through which unlawful activity is carried out, see Cedric Kushner Promotions, Ltd. v. King, 533 U.S. 158, 164, 121 S.Ct. 2087, 150 L.Ed.2d 198 (2001) (“RICO both protects a legitimate ‘enterprise’ from those who would use unlawful acts to victimize it, and also protects the public from those who would unlawfully use an ‘enterprise’ (whether legitimate or illegitimate) as a ‘vehicle’ through which ‘unlawful ... activity is committed.’ ” (quoting United States v. Turkette, 452 U.S. 576, 591, 101 S.Ct. 2524, 69 L.Ed.2d 246 (1981), and Nat’l Org. for Women, Inc. v. Scheidler, 510 U.S. 249, 259, 114 S.Ct. 798, 127 L.Ed.2d 99 (1994))). When the enterprise is an association-in-fact, members of the association may be both part of the “enterprise” and liable as “persons” under RICO if they conduct the enterprise’s affairs through racketeering activity. See, e.g., United States v. Richardson, 167 F.3d 621, 626 (D.C.Cir.1999) (upholding conviction of defendant member of association-in-fact enterprise). Here, defining the RICO enterprise as “a group of business entities and individuals associated-in-fact, including Defendants to this action, their agents and employees, and other organizations and individuals,” the district court held that the Defendant cigarette manufacturers and trade organizations had violated section 1962(c) by participating in the conduct of the enterprise’s affairs through multiple acts of mail and wire fraud. Philip Morris, 449 F.Supp.2d at 851, 867. Defendants challenge the district court’s acceptance of a RICO enterprise made up of individuals and corporations, arguing that the statute provides an exclusive list of possible enterprises that covers groups of individuals associated in fact, not mixed groups of individuals and corporations associated in fact. In United States v. Perholtz, 842 F.2d 343 (D.C.Cir.1988), however,- we squarely rejected this precise argument. There, we held that a group of seven individuals and eleven corporations and partnerships associated in fact may constitute a RICO “enterprise.” Id. at 351 n. 12, 353. We explained: “[RICO] defines ‘enterprise’ as including the various- entities specified; the list of entities is not meant to be exhaustive.” Id. at 353. As such, a group of individuals, corporations, and partnerships associated in fact can qualify as a RICO “enterprise,” even though section 1961(4) nowhere expressly mentions this type of association. - In so holding, we joined several other circuits that had 'reached the same conclusion. Perholtz, 842 F.2d at 353 (citing the Second, Third, Seventh, and Eleventh Circuits, as well as Fifth Circuit Unit B). Indeed, both prior to and since Perholtz, every circuit to consider the question has likewise held that corporations may be part of an association-in-fact enterprise. See United States v. London, 66 F.3d 1227, 1243-44 (1st Cir.1995) (holding that corporations can be part of an association-in-fact enterprise because section 1961(4)’s list is not exhaustive); United States v. Huber, 603 F.2d 387, 394 (2d Cir.1979) (same); United States v. Aimone, 715 F.2d 822, 828 (3d Cir.1983) (same); United States v. Thevis, 665 F.2d 616, 625-26 (5th Cir. Unit B 1982) (same), superseded on other grounds by Fed.R.Evid. 804(b)(6) (1997); United States v. Masters, 924 F.2d 1362, 1366 (7th Cir.1991) (same); Atlas Pile Driving Co. v. DiCon Fin. Co., 886 F.2d 986, 995 n. 7 (8th Cir.1989) (same); see also Dana Corp. v. Blue Cross & Blue Shield Mut. of N. Ohio, 900 F.2d 882, 887 (6th Cir.1990) (reaching same outcome and citing Huber, 603 F.2d at 393-94); United States v. Navarro-Ordas, 770 F.2d 959, 969 n. 19 (11th Cir.1985) (same); United States v. Feldman, 853 F.2d 648, 655-56 (9th Cir.1988) (reaching same outcome based on different statutory analysis); United States v. Najjar, 300 F.3d 466, 484 (4th Cir.2002) (upholding without discussion RICO convictions involving an association-in-fact enterprise that included corporations). The judges of these circuits are equally unanimous, for not one has dissented from the proposition that an association-in-fact enterprise may include corporations. Defendants argue that Perholtz has no applicability where, as here, the defendants are corporations. Because the Perholtz defendants were individual members of the enterprise, not its corporate members, Defendants here claim that Perholtz applies only when individuals, not corporations, are the RICO defendants. As Defendants see it, Perholtz merely ensures that individuals are unable to escape liability simply by including corporations in their enterprise; Perholtz, they argue, does not mean that the associated-in-fact corporations can themselves incur RICO liability. But nothing in Perholtz is so limited. Quoting the Supreme Court’s statement in United States v. Turkette that “[tjhere is no restriction upon the associations embraced by the definition [of enterprise],” 452 U.S. at 580, 101 S.Ct. 2524, Perholtz sets forth its holding in broad terms: “We therefore follow those courts that have held that individuals, corporations, and other entities may constitute an association-in-fact,” 842 F.2d at 353. Nowhere does Perholtz suggest that the rule varies depending on the identity of the defendants. Indeed; two of the cases Perholtz relies on involved corporate defendants. Id. (citing Thevis, 665 F.2d at 625-26 (upholding RICO convictions for one individual and one corporate defendant), and Bunker Ramo Corp. v. United Bus. Forms, Inc., 713 F.2d 1272, 1285 (7th Cir.1983) (upholding RICO charges against one individual and one corporation)). Many other decisions have similarly upheld RICO allegations involving corporate defendants who were also members of the association-in-fact enterprise. See, e.g., City of N.Y. v. Smokes-Spirits.com, Inc., 541 F.3d 425, 450-51 (2d Cir.2008); Odom v. Microsoft Corp., 486 F.3d 541, 553 (9th Cir.2007); Najjar, 300 F.3d at 484; United States v. Goldin Indus., Inc., 219 F.3d 1271, 1274 (11th Cir.2000); Dana Corp., 900 F.2d at 887; Shearin v. E.F. Hutton Group, Inc., 885 F.2d 1162, 1165-66 (3d Cir.1989), overruled on other grounds by Beck v. Prupis, 529 U.S. 494, 506, 120 S.Ct. 1608, 146 L.Ed.2d 561 (2000); Atlas Pile Driving, 886 F.2d at 995; Ocean Energy II, Inc. v. Alexander & Alexander Inc., 868 F.2d 740, 748-49 (5th Cir.1989). Moreover, Defendants’ proposed limitation on Perholtz is contrary to the statute’s language. As “persons” under section 1961(3), corporations may be RICO defendants regardless of the kind of enterprise charged. See 18 U.S.C. § 1962(c) (“It shall be unlawful for any person ... associated with any enterprise ... to conduct or participate, directly or indirectly, in the conduct of such enterprise’s affairs through a pattern of racketeering activity.” (emphases added)). Defendants cite not a single case lending even a shred of support to the idea that the meaning of “enterprise” can fluctuate depending on whom the government or the plaintiff chooses to name as the defendant. Perholtz’s interpretation of section 1961(4) thus applies regardless of whether the RICO defendants are individual “persons” or corporate “persons.” To hold otherwise would require us to rewrite section 1962(c). .In a further attempt to evade Perholtz, Defendants argue that even if Perholtz was correct when decided, it has been eroded by the Supreme Court’s 2001 decision in Cedric Kushner Promotions, Ltd. v. King, 533 U.S. 158, 121 S.Ct. 2087, 150 L.Ed.2d 198 (2001). Defendants’ argument begins with the premise that at the time we decided Perholtz, RICO presented a potential loophole: because the RICO defendant must be distinct from the RICO enterprise, Yellow Bus Lines, Inc. v. Drivers, Chauffeurs & Helpers Local Union 639, 839 F.2d 782, 790 (D.C.Cir.1988) (“[0]ne entity may not serve as the enterprise and the person associated with it .... ”), vacated on other grounds, 492 U.S. 914, 109 S.Ct. 3235, 106 L.Ed.2d 583 (1989), a sole shareholder who used his alter-ego corporation for racketeering might evade RICO liability because he wouldn’t be sufficiently distinct from.the alter-ego corporation “enterprise.” Defendants rely on Perholtz’s suggestion that a definition of “enterprise” that excluded associations-in-fact of corporations would lead to “the bizarre result that only criminals who failed to form corporate shells to aid their illicit schemes could be reached by RICO.” 842 F.2d at 353. According to Defendants, we were motivated in Perholtz by the underlying concern “that a criminal defendant conducting the affairs of an ‘enterprise’ that was his own closely held corporation, would be so closely tied to the enterprise that he would escape RICO liability.” Defs. Br. 37. Given that the Supreme Court has subsequently eliminated this concern — holding in Cedric Kushner that an individual sole shareholder is sufficiently distinct from his alter-ego corporation to sustain RICO liability, 533 U.S. at 160, 121 S.Ct. 2087 — Defendants assert that Perholtz no longer represents binding authority. We do not read Perholtz as motivated by the concerns addressed in Cedric Kushner. In contrast to Cedric Kushner, the enterprise in Perholtz involved multiple individuals and numerous corporations, with no indication that the corporations were either all closely held by the individual defendants or in any other way insufficiently distinct. 842 F.2d at 351 n. 12. Indeed, at least some of the Perholtz corporate enterprise members were not closely held. For example, enterprise member International Business Services, Inc. (IBS) existed in its own right prior to the scheme and was related to the defendants through employment relationships that would not have defeated RICO’s distinctness requirement: Perholtz himself was a consultant to IBS, and the other RICO defendant, Franklin Jackson, was an IBS project manager. Id. at 348. Similarly, enterprise member Remote Computer Services Corporation, although formed expressly for the purpose of the scheme, was jointly held in equal shares by three individuals — Perholtz and two other individual members of the enterprise, id. at 350 — and thus would have been sufficiently distinct from each of those non-sole shareholders. The enterprise also included two separate real estate companies both of which apparently existed independently of the scheme and were not otherwise affiliated with the individuals. Id. at 351 n. 12. At least one individual enterprise member, John Gentile, worked for the Postal Service and apparently had no formal stake in the corporate enterprise members. Id. at 346, 351 n. 12. In Perholtz, we held that all these corporations — not just those closely held or created solely for the scheme — could be part of an association-in-fact enterprise. Indeed, only after so holding did we turn to Perholtz’s entirely separate argument that he, as an individual, was insufficiently distinct from the enterprise. Far from basing our holding on this argument, we simply noted that we had “no occasion to consider the separateness requirement” because Perholtz associated not with himself but with others. Id. at 353. Given the structure of the Perholtz enterprise and the court’s acknowledgement that distinctness was not at issue, we think Perholtz reflected a different concern, namely that a group of sophisticated racketeers who would otherwise constitute an association-in-fact might evade RICO’s grasp by virtue of their ability to operate through corporations and establish complex networks of companies, kickbacks, and contracts to achieve their illicit ends. Indeed, immediately following its reference to “corporate shells,” Perholtz emphasized Congress’s desire that RICO serve “as a weapon against the sophisticated racketeer as well as (and perhaps more than) the artless.” Id. Perholtz itself presented just such a situation: the defendants worked through their own companies and multiple outside corporations in an intricate web of shared commissions to game the bidding process for government contracts. 'The success of the scheme required the participation of "companies to serve as contractors and subcontractors. “This relationship of individuals and corporations is precisely what section 1962(c) was designed to attack.” Id. at 354. Moreover, in asserting their Cedric Kushner argument, Defendants fail to explain how Perholtz’s interpretation would even solve the hypothetical problem they posit. According to Defendants, in order to preserve RICO liability for a sole shareholder who would be insufficiently distinct from his alter-ego corporation, the Perholtz court held that an “individual and his shell corporation could together ... constitute an association-in-fact enterprise.” Defs. Reply Br. 16. In Defendants’ view, the sole shareholder would then be liable under RICO for conducting the affairs of this association-in-fact enterprise. Yet if an individual is insufficiently distinct from his alter-ego corporation, we seriously doubt he would suddenly be sufficiently distinct from an enterprise consisting of his alter-ego corporation and himself. If Perholtz had been concerned with distinctness, its purported “solution” would make little sense. Further seeking to justify their reliance on Cedric Kushner, Defendants say that the government cites only one post-Cedric Kushner case—United States v. Najjar, 300 F.3d 466 (4th Cir.2002) — that upheld an association-in-fact enterprise of corporations. The relevance of this is hard to grasp, as other post-Cedric Kushner cases not cited by the government accept association-in-fact enterprises comprised of corporations. See Smokes-Spirits.com, 541 F.3d at 450-51 (holding that the plaintiff adequately pleaded an association-in-fact enterprise consisting of two corporations); Odom, 486 F.3d at 553 (holding that plaintiffs had sufficiently alleged an association-in-fact enterprise of two corporations); United States v. Cianci, 378 F.3d 71, 83 (1st Cir.2004) (“It is uncontroversial that corporate entities, including municipal and county ones, can be included within association-in-fact RICO enterprises.”); Living Designs, Inc. v. E.I. Dupont de Nemours & Co., 431 F.3d 353, 361 (9th Cir.2005) (“[T]here is no question that DuPont [corporation] and the law firms together can constitute an ‘associated in fact’ RICO enterprise.”). And as we noted above, no circuit has ever held the opposite. Cedric Kushner thus undermines neither the unanimous judicial view that association-in-fact enterprises may include corporations nor Perholtz’s binding effect on this case. Defendants’ argument that we should read section 1961(4) as an exhaustive list of possible RICO enterprises is therefore unavailing. Not only is it foreclosed by Perholtz, it is unpersuasive on its own terms. As Perholtz and many other circuits explain, the use of the word “includes” indicates that RICO’s list of “enterprises” is non-exhaustive. Indeed, section 1961 makes the non-exhaustive nature of “includes” clear by alternating between the words “means” and “includes” to introduce the section’s various definitions. Specifically, five of section 1961’s ten subsections introduce definitions with the word “means.” For example, section 1961(1) defines “racketeering activity,” explaining that the term “means” any of a list of specific state and federal crimes. Section 1961(2) likewise introduces a definitional list with the term “means”: “ ‘State’ means any State of the United States, the District of Columbia, the Commonwealth of Puerto Rico, any territory or possession of the United States, any political subdivision, or any department, agency, or instrumentality thereof.” 18 U.S.C. § 1961(2); see also id. § 1961(6), (7), (8) (introducing definitions of “unlawful debt,” “racketeering investigator,” and “racketeering investigation” with the term “means”). Section 1961(4), by contrast, says “ ‘enterprise’ includes any individual, partnership, corporation, association, or other legal entity, and any union or group of individuals associated in fact although not a legal entity.” Id. § 1961(4) (emphasis added). By switching between “means” and “includes” in the same definitional provision, Congress signaled its intent to distinguish between exhaustive and non-exhaustive lists. See Helvering v. Morgan’s, Inc., 293 U.S. 121, 126 n. 1, 55 S.Ct. 60, 79 L.Ed. 232 (1934) (describing a statute that introduced three definitions with the word “includes” and seven definitions with the word “means” and noting that “[t]he natural distinction would be that where ‘means’ is employed, the term and its definition are to be interchangeable equivalents, and that the verb ‘includes’ imports a general class, some of whose particular instances are those specified in the definition”). That Congress provided an exhaustive list of legal entity enterprises by adding the phrase “or other legal entity” hardly converts the list of wm-legal entity enterprises into an exhaustive list. Had Congress wanted to limit non-legal entity associations to those expressly listed, the most obvious way to do so would have been the way Congress wrote the five clearly exhaustive definitions in the same section: it could have said “ ‘enterprise’ means any individual, partnership, corporation, association, or other legal entity, or any union or group of individuals associated in fact although not a legal entity.” But Congress chose to say “ ‘enterprise’ includes ” the listed entities. Defendants think that the phrase “or other legal entity” would have been unnecessary if the list were otherwise non-exhaustive. Not so. Adding “or other legal entity” serves to ensure that all legal entities are covered while retaining the possibility that some additional nonlegal entities beyond those listed are also covered. Nor* does the use of the phrase “including, but not limited to” to indicate a non-exhaustive list in a different section of RICO, section 1964(a), demonstrate that the sole word “includes” in section 1961(4) must introduce an exhaustive list. Section 1964, which establishes civil remedies for RICO violations, lacks section 1961’s juxtaposition of the non-exhaustive term “includes” with the exhaustive term “means”; adding “but not limited to” helps to emphasize the non-exhaustive nature of section 1964(a)’s list of remedies. Section 1961 needed no such clarification because it employed the contrasting terms “means” and “includes” to distinguish exhaustive from non-exhaustive definitions. Contrary to Defendants’ argument, nothing about this interpretation renders the definition of “enterprise” devoid of meaning. Although encompassing non-enumerated enterprises, section 1961(4)’s list defines “enterprise,” in part, by listing the kinds of entities Congress had in mind. Indeed, the Supreme Court has acknowledged this meaning by requiring enterprises to exhibit common purpose, organization, and continuity. Turkette, 452 U.S. at 583, 101 S.Ct. 2524; see also Richardson, 167 F.3d at 625. In sum, as Perholtz clearly holds, because RICO’s “list of entities is not meant to be exhaustive,” “individuals, corporations, and other entities may constitute an association-in-fact.” 842 F.2d at 353. This binding precedent — confirmed by the statute’s language, buttressed by the unanimity among our sister' circuits, and undiminished by Defendants’ efforts to escape it — requires that we affirm the district court’s holding that the government properly alleged a RICO enterprise of individuals, cigarette manufacturers, and trade organizations. We also reject Defendants’ additional challenges to the district court’s findings regarding the existence of a RICO enterprise and their participation in its affairs. The district court found — permissibly in our view: — that the enterprise had the common purpose of obtaining cigarette proceeds by defrauding existing and potential smokers, Philip Morris, 449 F.Supp.2d at 869; possessed the requisite structure both through informal association and through the formation of several formal organizations, id. at 870-71; functioned as a continuous unit despite personnel changes, id. at 871-72; and constituted a separate entity distinct from each Defendant, id. at 875. Defendants give us neither any basis for concluding that the district court’s factual findings were clearly erroneous nor any reason to think them legally insufficient. The district court also found — again permissibly — that despite competing in some aspects of their business, Defendants jointly committed fraud and so participated in the conduct of not just their own affairs but the enterprise’s as well, id. at 875-78, and also that they conspired to do so, id. at 903-05. Accordingly, we affirm the district court’s findings that an enterprise existed and that Defendants participated in the conduct- of its affairs and conspired to do so. B. Identifying Racketeering Acts Defendants complain that' the district court failed to identify the racketeering acts that support the finding of liability. While it is true the district court’s opinion provided no single, discrete list of specific racketeering acts, the comprehensive findings — detailing over one-hundred racketeering acts — are sufficient to warrant affirmance. Defendants raise numerous challenges to the correctness of the district court’s findings that they committed racketeering acts, which we take up in Parts III and IV. In this section, however, we are concerned only with the existence of these findings, not their validity. By statutory definition, any violation of the mail or wire fraud statutes can qualify as “racketeering activity.” 18 U.S.C. § 1961(1). To prove a violation of the' mail and wire fraud statutes, the government must show (1) a scheme or artifice to defraud and (2) a mailing or wire transmission in furtherance thereof. Id. §§ 1341, 1343. “Where one scheme involves several mailings, the law is settled that each mailing constitutes a violation of the statute.” Hanrahan v. United States, 348 F.2d 363, 366 (D.C.Cir.1965). Where, as here, the mail and wire fraud statutes serve as the predicate offenses for a RICO violation, each racketeering act must be a mailing or wire transmission made in furtherance of a “scheme or artifice to defraud.” 18 U.S.C. §§ 1341, 1343. Thus, in order to identify the racketeering acts, the district court must first have found a scheme- to defraud, then concluded the alleged mailings or wire transmissions were in furtherance of such scheme. See Philip Morris, 449 F.Supp.2d at 852-54. Although Defendants question whether the district court clearly found a scheme to defraud, the finding on this question is explicit: “The Government has proven that the Enterprise knowingly and intentionally engaged in a scheme to defraud smokers and potential smokers, for purposes of financial gain, by making false and fraudulent statements, representations,, and promises.” Id. at 852. The district court explains, in great detail, the seven components of the scheme to defraud. . Id. at 852-67. The court also held that “each of the alleged mailings and wire - transmissions was in furtherance of the overarching scheme to defraud.” Id. at 881. Thus it follows that any mailing or wire transmission found to have been made was found to have been a mail or wire fraud offense and therefore a racketeering act. Seventy-nine of the alleged acts were established by Defendants’ own stipulations and admissions. Id. at 882 (enumerating 79 racketeering acts). Altogether, the court enumerated 108 racketeering acts in the opinion, as well as six others which it excluded on First Amendment grounds. See id. at 882, 884, 885 n. 62, 887. This total does not include the many other findings which may be tied to other racketeering acts, but for which the district court did not provide a specific list. See, e.g., id. at 883 (“[I]t is clear beyond any question that Defendants caused the mailings and wire transmissions underlying the 30 Racketeering Acts involving the news media’s dissemination of Defendants’ press releases and advertisements to their subscribers.”). The RICO statute requires “a pattern of racketeering activity” on the part of each defendant. 18 U.S.C. § 1962(c). “[A]t least two acts of racketeering activity” are necessary to form a pattern. H.J., Inc. v. Nw. Bell Tel. Co., 492 U.S. 229, 237, 109 S.Ct. 2893, 106 L.Ed.2d 195 (1989) (quoting 18 U.S.C. § 1961(5)). The district court found the requisite pattern committed by each Defendant, Philip Morris, 449 F.Supp.2d at 889-91, and this finding is not erroneous. A brief sampling of the 108 enumerated racketeering acts makes the point: Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, and TI committed racketeering acts 24-, 132, and 133 by mailing press releases containing false statements about the addictiveness and health consequences of smoking. Id. at 194, 282-83. Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, Liggett, and CTR committed racketeering acts 66, 73, and 88 by mailing letters regarding funding of CTR’s “special projects” to create data supporting their fraudulent claims. Id. at 101, 882, 972, 976. BATCo and Brown & Williamson committed racketeering acts 30, 50, 51, 53, and 63 through their mailings to each other concerning the enterprise’s position on the health effects and addictiveness of smoking as well as smoker compensation and nicotine. Id. at 253-54, 301, 882, 965, 969. Altria committed racketeering acts 71, 72, 74, and 75 in its efforts to coordinate Defendants’ public positions and fund CTR research projects to support their fraudulent claims. Id. at 295, 813, 884, 974. As these examples demonstrate, the district court found each Defendant engaged in a “pattern of racketeering activity,” and that finding is not erroneous. See infra Parts III, IV. The 108 enumerated acts give us ample basis to review the district court’s finding. Although the district court may have concluded other racketeering acts were proven as well, we need look no further. Defendants correctly argue we must ensure the remedy imposed is tailored to “the violation found,” United States v. Microsoft, 253 F.3d 34, 105 (D.C.Cir.2001); the voluminous findings detailing the contours of the scheme to defraud are more than sufficient to allow this review, see, e.g., Philip Morris, 449 F.Supp.2d at 852-67. Given that a mailing or wire transmission need not itself be fraudulent, the remedy needs to be tailored to the scheme to defraud, not the specific use of the mail or wires. For similar reasons, we need not resolve Defendants’ challenges to the racketeering acts involving denials of marketing to youth. As the district court imposed no remedies specifically relating to youth marketing, our assessment whether the remedies are tailored to the violation found is unaffected by the associated racketeering acts. The remaining racketeering acts are fully sufficient to support the district court’s finding of a pattern of racketeering activity as to each Defendant. Because these challenges have no impact on the outcome of this appeal, we decline to address them. The district court set forth findings sufficient to allow our review of its verdict of liability and imposition of sanction. III. General Challenges to Fraud Liability A. Specific Intent The predicate acts of racketeering in this case were all acts of mail or wire fraud, which require specific intent to defraud. Post v. United States, 407 F.2d 319, 329 (D.C.Cir.1968). Defendants challenge the district court’s conclusion that they acted with specific intent, arguing that the district court applied an impermissible “collective intent” standard and that the government did not present any evidence to support a finding of specific intent under the correct formulation. Corporations may be held'liable for specific intent offenses based on the “knowledge and intent” of their employees. N.Y. Cent. & Hudson River R.R. Co. v. United States, 212 U.S. 481, 495, 29 S.Ct. 304, 53 L.Ed. 613 (1909); see United States v. A & P Trucking Co., 358 U.S. 121, 125, 79 S.Ct. 203, 3 L.Ed.2d 165 (1958). Because a corporation only acts and wills by virtue of its employees, the proscribed corporate intent depends on the wrongful intent of specific employees. See Saba v. Compagnie Nationale Air France, 78 F.3d 664, 670 (D.C.Cir.1996). Thus, to determine whether a corporation made a false or misleading statement with specific intent to defraud, we look to the state of mind of the individual corporate officers and employees who made, ordered, or approved the statement. Southland Sec. Corp. v. INSpire Ins. Solutions Inc., 365 F.3d 353, 366 (5th Cir.2004). A person’s state of mind is rarely susceptible of proof by direct evidence, so specific intent to defraud may be, and most often is, inferred from the totality of the circumstances, including indirect and circumstantial evidence. United States v. Alston, 609 F.2d 531, 538 (D.C.Cir.1979); United States v. Reid, 533 F.2d 1255, 1264 (D.C.Cir.1976). We refer to this inference when, in the common law fraud context, we say that the factfinder “is permitted to impute knowledge of the falsity of the statements to the accused, not as a matter of law but as a consequence of inferences reasonably drawn from the facts shown.” United States v. Avant, 275 F.2d 650, 653 (D.C.Cir.1960). Here, the district court concluded that the chief executive officers and other highly placed officials in the Defendant corporations made or approved statements they knew to be false or misleading, evincing their specific intent to defraud consumers. In some instances, the court found by direct evidence that representatives of the Defendant companies “willfully stat[ed] something which they knew to be untrue.” Philip Morris, 449 F.Supp.2d at 895. For example, the court found that, in a televised interview in 1971, Philip Morris President Joseph Cullman III denied that cigarettes posed a health hazard to pregnant women or their infants, “contradicting] the information Helmut Wake-ham, Philip Morris’s Vice President for Corporate Research and Development, had given him two years earlier.” Id. at 193-94. In the main, however, the district court relied on indirect and circumstantial evidence indicating that the senior corporate officials knew that their public statements, and those that they approved for their corporations, were false or misleading. In the majority of instances, the authors of the fraudulent statements alleged as Racketeering Acts were executives, in- ■ eluding high level scientists — CEOs, Vice Presidents, Heads of Research & Development, not entry level employees — at each of the Defendant companies who would reasonably be expected to have knowledge of the company’s internal research, public positions, and long term strategies. Id. at 897. The court reasoned: [I]t is absurd to believe that the highly-ranked representatives and agents of these corporations and entities had no knowledge that their public statements were false and fraudulent. The Findings of Fact are replete with examples of C.E.O.s, Vice-Presidents, and Directors of Research and Development, as well as the Defendants’ lawyers, making statements which were inconsistent with the internal knowledge and practice of the corporation itself. Id. at 853. The district court did not commit legal error by imputing to Defendants’ executives knowledge of the falsity of their statements based on inferences reasonably drawn from the facts shown, and sufficient evidence supported these inferences. The government presented decades of evidence that scientists within the Defendant corporations and outside scientists hired by the corporations and their joint entities were continually conducting research and reviewing the research of other scientists regarding cigarettes and health, addiction, nicotine and tar manipulation, and secondhand smoke. The evidence at trial demonstrated that the results of this research — essential to the core of Defendants’ operations, including strategic planning, product development, and advertising — were well known, acknowledged, and accepted throughout the corporations. These results established that cigarette smoking causes disease, that nicotine is addictive, that light cigarettes do not present lower health risks than regular cigarettes due to smoker compensation, and that secondhand smoke is hazardous to health. Dr. William Farone, a scientist who worked at Philip Morris for eighteen years and whom the district court found to be “impressive and credible as both a fact and expert witness,” id. at 186, testified about the understanding within Philip Morris on the question of whether cigarette smoking is a cause of lung cancer and other diseases: There was widespread acceptance that smoking caused disease. I never talked with a scientist at Philip Morris who said that smoking doesn’t cause disease. [This was based on the] compelling epidemiology such as that recounted in the Surgeon’s [sic] General’s reports, and our knowledge about the chemicals that were created by cigarettes and what was delivered to the smoker, hundreds of times per day on average. Id. at 187 (quoting Farone testimony). When asked whether, in his discussions with Philip Morris executives, any of them challenged the validity of the scientific evidence that smoking causes disease, Farone answered, No. Their comments generally focused on how the company could or should respond, not to whether the scientific evidence was valid. Remember, a main reason why they hired me in 1976 was to help develop a less hazardous cigarette. It seemed to me at the time I was hired, and certainly was the case during my entire time there, that hiring me for that job was itself implicit recognition that the cigarettes that were out there being sold were causing disease. Id. (quoting Farone testimony). The Defendant corporations documented the results of the studies regarding disease, nicotine addiction, and smoker compensation in numerous memoranda and reports; the evidence at trial, including internal corporate documents, demonstrated that the executives crafted their corporate priorities and strategies in response to these findings. See, e.g., id. at 165, 180, 218, 219, 232, 240, 258-59, 270, 336, 720. Defendants’ own documents also support the' inference that Defendants’ executives were aware that their public relations strategy of creating the impression of an “open question” about the link between smoking and disease did not square with them own knowledge about the established link between the two. For example, William Kloepfer, Vice President of Public Relations for the Tobacco Institute, wrote to Earle Clements, President of the Tobacco Institute, admitting that “[o]ur basic position in the cigarette controversy is subject to the charge, and may be subject to a finding, that we are making false or misleading statements to promote the sale of cigarettes.” Id. at 855. Other documents demonstrate that Defendants’ top officials were directly informed of negative research results. For example, in 1977 Philip Morris Assistant General Counsel Alexander Holtzman sent a “warning” to the company’s President, Joseph Cullman, informing him that a research project jointly sponsored by a group of the Defendant companies had concluded that .exposure to cigarette smoke causes emphysema. Id. at 183. The government presented similar evidence regarding the other aspects of Defendants’ scheme, such as addiction and nicotine. A few examples cannot adequately present the volumes of evidence underlying the district court’s findings of fact, but the following provide a fair sample: A 1991 Reynolds Research and Development report acknowledged that “[w]e are basically in the nicotine business.” Id. at 237. Dr. Farone testified that during his time at Philip Morris there was “widespread acceptance internally throughout the company — among, executives, scientists, and marketing people” that nicotine was primarily responsible for addiction to smoking. Id. at 858. Indeed, the district court found that “internal documents and testimony from former company employees affirmed that within their corporate walls, Defendants openly recognized the addictiveness of cigarettes.” Id. Regarding light cigarettes, internal research reports and memoranda at the Defendant companies revealed that they understood the phenomenon of smoker compensation and studied how to manipulate it in order to make their light brands appealing to addicted smokers while continuing to be able to advertise the brands as low tar. For example, a 1978 BATCo memorandum about that company’s internal research acknowledged that “a majority of habitual smokers compensate for changed delivery” and explained that if smokers “choose [a] lower delivery brand ... than their usual brand” they “will in fact increase the amounts of tar and gas phase that they take in, in order to take in the same amount of nicotine.” Id. at 861. Dr. Far-one testified that Defendants’ superior knowledge of compensation (compared to that of scientists outside the industry, including the government) was closely held within Philip Morris and the tobacco industry and there was an “effort on the part of [his] coworkers at Philip Morris, including [his] supervisors, to restrict any public acknowledgment on the part of Philip Morris of the phenomena of compensation.” Id. As these examples and hundreds more findings in the district court’s opinion demonstrate, the court had before it sufficient evidence from which to conclude that Defendants’ executives, who directed the activities of the Defendant corporations and their joint entities, knew about the negative health consequences of smoking, the addictiveness and manipulation of nicotine, the harmfulness of secondhand smoke, and the concept of smoker compensation, which makes light cigarettes no less harmful than regular cigarettes and possibly more. The government presented evidence indicating that specific high-ranking corporate officials were directly informed about these matters, as well as evidence of pervasive knowledge and acceptance of these propositions throughout the Defendant organizations. The overwhelming indirect and circumstantial evidence was sufficient to allow the district court to reasonably infer that the high level executives, including “CEOs, Vice Presidents, [and] Heads of Research & Development” for Defendants knew about their respective