Opinion for the Court filed by Circuit Judge TATEL.
TATEL, Circuit Judge:In this appeal, the fifth in this long-running RICO case against the nation’s cigarette manufacturers, defendants challenge a district court order requiring that they add two statements to their cigarette packages and advertisements: an announcement that a federal court has ruled that they “deliberately deceived the American public” about the dangers of cigarettes; and a declaration that they “intentionally designed cigarettes” to maximize addiction. Reading the extensive briefs the parties and their amici have submitted, one might think this case presents thorny, unresolved questions under both RICO and the First Amendment. As we explain below, however, the heavy lifting has already been done. Given our earlier decisions in this case, the manufacturers’ objection to disclosing that they intentionally designed cigarettes to ensure addiction is both waived and foreclosed by the law of the case. Those decisions make equally clear that the district court, in ordering defendants to announce that they deliberately deceived the public, exceeded its authority under RICO to craft remedies that “prevent and restrain” future violations. 18 U.S.C. § 1964(a). .
I.
Fifteen years ago, the United States filed this suit in the U.S. District Court for the District of Columbia alleging that Phil*1017ip Morris and eight other cigarette manufacturers violated the Racketeer Influenced and Corrupt Organizations Act (RICO), 18 U.S.C. §§ 1961-1968, by engaging in a then still-ongoing conspiracy to deceive the American public about the health consequences and addictiveness of smoking cigarettes. Pretrial proceedings lasted for years, and when the bench trial finally began in 2004, it spanned nine months, involved hundreds of witnesses, and saw nearly 14,000 exhibits entered into evidence.
Two years later, supported by more than 4,000 findings of fact detailing the cigarette manufacturers’ “pervasive scheme to defraud consumers and potential consumers of cigarettes,” carried out “over the course of more than 50 years,” the district court entered final judgment against the defendants. United States v. Philip Morris USA, Inc., 449 F.Supp.2d 1, 851-54 (D.D.C.2006); see also id. at 936. Finding that they joined together to “maximize their profits” through “false and fraudulent statements, representations, and promises” about “the devastating health effects of smoking,” id. at 852, the court concluded that the manufacturers operated an illegal racketeering enterprise in violation of RICO section 1962(c), and that they conspired to do so in violation of RICO section 1962(d), id. at 851, 903. Given the defendants’ then-ongoing business practices, the district court also determined that many of them, including appellants Philip Morris, R.J. Reynolds, Brown & Williamson, Altria, and Lorillard, were, unless enjoined, likely to commit future RICO violations, id. at 909, a prerequisite to ordering relief under RICO, see SEC v. Savoy Industries, Inc., 587 F.2d 1149, 1168 (D.C.Cir.1978). In 2009, we affirmed the district court’s finding of RICO liability with respect to each cigarette manufacturer, United States v. Philip Morris USA Inc., 566 F.3d 1095, 1150 (D.C.Cir.2009) (2009 Opinion), along with its conclusion that many of the manufacturers, unless enjoined, would likely commit similar RICO violations in the future, id. at 1134.
This overview tells only half the story. Because the government initially sought not only injunctive relief under 18 U.S.C. § 1964(a), but also disgorgement of $280 billion in proceeds from the manufacturers’ fraudulent sale of cigarettes, the issue of available remedies under RICO’s civil-remedy provision has from the very beginning loomed just as large as the liability question itself. The district court determined that were it to find that the manufacturers had violated RICO, it had authority under the statute to order disgorgement. On pretrial interlocutory appeal, we reversed. Using language central to the issues before us here, we held that “because disgorgement is aimed at past violations,” it does not “prevent or restrain” future RICO violations as required by section 1964. United States v. Philip Morris USA Inc., 396 F.3d 1190, 1192 (D.C.Cir.2005) (emphasis added) {Disgorgement Opinion).
After our disgorgement decision, the government reformulated its remedial request, and the district court permitted a handful of public health organizations to intervene to assert their interests in the proposed remedies. Those same organizations — 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— are parties to this appeal.
Following a two-week trial on remedies, the district court enjoined the manufacturers from making any false or misleading public representation about cigarettes, and, most relevant here, ordered them to *1018make corrective disclosures about five topics on which the court found they had made fraudulent public claims: (1) the adverse health effects of smoking; (2) the addictiveness of smoking and nicotine; (3) the lack of any significant health benefit from smoking “low tar” or “light” cigarettes as opposed to regular cigarettes; (4) the manufacturers’ manipulation of cigarette design to ensure optimum nicotine delivery; and (5) the dangers of exposure to secondhand smoke. Philip Morris USA, Inc., 449 F.Supp.2d at 938-39. The district court also directed the manufacturers to disseminate the statements via their websites, retail point-of-sale displays, newspaper and television ads, and cigarette-package “onserts,” i.e., “communication[s] affixed to” cigarette packs. Id. at 939-41, 948. The district court rejected other remedies the government and public-health intervenors had requested, including counter-marketing and national smoking-cessation programs. Id. at 933, 936-37. Both sides appealed.
In our 2009 opinion, we largely affirmed the district court’s remedial order. Recognizing that “breadth is warranted to prevent further violations where, as here, a proclivity for unlawful conduct has been shown,” we upheld the broad injunction prohibiting defendants from making any false or misleading public statement about cigarettes. 2009 Opinion, 566 F.3d at 1137 (citation, internal quotation marks, and alteration omitted). We also rejected the manufacturers’ RICO and First Amendment challenges to the corrective-disclosure remedy, vacating only the requirement that the statements be published on retail displays. Id. at 1141 — 44. Although the statements’ precise content had yet to be determined, we concluded that ordering the manufacturers to issue corrective statements on the proposed topics complied with RICO since “[rjequiring Defendants to reveal the previously hidden truth about their products [would] prevent and restrain” future RICO violations. Id. at 1140. We further explained that, in light of their subject matter, the corrective statements would qualify as commercial speech and satisfy the First Amendment if designed to prevent defendants from misleading consumers through fraudulent marketing in the future. Id. at 1144-45. Finally, we agreed with the manufacturers that the counter-marketing campaign and smoking-cessation program exceeded the district court’s RICO authority. These programs, we explained, sought not to prevent and restrain future RICO violations— section 1964’s sole permissible objective— but rather to “remedy the continuing effects of past illegal conduct” and generally reduce the manufacturers’ “incentive to market their products.” Id. at 1147-48 (emphasis added).
On remand, the district court set about drafting the required corrective disclosures. After additional briefing and oral argument, and over defendants’ objections on RICO and First Amendment grounds, the court ordered the manufacturers to disseminate the following statements, which we .reproduce in full for the reader’s benefit (at issue in this case are the five preambles announcing that a federal court has ruled that defendants “deliberately deceived the American public,” as well as the underlined bulleted statements):
A. Adverse Health Effects of Smoking
A Federal Court has ruled that Altria, R.J. Reynolds Tobacco, Lorillard, and Philip Morris USA deliberately deceived the American public about the health effects of smoking, and has ordered those companies to make this statement. Here is the truth:
• Smoking kills, on average, 1200 Americans. Every day.
*1019• More people die every year from smoking than from murder, AIDS, suicide, drugs, car crashes, and alcohol, combined.
• Smoking causes heart disease, emphysema, acute myeloid leukemia, and cancer of the mouth, esophagus, larynx, lung, stomach, kidney, bladder, and pancreas.
• Smoking also causes reduced fertility, low birth weight in newborns, and cancer of the cervix.
B. Addictiveness of Smoking and Nicotine
A Federal Court has ruled that Altria, R.J. Reynolds Tobacco, Lorillard, and Philip Morris USA deliberately deceived the American public about the addictiveness of smoking and nicotine, and has ordered those companies to make this statement. Here is the truth:
• Smoking is highly addictive. Nicotine is the addictive drug in tobacco.
• Cigarette companies intentionally designed cigarettes with enough nicotine to create and sustain addiction.
• It’s not easy to quit.
• When you smoke, the nicotine actually changes the brain — that’s why quitting is so hard.
C. Lack of Significant Health Benefit From Smoking “Low Tar,” “Light,” “Ultra Light,” “Mild,” and “Natural” Cigarettes
A Federal Court has ruled that Altria, R.J. Reynolds Tobacco, Lorillard, and Philip Morris USA deliberately deceived the American public by falsely selling and advertising low tar and light cigarettes as less harmful than regular cigarettes, and has ordered those companies to make this statement. Here is the truth:
• Many smokers switch to low tar and light cigarettes rather than quitting because they think low tar and light cigarettes are less harmful. They are not.
• “Low tar” and filtered cigarette smokers inhale essentially the same amount of tar and nicotine as they would from regular cigarettes.
• All cigarettes cause cancer, lung disease, heart attacks, and premature death — lights, low tar, ultra lights, and naturals. There is ho safe cigarette.
D. Manipulation of Cigarette Design and Composition to Ensure Optimum Nicotine Delivery
A Federal Court has ruled that Altria, R.J. Reynolds Tobacco, Lorillard, and Philip Morris USA deliberately deceived the American public about designing cigarettes to enhance the delivery of nicotine, and has ordered those companies to make this statement. Here is the truth:
• Defendant tobacco companies intentionally designed cigarettes to make them more addictive.
• Cigarette companies control the impact and delivery of nicotine in many ways, including designing filters and selecting cigarette paper to maximize the ingestion of nicotine, adding ammonia to make the cigarette taste less harsh, and controlling the physical and chemical make-up of the tobacco blend. ■
• When you smoke, the nicotine actually changes the brain — that’s why quitting is so hard.
E. Adverse Health Effects of Exposure to Secondhand Smoke
A Federal Court has ruled that Altria, R.J. Reynolds Tobacco, Lorillard, and Philip Morris USA deliberately deceived the American public about the health *1020effects of secondhand smoke, and has ordered those companies to make this statement. Here is the truth:
• Secondhand smoke kills over 38,000 Americans each year.
• Secondhand smoke causes lung cancer and coronary heart disease in adults who do not smoke.
• Children exposed to secondhand smoke are at an increased risk for sudden infant death syndrome (SIDS), ' acute respiratory infections, ear problems, severe asthma, and reduced lung function.
• There is no safe level of exposure to secondhand smoke. '
United States v. Philip Morris USA, Inc., 907 F.Supp.2d 1, 8-9 (D.D.C.2012); see also United States v. Philip Morris USA Inc., No. 99-CV-2496, 2014 WL 2506611, at *1 (D.D.C. June 2, 2014) (slightly modifying corrective statements).
Four of the original defendants — Philip Morris USA, Inc., Altria Group, Inc., R.J. Reynolds Tobacco Company (individually and as successor to Brown & Williamson Tobacco Corporation), and Lorillard Tobacco Company — appeal, contending that the corrective statements exceed the district court’s remedial authority under RICO and violate the First Amendment. Reviewing the district court’s conclusions of law de novo, we begin, as usual, with the statutory challenge. See Blum v. Bacon, 457 U.S. 132, 137, 102 S.Ct. 2355, 72 L.Ed.2d 728 (1982) (“Where a party raises both statutory and constitutional arguments ... ordinarily [federal courts] first address the statutory argument in order to avoid unnecessary resolution of the constitutional issue.”). And with respect to the principal issues before us, due to claims waived and questions already settled, we end there too.
II.
Federal courts “possess only that power authorized by Constitution and statute, which is not to be expanded by judicial decree.” Kokkonen v. Guardian Life Insurance Co. of America, 511 U.S. 375, 377, 114 S.Ct. 1673, 128 L.Ed.2d 391 (1994) (citations omitted).
In this case, the government sued defendants under RICO’s civil-remedy provision, 18 U.S.C. § 1964(a), which grants district courts jurisdiction “to prevent and restrain violations [of the Act] by issuing appropriate orders.” We have carefully defined the power authorized by section 1964. In our disgorgement opinion, we held that Congress limited relief under section 1964(a) to “forward-looking remedies that prevent and restrain [future] violations of the Act.” 396 F.3d at 1192. Accordingly, we rejected remedies like disgorgement that seek to punish prior wrongdoing or correct the effects of past conduct. Id. Recognizing that although RICO must be “liberally construed to effectuate its remedial purposes,” id. at 1201 (quoting Organized Crime Control Act of 1970, Pub.L. No. 91-452, § 904(a), 84 Stat. 947 (1970)), we stressed that section 1964 is no “plenary grant of equitable jurisdiction” that broadly sanctions general deterrence remedies, id. at 1198-200. Indeed, echoing the Second Circuit, we explained that if general deterrence were a permissible objective, “the phrase ‘prevent and restrain’ would read- ‘prevent, restrain, and discourage,’ and would allow any remedy that inflicts pain.” Id. at 1200 (quoting United States v. Carson, 52 F.3d 1173, 1182 (2d Cir.1995)). Reiterating as much in our 2009 opinion, we rejected “general deterrence remedies aimed [] wide of the statutorily-ordained mark” and emphasized that “a remedy ‘may not be justified simply on the ground that whatever hurts a civil RICO *1021violator necessarily serves to “prevent and restrain” future RICO violations.’ ” 566 F.3d at 1148 (quoting Carson, 52 F.3d at 1182). Section 1964, in short, empowers district, courts to issue remedies for one purpose — to “prevent and restrain” future RICO violations — and our decisions read this mandate narrowly, permitting only remedies that, through reasonably direct means, keep RICO violators from again violating the Act.
Although we endorsed the district court’s corrective-disclosure remedy and the statements’ proposed topics, we did so on exceedingly narrow grounds. Specifically, we declined to adopt the government’s argument that the statements were necessary to correct and prevent ongoing consumer misconception about cigarettes. Instead, we held simply that the corrective-statement remedy was permissible under section 1964 because defendants, if compelled to tell the truth about cigarettes, would, at the same time, be “impaired in making false and misleading assurances.” Id. at 1140. In other words, “[r]equiring Defendants to reveal the previously hidden truth about their products will prevent and restrain them from disseminating false and misleading statements, thereby violating RICO, in the future.” Id.
In addition to these carefully defined parameters for RICO remedies, two basic principles of judicial review guide our resolution of this case. The first, law of the case, reflects the understanding that “[[Inconsistency is the antithesis of the rule of law.” LaShawn A. v. Barry, 87 F.3d 1389, 1393, (D.C.Cir.1996). Developed to “maintain consistency and avoid reconsideration of matters' once [settled],” 18B C. Wright & A. Miller, Federal Practice and Procedure § 4478 (2d ed.), the doctrine recognizes that “eourt[s] involved in later phases of a lawsuit should not re-open questions decided,” Crocker v. Piedmont Aviation, Inc., 49 F.3d 735, 739 (D.C.Cir. 1995). Of particular relevance here, “[w]hen there are multiple appeals taken in the course of a single piece of litigation, law-of-the-case doctrine holds that decisions rendered on the first appeal should not be revisited on later trips to the appellate court.” Id. This is especially so where, as here, each of those appeals was heard by a different panel. Because this panel has no authority to overrule another, “an even stronger than usual version of the law-of-the-case doctrine,” law of the circuit, governs. LaShawn A., 87 F.3d at 1395. “[W]hen both doctrines are at work, the law-of-the-circuit doctrine should increase a panel’s reluctance to reconsider a decision made in an earlier appeal in the same case.” Id.
The second, related principle— waiver — is sometimes understood as an application of law-of-the-case doctrine to “prior rulings of the trial court that could have been but were not challenged on an earlier appeal.” Id. Critical to “the orderly conduct of litigation,” this rule means that “a party waives a contention that could have been but was not raised on a prior appeal.” Laffey v. Northwest Airlines, Inc., 740 F.2d 1071, 1089 (D.C.Cir. 1984) (alterations, internal quotation marks, and citations omitted). Thus, “a legal decision made at one stage of litigation, unchallenged in a subsequent appeal when the opportunity to do so existed, governs future stage's of the same litigation, and the parties are deemed to have waived the right to challenge that decision at a later time.” United States v. Thomas, 572 F.3d 945, 949 (D.C.Cir.2009) (alterations, internal quotation marks, and citations omitted).
With these remedial and procedural principles in mind, we turn to the manufacturers’ claim that the district court ex*1022ceeded the bounds of its remedial power under RICO when it ordered them to disseminate the five corrective disclosures listed above. The manufacturers principally challenge (1) the bulleted statements in disclosures B and D, which reveal that they “intentionally designed cigarettes” to ensure addiction and (2) the preambles announcing that a federal court has ruled that they “deliberately deceived the American public” about the dangers of cigarettes. Characterizing both as imper-missibly backward looking and conduct focused, the manufacturers maintain that these disclosures “force Defendants to vilify and shame themselves for past wrongdoing,” rather than “reveal the previously hidden truth” about cigarettes as required by our prior decisions. Defs. Br. 53-55; see also 2009 Opinion, 566 F.3d at 1140 (concluding that “[requiring Defendants to reveal the previously hidden truth about their products will prevent and restrain” future RICO violations).
A.
We begin with the bulleted statements. Recall that the district court’s 2006 remedial order warned defendants that they would be required to make just such corrective statements about their “manipulation of cigarette design and composition to ensure optimum nicotine delivery,” 449 F.Supp.2d at 939 — statements, in other words, revealing that they “do manipulate [the] design of cigarettes in order to enhance the delivery of nicotine,” id. at 928. The manufacturers did not object to this requirement when they appealed the remedial order in 2008, so they are “deemed to have waived the right to challenge [it].” Thomas, 572 F.3d at 949. True, they argued that the corrective statements as a whole focused improperly on righting past wrongs — an argument we rejected, 2009 Opinion, 566 F.3d at 1139-40—but they raised no specific objection to the requirement that they disclose their “manipulation of [the] physical and chemical design of cigarettes,” 449 F.Supp.2d at 928. Moreover, they challenged none of the district court’s findings of fact supporting that requirement. For example, they never challenged the district court’s finding that “Defendants have designed their cigarettes to precisely control nicotine delivery levels and provide doses of nicotine sufficient to create and sustain addiction.” Id. at 309 (finding 1366). Nor did they object to the district court’s determination that “[e]very aspect of a cigarette is precisely tailored to ensure that a cigarette smoker can pick up virtually any cigarette on the market and obtain an addictive dose of nicotine.” Id. (finding 1368); see also id. at 320, 374 (findings 1427 and 1703 discussing manufacturer strategies to “maximize” nicotine content and migration to outer periphery of the cigarette).
In our 2009 opinion, moreover, we recognized that the district court had ordered corrective disclosures on five topics, including “the manufacturers’ manipulation of cigarette design and composition to ensure optimum nicotine delivery.” 566 F.3d at 1138. And we approved those topics across the board, concluding that such disclosures would “prevent and restrain [defendants] from disseminating false and misleading statements, thereby violating RICO, in the future.” Id. at 1140. Having thus decided the issue in the earlier appeal, we will not revisit it here. See Crocker, 49 F.3d at 739.
Of course, as the manufacturers point out, when we reviewed the remedial order in 2009, the district court had yet to determine the precise wording of the corrective statements. Given this, the manufacturers’ challenge to these statements would be barred by neither law-of-the-case nor waiver doctrine if the statements the dis*1023trict court drafted went beyond the defendants’ manipulation of cigarette design. But the manufacturers have identified no way in which they do, and none is apparent to ~us. Statement B asserts that “[Cigarette companies intentionally designed cigarettes with enough nicotine to create and sustain addiction.” Likewise, Statement D says that “[defendant tobacco companies intentionally designed cigarettes to make them more addictive.” Both statements fit squarely within the bounds of the district court’s order directing defendants to reveal that they “manip-ulare] [ ] cigarette design and composition to ensure optimum nicotine delivery.” This is also true of Statement D’s description of just how cigarette companies design cigarettes to “ensure optimum nicotine delivery.” That statement simply explains that “[Cigarette companies control the impact and delivery of nicotine in many ways, including designing filters and selecting cigarette paper to maximize the ingestion of nicotine, adding ammonia to make the cigarette taste less harsh, and controlling the physical and chemical make-up of the tobacco blend.”
The manufacturers have likewise waived their First Amendment challenge. Statements B and D fall within the scope of the district court’s remedial order requiring defendants to disclose their manipulation of cigarette design, and the manufacturers failed to challenge that requirement on any ground — statutory or constitutional — in their appeal leading to our 2009 opinion. See Crocker, 49 F.3d at 739 (explaining that “prior rulings of the trial court that could have been but were not challenged on an earlier appeal” fall within “subsidiary waiver principle” of law-of-the-case doctrine). At oral argument, counsel for defendants insisted that “the normal legal consequences” of “law of the case and estoppel and forfeiture” do not apply to the constitutional standard for compelled commercial speech. Oral Arg. Recording at 20:20-24:21. But counsel offered no authority for this novel claim, nor are we aware of any. Indeed, “[n]o procedural principle is more familiar ... than that a constitutional right may be forfeited in criminal as well as civil cases by the failure to make timely assertion of the right before a tribunal having jurisdiction to determine it.” Yakus v. United States, 321 U.S. 414, 444, 64 S.Ct. 660, 88 L.Ed. 834 (1944).
We are left with a few loose ends.
First, the manufacturers maintain that because the Family Smoking Prevention and Tobacco Control Act, passed shortly after our 2009 opinion, now prohibits them from using descriptors such as “light” and “low-tar,” Statement C “cannot possibly ‘prevent and restrain’ future RICO violations.” Defs. Br. 55-56. In other words, because the statute now prohibits the manufacturers from using such descriptors, they contend that Statement C is unnecessary and will do nothing to prevent RICO violations. The manufacturers, however, previously pressed a broader version of this argument, and we rejected it. In 2012, in yet another appeal in this case, they argued that the new Act’s stringent marketing restrictions “eliminated any reasonable likelihood they would commit future RICO violations,” thus depriving the district court of any remedial authority and rendering moot its 2006 injunctive orders. United States v. Philip Morris USA Inc., 686 F.3d 832, 835 (D.C.Cir.2012) (internal quotation marks omitted). We disagreed given “defendants’ history of noncompliance with various legal requirements” and the fact that the new law “does not provide for penalties as sweeping as those available under RICO.” Id. at 836-37. Concluding that the manufacturers were “not likely to comply with” the new *1024law, we held that the district court retained its remedial authority even with respect to those “portions of the injunctions that overlapped with certain restrictions in the Act.” Id. at 837 & n. 1. The new law’s prohibition on misleading descriptors like “light” and “low-tar” does not, then, deprive the district court of authority to order remedies under RICO on the same subject. And for good reason: consumers know that cigarettes once dubbed “light” and “low-tar” remain on the market. The manufacturers made sure of this. For example, Altria Group placed notes on the last packages of Marlboro Lights informing purchasers that “Your Marlboro Lights package is changing, but your cigarette stays the same” — just “ask for Marlboro in the gold pack.” See Intervenors’ Supplemental Br. on Corrective Statements (Docket No. 5986) (filed Sept. 24, 2012) (citing Duff Wilson, FDA Seeks Explanation of Marlboro Marketing, N.Y. Times, June 18, 2010, at B6). Statement C therefore prevents and restrains defendants from making false health assurances about these cigarettes, whatever their new look.
Next, the manufacturers argue that some of the bulleted statements run afoul of the First Amendment. According to the manufacturers, the statements find no support in the district court’s findings of facf and thus are not “purely factual.” See American Meat Institute v. U.S. Department of Agriculture, 760 F.3d 18, 27 (D.C.Cir.2014) (en banc) (explaining that compelled commercial disclosures must constitute “purely factual and uncontroversial information”). One such disclosure, the second bullet point in Statement C, reads: “‘Low tar’ and filtered cigarette smokers inhale essentially the same amount of tar and nicotine as they would from regular cigarettes.” According to the manufacturers, this claim erroneously suggests that “regular” cigarettes are unfiltered. We take their point, but believe that the word “filtered” is probably a typo. Indeed, both the preamble to statement C and the first bullet point contrast regular cigarettes with their low-tar and light counterparts, not with filtered cigarettes, and counsel for the manufacturers conceded at oral argument that changing “filtered” to “light” would fix the problem. Although “loathe to attribute this to a simple typo,” Oral Arg. Recording at 53:46-50, government counsel offered no plausible alternative reading. We therefore direct the district court to correct the statement on remand.
The manufacturers also contend that Statement C’s claim about compensation— a phenomenon by which many smokers who switch to lower-yield cigarettes unconsciously “inhale essentially the same amount of tar and nicotine as they would from regular cigarettes” — lacks support in the district courts’ findings of fact. The statement, they say, suggests that all smokers compensate yet the district court found merely that the phenomenon is “substantial.” Defs. Br. 43. In fact, however, the district court found that “[vjirtually all smokers, over 95%, compensate for nicotine,” 449 F.Supp.2d at 438 (finding 2072), and that the compensation evidence “as a whole” shows that “compensation for daily nicotine is substantiál if not complete,” id. at 444 (finding 2103) (emphasis added). The statement thus finds ample support in the district court’s findings of fact.
Finally, the manufacturers complain that the second bullet point in Statement D, which explains that “[c]igarette companies control the impact and delivery of nicotine in many ways, including ... adding ammonia,” is inaccurate since one manufacturer, Lorillard Tobacco Company, adds no ammonia at all. But the man*1025ufacturers had an opportunity to challenge this claim in the district court and failed to do so. “It is well settled that issues and legal theories not asserted at the District Court level ordinarily will not be heard on appeal.” District of Columbia v. Air Florida, Inc., 750 F.2d 1077, 1084 (D.C.Cir.1984). Besides, the district court found that “[b]y 1993, all the cigarette company Defendants used some form of ammonia technology in some of their cigarette products,” 449 F.Supp.2d at 356 (finding 1611) (emphasis added), and even if Lorillard does not do so now, it could resume the practice in the future. Indeed, the district court found that “[a]mmonia compounds are among the most frequently used additives, measured by volume, in the industry.” Id. (finding 1610). Accordingly, as with Statement C, we are satisfied that the district court’s findings of fact support this disclosuré.
B.
This, then, brings us to the preambles. Each preamble announces that “[a] Federal Court has ruled that [the manufacturers] deliberately deceived the American public” about the dangers of cigarettes and has “ordered [them] to make this statement.” Unlike the corrective-disclosure topics, the preambles were nowhere presaged in the district court’s 2006 remedial order. Nor obviously were they before us in 2009. Accordingly, neither waiver nor law-of-the-case doctrine bars the manufacturers’ challenge. We must therefore address their argument that the district court, in ordering the manufacturers to disseminate what they call “backward-looking” language that condemns their “past wrongdoing,” exceeded its limited remedial authority under RICO. Defs. Br. 53-55.
As mentioned above, we explained in our 2009 opinion that the corrective-disclosure remedy complied with RICO because the manufacturers would be “impaired in making false and misleading assurances” about cigarettes if simultaneously required to tell the truth. See supra at 1021. In other words, we held, disseminating corrective statements on the proposed topics would prevent and restrain future RICO violations by “[requiring Defendants to reveal the previously hidden truth about their products.” 2009 Opinion, 566 F.3d at 1140 (emphasis added). But unlike the bulleted statements, which do just that, the preambles reveal nothing about cigarettes; instead, they disclose defendants’ prior deceptive conduct. Accordingly, they cannot be justified on the basis of our 2009 opinion. See id. (holding that corrective statements, in revealing the truth about cigarettes, will prevent and restrain defendants from again violating RICO).
The government nonetheless insists that the district court did have authority under RICO to order defendants to publish the preambles. Quoting the district court, the Government maintains that the preamble is essential to “protect consumers from deception,” as it “alert[s] [ ] consumers] to the fact that they have been misinformed, and then provide[s] the accurate information.” Govt. Br. 42 (quoting Philip Morris, 907 F.Supp.2d at 19); see also Amicus Br. of Tobacco Control Legal Consortium 27-31 (arguing that preambles are necessary to correct and prevent, consumer deception). In support, the government submitted to the district court a 500-page expert report demonstrating that introductory language along the lines of the preambles would play an important role in inoculating consumers against future misinformation. See Executive Summary, Expert Report of Kelly Blake, Feb. 3, 2011 (Docket No. 5875) (filed Feb. 23, 2011). Similarly, the district court concluded that “the preamble is reasonably related to cor*1026recting and preventing future consumer deception.” 907 F.Supp.2d at 23.
This may be true. The preamble might provide an effective — perhaps even the very best — means of curing consumer misconception and preventing consumer deception going forward. Were this an enforcement proceeding brought by the Federal Trade Commission, an action that permits remedies intended to “dissipate future effects of a company’s past wrongful conduct,” Warner-Lambert Co. v. FTC, 562 F.2d 749, 761 n. 60 (D.C.Cir.1977), the preamble might well represent a proper exercise of the court’s remedial power. But this is a civil RICO case, and as we have explained, that statute empowers district courts to issue injunctions for one purpose and one purpose only: to prevent and restrain future RICO violations. 18 U.S.C. § 1964(a). Correcting consumer misinformation, which “focuse[s] on remedying the effects of past conduct,” is thus an impermissible objective under RICO. Disgorgement Opinion, 396 F.3d at 1198 (emphasis added). Seeking to prevent consumer deception is similarly impermissible because, although forward-looking, it focuses not on restraining the RICO violator, but on safeguarding consumers against RICO violations.
To be sure, although the district court’s reasoning was largely consumer focused, see, e.g., Philip Morris, 907 F.Supp.2d at 20, it did at one point suggest that the preambles might also discourage the manufacturers from again violating RICO. “By ensuring that consumers know that Defendants have misled the public in the past on the issue of secondhand smoke ...,” the district court stated, “Defendants will be less likely to attempt to argue in the future that such a consensus does not exist.” Id. at 26. But even were we to extend this deterrence rationale beyond secondhand smoke to every corrective statement, our case law makes clear that when it comes to RICO remedies, it fails.
As we explained when rejecting disgorgement as an available remedy, district courts may order injunctions under section 1964(a) only to “prevent and restrain” RICO violations, not to discourage such violations through “any remedy that inflicts pain.” Disgorgement Opinion, 396 F.3d at 1200 (citing Carson, 52 F.3d at 1182). Indeed, the dissent in that case, like the district court here, embraced the deterrence rationale, pointing out that “[t]he government offer[ed] expert testimony to the effect that a disgorgement order [would] deter the tobacco companies from violating RICO in the future.” Id. at 1223 (Tatel, J., dissenting); see also id. at 1222-27. But the court rejected the dissent’s reasoning. Acknowledging that “disgorgement may act to ‘prevent and restrain’ future violations by general deterrence insofar as it makes RICO violations unprofitable,” the court nonetheless concluded that “this argument goes too far.” Id. at 1200. After all, the court pointed out, the statute reads “prevent and restrain,” not “prevent, restrain, and discourage.” Id. (quoting Carson, 52 F.3d at 1182).
We said the same thing in our 2009 opinion when affirming the district court’s rejection of the counter-marketing and smoking-cessation programs, both of which had been sought by the government and intervenors. By “shrinking Defendants’ customer base,” we recognized, these programs might reduce defendants’ “incentive to market their products” in general, and thus to falsely market their products as well. 2009 Opinion, 566 F.3d at 1148. But we nonetheless rejected such “general deterrence remedies aimed so wide of the statutorily-ordained mark.” Id. A remedy, we reiterated, “may not be justified simply on the ground that whatever hurts a civil *1027RICO violator necessarily serves to ‘prevent and restrain’ future RICO violations.’” Id. (quoting Carson, 52 F.3d at 1182).
So too here. Even if the preambles would discourage cigarette manufacturers from falsely marketing cigarettes by arming consumers against misinformation, thus making RICO violations unprofitable — something the government never even attempted to prove — “[s]uch a remedy [would] reach[] beyond the bounds of section 1964(a), which authorizes the district court to order injunctions [only] to prevent and restrain fraudulent statements about smoking and health and addiction.” Id. at 1149. The bulleted statements will achieve this goal because they “reveal[ ] the previously hidden truth about [the manufacturers’] products.” Id. at 1140 (emphasis added). The preambles, however, do no such thing and may not be justified on grounds of general deterrence.
III.
In addition to objecting to the corrective statements’ content, the manufacturers challenge on First Amendment grounds the requirement that they publish the disclosures on their company websites and cigarette packages, as well as in newspaper and television ads. These “overlapping channels of communication,” they say, are “needlessly duplicative” and thus unduly burden their First Amendment rights. Defs. Br. 45-46; see Zauderer v. Office of Disciplinary Counsel of Supreme Court of Ohio, 471 U.S. 626, 651, 105 S.Ct. 2265, 85 L.Ed.2d 652 (1985) (cautioning against “unduly burdensome disclosure requirements” that chill protected commercial speech).
As explained above, however, the district court’s 2006 remedial order required defendants to disseminate the corrective statements by each of these means, in addition to retail point-of-sale displays. The manufacturers objected only to the point-of-sale-display requirement (which we invalidated) and publication via cigarette-package onserts (which we upheld). See 2009 Opinion, 566 F.3d at 1140-42. This question is thus settled. See Thomas, 572 F.3d at 949.
The manufacturers insist that five years later, in a 2014 consent order providing for implementation of the corrective-statement remedy, they “reserve[d] the right to challenge ... the requirement that the court-ordered corrective statements appear in the multiple media[.]” Defs. Reply Br. 23. Such a reservation, however, cannot operate retroactively or otherwise resurrect waived claims. See Crocker, 49 F.3d at 739.
IV.
For the reasons set forth above, we affirm in part, reverse in part, and remand for further proceedings consistent with this opinion.
So ordered.