Affirmed by published opinion. Judge DUNCAN wrote the opinion, in which Senior Judge HAMILTON and Senior Judge HOWARD joined. Senior Judge HOWARD wrote a separate concurring opinion.
OPINION
DUNCAN, Circuit Judge:
This long-running antitrust suit is on appeal for the fourth time. Maryland now asks us -to revisit and reverse our earlier holding that the state’s liquor and wine (collectively, “liquor”) regulatory scheme is a form of horizontal price fixing in per se violation of the Sherman Act. We decline to do so because the Supreme Court’s intervening decision in Leegin Creative Leather Products, Inc. v. PSKS, Inc., 551 U.S. 877, 127 S.Ct. 2705, 168 L.Ed.2d 623 (2007), on which Maryland primarily relies, concerned vertical, rather than horizontal, price fixing, and Maryland’s other arguments are unavailing. Moreover, as to the only issue not controlled by the law of the case, we affirm the district court’s holding that the state’s regulatory scheme is preempted by the Sherman Act.
I.
In 1999, TFWS, Inc., a large liquor retailer in Maryland, sought declaratory and injunctive relief in federal district court alleging that the state’s liquor and wine regulations violate, and are preempted by, Section 1 of the Sherman Act, 15 U.S.C. § 1. In particular, TFWS challenged Maryland’s “post-and-hold” pricing system and its “volume discount ban.” See Md. [189]*189Code Ann., Art. 2B, § 12-102 & 103. The post-and-hold pricing system prescribes how and when liquor wholesalers may change their prices. Specifically, wholesalers must post a schedule of prices with the Comptroller by a fixed date every month. That schedule is made available to other wholesalers and the prices are locked in for the following month. Under the volume discount ban, a wholesaler must offer every retailer the same price for a given product, thus preventing wholesalers from cutting prices to large retailers.
Maryland moved to dismiss the suit on two grounds: (1) the suit was barred by 11th Amendment state immunity and (2) Section 1 of the Sherman Act did not apply to a state official’s enforcement of state law (so-called “state actor antitrust immunity”). On September 1, 1999, the district court issued its opinion. Responding to Maryland’s motion, the court held that (1) the suit was not barred by the 11th Amendment and (2) Maryland did not enjoy state actor antitrust immunity. Responding to TFWS’s complaint, the court held that Maryland’s “post-and-hold” pricing system and its “volume discount ban” are hybrid restraints on trade1 and per se violations2 of the Sherman Act.
Nevertheless, the district court dismissed the suit on 21st Amendment grounds.3 The court held that, notwithstanding the anticompetitive effects of the challenged regulatory scheme, it was a valid exercise of Maryland’s 21st Amendment powers4 and that the state’s interest in promoting temperance trumped the federal interest in promoting competition under the Sherman Act. Consequently, the court concluded, the scheme was not preempted. TFWS appealed the district court’s ruling on the 21st Amendment issue. Maryland cross-appealed on the other issues. A lengthy process of litigation ensued, which we summarize here as background to the current appeal.
In TFWS, Inc. v. Schaefer (“TFWS /”), 242 F.3d 198 (4th Cir.2001), in the portion of our holding relevant to the current appeal, we affirmed the district court’s Sherman Act holding and vacated its dismissal of the action. We held that the “post-and-hold” pricing system and the “volume discount ban” (a) are part of a single regulatory scheme; (b) both constitute hybrid restraints on trade; and (c) both are per se violations of the Sherman Act. We reasoned that
[t]he post-and-hold system is a classic hybrid restraint: the State requires wholesalers to set prices and stick to them, but it does not review those privately set prices for reasonableness; the wholesalers are thus granted a significant degree of private regulatory power. The volume discount ban is a part of the [190]*190hybrid restraint because it reinforces the post-and-hold system by making it even more inflexible.
TFWS I, 242 F.3d at 208-09. We further held that these hybrid restraints mandated activity that was “essentially a form of horizontal price fixing,” id. at 209, making them per se violations of § 1 of the Sherman Act.5 See N.C.A.A. v. Bd. of Regents of the Univ. of Okla., 468 U.S. 85, 100, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984) (labeling horizontal price fixing “the paradigm of an unreasonable restraint of trade”); see also Catalano, Inc. v. Target Sales, Inc., 446 U.S. 643, 649-50, 100 S.Ct. 1925, 64 L.Ed.2d 580 (1980) (per curiam).
In vacating the district court’s ruling on the 21st Amendment issue, we remanded to the district court to give the parties the opportunity to argue the issue and develop the record. See TFWS I, 242 F.3d at 211-13. Subsequent district court decisions in 2002, 2004 and 20076 as well as this court’s decisions in 2003 and 20057 dealt solely with the 21st Amendment and related issues. Following our vacatur in TFWS I, Maryland moved the district court for summary judgment based on a 21st Amendment defense. The district court granted Maryland’s motion, holding that Maryland’s interests in promoting temperance under the 21st Amendment prevailed over the federal interest under the Sherman Act.
On appeal from that decision, we again vacated the district court’s grant of summary judgment, holding that there was a disputed question of fact as to whether (and to what extent) Maryland’s regulations were effective in serving their claimed purpose of promoting temperance. TFWS, Inc. v. Schaefer (“TFWS II”), 325 F.3d 234, 242 (4th Cir.2003). Without determining the effectiveness of the regulatory scheme, the district court could not properly weigh the competing state and federal interests. See id. at 242-43.
On remand from TFWS II, the district court heard testimony and took evidence from the parties on the effect of the regulations on liquor price, and consequently on liquor consumption and temperance. The parties compared Maryland’s liquor and wine prices with those in Delaware, where TFWS also had retail operations. The district court found that Maryland’s regulatory scheme was ineffective in furthering the state’s purported interest in temperance and that the balance weighed in favor of the federal interest in promoting competition. Consequently, the district court concluded that the statutes and associated regulations at issue were preempted by the Sherman Act. Maryland appealed.
Once again, we vacated the district-court’s ruling, finding that it was clearly erroneous because it failed to take into account (or explain why it was not necessary to take into account) the effect of excise taxes on the price of liquor and [191]*191wine. TFWS, Inc. v. Schaefer ("TFWS III”), 147 Fed.Appx. 330, 334-36 (4th Cir. 2005) (unpublished). On remand from TFWS III, the district court took evidence on the effect of the excise tax on liquor prices (comparing Maryland and Delaware). The district court again found that Maryland’s regulatory scheme was ineffective in furthering its purported interest in temperance and was therefore preempted by the Sherman Act.
In the matter now before us, Maryland timely appealed. Maryland primarily argues that we erred in holding in TFWS I that its scheme is a per se violation of the Sherman Act. Maryland further contends that the district court erred in finding that its regulatory scheme is ineffective and preempted by the Sherman Act. We examine these issues in turn.
II.
Maryland argues that we should reverse our 2001 decision in TFWS I — after five additional court decisions — in which we held that Maryland’s “post-and-hold” pricing system and “volume discount ban” are hybrid restraints on trade and per se violations of § 1 of the Sherman Act. Maryland recognizes that our prior holding constitutes the law of the case. It nevertheless asserts that reconsideration is warranted here.
The law of the case doctrine “posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case.” United States v. Aramony, 166 F.3d 655, 661 (4th Cir.1999) (quoting Christianson v. Colt Indus. Operating Corp., 486 U.S. 800, 815-16, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988)). As a practical matter, then, once the decision of an appellate court establishes the law of the case, it “must be followed in all subsequent proceedings in the same case in the trial court or on a later appeal [ ] unless; (1) a subsequent trial produces substantially different evidence, (2) controlling authority has since made a contrary decision of law applicable to the issue, or (3) the prior decision was clearly erroneous and would work manifest injustice.” Aramony, 166 F.3d at 661 (citations and internal quotations omitted); see also United States v. Lentz, 524 F.3d 501, 528 (4th Cir.2008). In attempting to convince us to overturn the law of the case, Maryland presents several arguments, which we consider in turn.
A.
Relying on the second exception (i.e., material change in controlling authority), Maryland first argues that “[t]his Court should ... revisit the preemption analysis in TFWS I in light of intervening Supreme Court authority that renders untenable the precedents that were central to the panel’s holding.”8 Appellant’s Br. at 26. Maryland points to the Supreme Court’s 2007 decision in Leegin, arguing that “resale price maintenance is no longer subject to per se analysis under federal antitrust law, but must instead be judged under a rule-of-reason standard.” Appellant’s Br. at 28.
Maryland’s analysis is flawed. First, in Leegin, the Supreme Court did not overrule, or even question, any Supreme Court precedent on which we relied in [192]*192TFWS I.9 The Supreme Court has repeatedly instructed that only the Supreme Court itself may exercise the prerogative of determining whether any of its own prior holdings have been overturned. See, e.g., Rodriguez de Quijas v. Shearson/Am. Express, Inc., 490 U.S. 477, 484, 109 S.Ct. 1917, 104 L.Ed.2d 526 (1989). The Court has also clarified that it “does not normally overturn, or [ ] dramatically limit, earlier authority sub silentio.” Shalala v. Ill. Council on Long Term Care, Inc., 529 U.S. 1, 18, 120 S.Ct. 1084, 146 L.Ed.2d 1 (2000).
Second, in TFWS I, we ruled that Maryland’s regulatory scheme was “a form of horizontal price fixing.” TFWS I, 242 F.3d at 209 (emphasis added). Leegin, in contrast, concerned vertical resale price maintenance, holding that such arrangements were no longer subject to the per se rule. Leegin, 127 S.Ct. at 2714-15. That holding is inapposite. In fact, Leegin, far from undermining our conclusion that horizontal price fixing is per se illegal under the Sherman Act, actually reiterates that rule. See Leegin, 127 S.Ct. at 2723 (noting that “[t]he same legal standard (;per se unlawfulness) applies to horizontal market division and horizontal price fixing because both have similar economic effect”). Indeed, our holding in TFWS I that Maryland’s horizontal price fixing was a per se violation of the Sherman Act explicitly flowed from prior Supreme Court precedent. See TFWS I, 242 F.3d at 209 (citing Bd. of Regents of the Univ. of Okla., 468 U.S. at 100, 104 S.Ct. 2948 (1984), for the principle that horizontal price fixing is “the paradigm of an unreasonable restraint of trade”); see also Catalano, 446 U.S. at 649-50, 100 S.Ct. 1925 (holding that there is “a plain distinction between the lawful right to publish prices ... on the one hand, and an agreement among competitors limiting action with respect to the published prices, on the other”); Sugar Inst. v. United States, 297 U.S. 553, 581, 56 S.Ct. 629, 80 L.Ed. 859- (1936) (noting that steps taken to secure “adherence, without deviation, to the prices and terms ... announced” violate § 1 of the Sherman Act). Consequently, the second exception to the law of the case doctrine does not undermine our analysis in TFWS I.
B.
Maryland’s remaining challenges to the law of the case appear to be directed at the third exception to the law of the case doctrine, which permits a departure from the law of the case when the previous decision was “clearly erroneous and would work manifest injustice.” Aramony, 166 [193]*193F.3d at 661. We now consider these challenges.
In TFWS' I, we ruled that the volume discount ban was part of the hybrid restraint and a per se violation.10 Maryland contends on appeal that even if the “post- and-hold” pricing system is a hybrid restraint and a per se violation of the Sherman Act, the “volume discount ban” is a unilateral — not hybrid — restraint that should not have been bundled with the “post-and-hold” pricing system. Appellant’s Br. at 33-35. Maryland asserts that “the volume discount ban can stand on its own. Standing alone, it is clearly a unilateral restraint.”11 Appellant’s Br. at 34.
Significantly, although Maryland now challenges this ruling, in prior pleadings, it essentially agreed with our position in TFWS I. For instance, Maryland earlier described the challenged statutes as “part of the State of Maryland’s longstanding statutory system to regulate and control sale and distribution of alcoholic beverages.” Maryland’s Br. for TFWS I, No. 04-1688, at 7 (March 7, 2005) (emphasis added). Additionally, Maryland cited with approbation the Maryland Court of Appeals’s interpretation of the statutes at issue as “part of a comprehensive scheme,” J.A. 77 (citation and internal quotation marks omitted), as well as that court’s holding that “the proper rule of construction is that all parts of Article 2B [which includes the statutes at issue here] must be read together as they form part of a general system,” J.A. 78 (citation and internal quotation marks omitted). Further, Maryland’s own witness testified that the post-and-hold pricing system is utilized in part to enforce the volume discount ban. J.A. 2321-24. Similarly, in its latest appeal, Maryland agreed that the post-and-hold pricing system and.the volume discount ban operate together, conceding that “the post-and-hold system facilitates monitoring and enforcement of the volume discount ban.” Appellant’s Br. at 34.
Moreover, as we held in TFWS I, Maryland’s volume discount ban does “reinforce! ] the post-and-hold system” and makes it “even more inflexible.” TFWS I, at 209. For instance, the volume discount ban facilitates self-policing among market participants because departures from established prices are readily recognizable. See, e.g., Catalano, 446 U.S. at 649-50, 100 S.Ct. 1925. In Maryland, a wholesaler who notices a low retail price for a competitor’s product has all the information needed to report a violation: the filed wholesale price and the knowledge that the retailer cannot have received a discount. The challenged regulations allow private businesses to set prices, mandate price-filing and price-holding, and allow industry players to facilitate detection of would-be price cutters — especially in a state like Maryland where just two wholesalers control 85%-90% of the liquor market. In short, the two provisions at issue together grant private actors the tools to engage in coordinated pricing, and so constitute hybrid— not unilateral — restraints.
Maryland presents its argument for severance of its volume discount ban as [194]*194though for review in the first instance, and does not attempt to meet the high burden of showing that our holding in TFWS I was clearly erroneous and would work a manifest injustice. A prior decision does not qualify for this third exception by being “just maybe or probably wrong; it must ... strike us as wrong with the force of a five-week-old, unrefrigerated dead fish.” BellSouth Telesensor v. Info. Sys. & Networks Corp., 1995 WL 520978, *5 n. 6 (4th Cir.1995) (unpublished) (quoting Parts & Elec. Motors, Inc. v. Sterling Elec., Inc., 866 F.2d 228, 233 (7th Cir.1988)). It must be “dead wrong.” Sterling Elec., 866 F.2d at 233. Maryland provides insufficient basis for us to find clear error or manifest injustice in this court’s earlier holding that Maryland’s volume discount ban is a hybrid restraint and a per se violation of the Sherman Act.
Maryland’s final challenge to the law of the case is the assertion that we erred by not giving proper deference to legislative findings. The state maintains that the validity of its challenged regulatory scheme should not “depend on a judicial assessment of its effectiveness.” Appellant’s. Br. at 41.
This argument fails to meet its required burden for two reasons. First, the primary Supreme Court precedent that Maryland relies upon, Exxon Corp. v. Governor of Md., 437 U.S. 117, 98 S.Ct. 2207, 57 L.Ed.2d 91 (1978), is inapposite. In Exxon, the Supreme Court found that Exxon Corp.’s substantive due process challenge to Maryland’s legislation rested on an evaluation of the economic wisdom of that legislation. The Supreme Court held that “the Due Process Clause does not empower the judiciary to sit as a superlegislature to weigh the wisdom of legislation.” Id. at 124, 98 S.Ct. 2207 (citations and internal quotation marks omitted). The judiciary’s role in such a challenge is limited to rational basis review. See id. at 124-25, 98 S.Ct. 2207 (“Regardless of the ultimate economic efficacy of the statute, we have no hesitancy in concluding that it bears a reasonable relation. to the State’s legitimate purpose in controlling the gasoline retail market, and we therefore reject appellants’ due process claim.”). This holding simply reiterates the Supreme Court’s long-standing jurisprudence that due process challenges to economic regulations receive only the highly deferential rational basis review.
The nature of the challenge here is fundamentally different. The regulatory scheme at issue has been found to be a per se violation of the Sherman Act. This court’s determination of the effectiveness of this scheme is an effort to salvage the scheme despite this violation because of the state’s authority under the 21st Amendment. See, e.g., Midcal, 445 U.S. at 112-14, 100 S.Ct. 937. In other words, despite the scheme’s violation of federal law, the state is given the opportunity to demonstrate that its own interests outweigh those of the federal government. Here, a determination of effectiveness is essential to weigh the competing interests because the state’s interests are weighed in the balance only insofar as they are actually advanced by the regulatory scheme. Id. at 113-14,100 S.Ct. 937. The 21st Amendment may provide “shelter” for a state’s liquor statutes that violate the Sherman Act only if the state’s interest truly outweighs the federal interest. Id. at 114, 100 S.Ct. 937. The rational basis test, with its accompanying legislative deference, is simply irrelevant in this context.
Second, in remanding in TFWS I to determine regulatory effectiveness this court was following Supreme Court guidance instructing that judicial determination of the effectiveness of a state’s liquor regulations is necessary when those regulations [195]*195violate the Sherman Act. See, e.g., Midcal, 445 U.S. at 113, 100 S.Ct. 937 (“Nothing in the record in this case suggests that the wine pricing system helps [further the state’s interest in] sustaining] small retail establishments.”); 321 Liquor, 479 U.S. at 350, 107 S.Ct. 720 (“[I]n this case the New York Court of Appeals cited no legislative or other findings that either the minimum markup requirement or the ‘bottle price’ definition of cost has been effective in [furthering the state’s interest in] preserving small retail establishments, and made no findings of its own.”) (emphases added). Supreme Court precedent clarifies the importance of determining regulatory effectiveness and permits the use of multiple sources to make such a determination. Legislative findings, empirical studies (i.e., “other findings”), or findings by the court can all be useful in assessing the effectiveness of a state’s regulatory scheme in achieving its stated purpose. See 324 Liquor, 479 U.S. at 350,107 S.Ct. 720.
As we summarized in TFWS I, drawing extensively on Supreme Court precedent:
Unsubstantiated state concerns under the Twenty-first Amendment are not sufficient to trump the goals of the Sherman Act; a state must demonstrate that its liquor regulatory policies directly serve [i.e., are effective in furthering] the interests it proffers under the Twenty-first Amendment.... In the end, the state’s interests must be of sufficient weight to prevail against the federal interest in enforcement of the antitrust laws.
TFWS I, 242 F.3d at 212 (citations and quotations omitted).
Finding no exceptions to the law of the case, we decline to revisit our prior holdings on these points.
III.
We turn now to the only issue not controlled by the law of the case. In TFWS III, we vacated the district court’s order finding that Maryland’s regulatory scheme was ineffective and preempted by the Sherman Act because the district court failed to take into account, or explain why it was unnecessary to take into account, Maryland’s and Delaware’s excise tax rates and their effect on prices. TFWS III, 147 Fed.Appx. at 331-32. We remanded with instructions that the states’ excise taxes must be considered to determine the effectiveness of Maryland’s regulatory scheme.
On remand, the district court, following our instructions, conducted additional fact-finding. Following this fact-finding, the district court held that (1) controlling for excise taxes is a logical means of eliminating a separate variable and any excise tax differentials should be eliminated; (2) controlling for excise tax, Maryland’s prices are on average only 0.2% more expensive than Delaware’s prices; (3) economic theory shows that a uniform 0.2% increase in price will cause a 0.2% decrease in wine consumption and a 0.3% decrease in liquor consumption and studies of states that have abolished similar laws indicate no significant change in alcohol consumption patterns; and (4) Maryland proved only that the challenged regulations have (at best) a minimal impact in furthering the state’s interest in temperance. Consequently, the district court concluded that the federal interest in promoting competition outweighs the state’s interest and so Maryland’s regulatory scheme is preempted by the Sherman Act. Although Maryland challenges the district court’s legal conclusion that the federal interest outweighs the state interest, it does so primarily by challenging the court’s second factual finding regarding [196]*196the minimal impact of Maryland’s challenged regulations on prices.
Our standard of review is well established. “We defer to the district court’s factual findings and do not set them aside unless clearly erroneous; and we review legal conclusions de novo.” United States v. Stevenson, 396 F.3d 538, 541 (4th Cir. 2005). A factual finding is clearly erroneous when we are “left with the definite and firm conviction that a mistake has been committed.” Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) (internal quotation marks and citation omitted). But “[i]f the district court’s account of the evidence is plausible in light of the record viewed in its entirety,” we will not reverse the district court’s finding simply because we have become convinced that we would have decided the question of fact differently. Id. at 573-74, 105 S.Ct. 1504. Thus, when “there are two permissible views of the evidence, the [district court’s] choice between them cannot be clearly erroneous.” Id. at 574, 105 S.Ct. 1504.
Maryland challenges the district court’s finding that the state’s regulatory scheme has a minimal impact on pricing by arguing that the pricing data that TFWS provided, and on which the court relied, was flawed. Maryland employs two primary arguments in attempting to demonstrate the unreliability of this data. First, Maryland argues that in TFWS III “this Court reversed, finding that [TFWS’s analyses] were not ‘sufficiently reliable to provide an indication of the effect the challenged regulations have on Maryland prices.’ ” Appellant’s Br. at 49 (quoting TFWS III, 147 Fed.Appx. at 335). However, Maryland’s attempt to find support in TFWS III for its current position (i.e., that TFWS’s data is flawed) is misguided. The contextualized quote from our holding in TFWS III is as follows:
[W]e cannot say at this point that the price comparisons cited by the district court are sufficiently reliable to provide an indication of the effect the challenged regulations have on Maryland prices. There is no factfinding or analysis by the district court that explains the extent of the impact excise taxes have on prices or why a comparison of prices need not be adjusted for excise taxes.
Id. In other words, we did not hold that TFWS’s analyses were not reliable — we simply held that we could not evaluate whether or not the analyses were reliable because of the lack of information about excise tax rates. Maryland has conceded that this “most conspicuous” methodological flaw “was corrected in TFWS’s revised price comparisons [which incorporated the effect of the states’ excise tax rates].” Appellant’s Br. at 52. The revised data took into account the excise tax rate in each state in order to more accurately compare Maryland’s liquor and wine prices with those in Delaware. Consequently, our pri- or finding provides no support for Maryland’s current challenge.
Second, Maryland questions the assumption underlying TFWS’s data that retailers buy their stock exclusively in the months when the prices are lowest. Maryland labels this type of purchasing an “extreme form of bridge buying,” and argues that most retailers do not have the credit or storage capacity to engage in it. Appellant’s Br. at 54. TFWS responds that since the assumption was made for both Maryland and Delaware, and the point of the study was to provide comparative data, this assumption was valid.12 See Appel[197]*197lee’s Br. at 54-56. The point of the analysis was not to claim that all retailers actually buy when prices are at their lowest but simply to find a reference point that provides a fair basis of comparison for the two states’ liquor and wine prices. See Appellee’s Br. at 55. For instance, it would also have made sense to compare average prices to average prices or highest prices to highest prices. Id. The district court found that “[although TFWS’s data are far from perfect, they permit a more reliable comparison of Maryland and Delaware wholesale prices. The State has produced nothing better, and relies on TFWS’s data in conducting its analysis.”13 J.A. 5667.
In reviewing the record in its entirety, we find that the district court’s reliance on the data provided by TFWS was reasonable. Maryland’s arguments provide no basis for us to conclude that the district court’s findings of fact — and, in particular, its finding that Maryland’s regulatory scheme is ineffective in furthering Maryland’s purported interest in temperance— are clearly erroneous. Judging from the record, the district court relied on the best evidence available and made a reasoned judgment on the basis of that record. Once the district court made its finding of fact that the challenged regulatory scheme had minimal impact in furthering the state’s interests, the legal conclusion that the federal interest outweighed the state interest followed more or less as a matter of course. Finding no error, we affirm.
IV.
For the foregoing reasons, the judgment appealed from is
AFFIRMED.