Wood, Chief Judge.

W. Joseph Bruckner, Attorney, Brian D. Clark, Attorney, Devona L. Wells, Attorney, Lockridge Grindal Nauen P.L.L.P., Minneapolis, MN, Michael J. Freed, Attorney, Steven A. Kanner, Attorney, Robert J. Wozniak, Attorney, Freed Kanner London & Millen LLC, Bannockburn, IL, Daniel J. Mogin, Attorney, Jodie M. Williams, Attorney, Mogin Law Firm, San Diego, CA, Aaron Martin Panner, Attorney, Gregory G. Rapawy, Attorney, Kellogg, Huber, Hansen, Todd, Evans & Figel, PLLC, Washington, DC, for Plaintiffs–Appellees.

Matthias A. Lydon, Attorney, James Franklin Herbison, Attorney, Michael P. Mayer, Attorney, Chicago, IL, Elizabeth Petrela Papez, Attorney, Washington, DC, Winston & Strawn LLP, William P. Ferranti, Attorney, Ferranti Firm LLC, Portland, OR, for Defendant–Appellant.

Before Wood, Chief Judge, and Bauer and Williams, Circuit Judges.

Wood, Chief Judge.

The antitrust laws prohibit competing economic actors from colluding to agree on prices, either directly or through such mechanisms as output restrictions. See United States v. Socony–Vacuum Oil Co. , 310 U.S. 150, 60 S.Ct. 811, 84 L.Ed. 1129 (1940) ; Palmer v. BRG of Georgia, Inc. , 498 U.S. 46, 111 S.Ct. 401, 112 L.Ed.2d 349 (1990). That is just what the plaintiffs in the case before us allege the producers and sellers of containerboard did. The plaintiff-purchasers filed this suit under Sherman Act § 1, 15 U.S.C. § 1, seeking to recover treble damages for the overcharges they allegedly paid. See Clayton Act § 4, 15 U.S.C. § 15. What brings the case before us at this time—well before the merits have been resolved—is the district court's decision to certify a nationwide class of purchasers under Federal Rule of Civil Procedure 23. The defendants, International Paper Company, Georgia–Pacific LLC, Temple–Inland Inc., RockTenn CP, LLC, and Weyerhauser Company (to whom we will refer collectively as Defendants unless the context requires otherwise), asked us to accept this interlocutory appeal from the certification decision pursuant to Rule 23(f). We agreed to do so. Finding no abuse of discretion in the district court's decision, however, we affirm.

I

The Purchasers allege in their complaint that the defendant companies agreed “to restrict the supply of containerboard by cutting capacity, slowing back production, taking downtime, idling plants, and tightly restricting inventory.” These actions predictably led to an increase in the price of containerboard—a price increase that caused Purchasers to pay more for containerboard products than they would have paid in the absence of the illegal agreement. The named plaintiff on the complaint is Kleen Products LLC. It asked the district court to certify the following class:

All persons that purchased Containerboard Products directly from any of the Defendants or their subsidiaries or affiliates for use or delivery in the United States from at least as early as February 15, 2004 through November 8, 2010.

The proposed definition carved out the defendants themselves, entities or personnel related to them, and governmental entities. The Defendants opposed class certification on a number of grounds: whether common questions predominate; whether antitrust injury can be proved using a common method; whether the amount of damages can be proved using a common method; and whether a class action is superior.

As the Supreme Court emphasized in Wal–Mart Stores, Inc. v. Dukes , 564 U.S. 338, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011), “Rule 23 does not set forth a mere pleading standard. A party seeking class certification must affirmatively demonstrate his compliance with the Rule....” Id. at 350, 131 S.Ct. 2541. We must therefore take a careful look at the evidence that the Purchasers presented in support of class certification as we assess the district court's ruling. Some of that evidence was provided by experts, but at this stage we need say little about them, because no defendant challenged the Purchasers' experts under Federal Rule of Evidence 702 or the Supreme Court's decision in Daubert v. Merrell Dow Pharm., Inc. , 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). See Tyson Foods, Inc. v. Bouaphakeo , –––U.S. ––––, 136 S.Ct. 1036, 1049, 194 L.Ed.2d 124 (2016) (where there is no Daubert challenge, district court may rely on expert evidence for class certification). The district court also pointed out that “[f]or the most part, the parties agree on the basic facts, and both parties' experts rely upon the same data, so there are little if any factual disputes that the Court must resolve to decide class certification.” For that reason, the court concluded that there was no need for a comprehensive evidentiary hearing. This, in our view, was a case-management decision that we have no reason to second-guess, despite Defendants' complaints. See American Honda Motor Co. v. Allen , 600 F.3d 813, 815 (7th Cir. 2010) (evidentiary hearing should be held “if necessary”); West v. Prudential Sec., Inc. , 282 F.3d 935, 938 (7th Cir. 2002) (same).

Two final points are worth making before we turn to the evidence. First, nothing in Wal–Mart changed the applicable standard of review, which is deferential (as the cases say, only for “abuse of discretion”). Messner v. Northshore Univ. HealthSystem , 669 F.3d 802, 811 (7th Cir. 2012). Second, it remains true that Rule 23 does not demand that every issue be common; classes are routinely certified under Rule 23(b)(3) where common questions exist and predominate, even though other individual issues will remain after the class phase. See, e.g., McMahon v. LVNV Funding , 807 F.3d 872, 875–76 (7th Cir. 2015) ; Pella Corp. v. Saltzman , 606 F.3d 391, 393 (7th Cir. 2010).

II

Although the requirements for class certification under Rule 23 are familiar, we set out the critical sections of the rule here for ease of reference:

(a) Prerequisites. One or more members of a class may sue or be sued as representative parties on behalf of all members only if:

(1) the class is so numerous that joinder of all members is impracticable;

(2) there are questions of law or fact common to the class;

(3) the claims or defenses of the representative parties are typical of the claims or defenses of the class; and

(4) the representative parties will fairly and adequately protect the interests of the class.

* * *

(b) Types of Class Actions. A class action may be maintained if Rule 23(a) is satisfied and if:

* * *

(3) the court finds that the questions of law or fact common to class members predominate over any questions affecting only individual members, and that a class action is superior to other available methods for fairly and efficiently adjudicating the controversy. The matters pertinent to these findings include:

(A) the class members' interests in individually controlling the prosecution or defense of separate actions;

(B) the extent and nature of any litigation concerning the controversy already begun by or against class members;

(C) the desirability or undesirability of concentrating the litigation of the claims in the particular forum; and

(D) the likely difficulties in managing a class action.

Our focus is on the predominance requirement of subpart (b)(3), since, as the district court noted, “Defendants have conceded that typicality, commonality, and adequacy have been satisfied so long as [Purchasers] have adequately proven predominance,” and no one is arguing about numbers either.

A

We begin with some background facts about the containerboard industry. “Containerboard” is the term for a sheet of heavy paper with a smooth top and bottom (the linerboard) and a fluted layer between the two (the corrugated medium). It is made in large, expensive mills; as of 2008, no new mills had been built in the United States for more than 12 years. The containerboard sheets are cut and folded into products such as boxes of varying sizes. The industry is dominated by vertically integrated producers, which means simply that the fabrication of the containerboard and then its processing into final products are handled internally by a firm. This means, importantly for antitrust purposes, that the Purchasers bought directly from the alleged conspirators, not through intermediaries. See Illinois Brick Co. v. Illinois , 431 U.S. 720, 97 S.Ct. 2061, 52 L.Ed.2d 707 (1977) (distinguishing between direct-purchaser suits, which are permitted under Clayton Act § 4, and indirect-purchaser suits, which are not).

Containerboard is a commodity, sold in standardized compositions and weights. The final products are also standardized; one trade association commented that “boxes are essentially commodity items used in well established markets.” The most common containerboard product sold in the United States in 2010 was unbleached kraft linerboard weighing 42 pounds per thousand square feet. Pulp & Paper Week (PPW), an industry periodical, publishes weekly price indices that include the price for the 42-pound linerboard for delivery east of the Rocky Mountains. The PPW index, as it is called, is widely used within the industry as a benchmark.A small and shrinking number of firms produce most of the containerboard in North America. As of 1997, the five largest firms (i.e. the current defendants or their predecessors) were responsible for 41% of North American production. By 2007, the Defendants furnished 74% of that production. Add in the next two firms, and the number swelled to 84%. (This evidence is ambiguous: a cartel's market share will shrink over time, to the extent that the high prices attract new entry from fringe competitors or imports, but its market share will grow to the extent that the cartel successfully uses exclusionary devices. The existing record does not resolve that ambiguity, but it does not matter for purposes of class certification.)

There was a great deal of evidence designed to show that the hypothesis that Defendants had organized a cartel was one that a jury could accept. We do not need to review all of it, but we offer some key points. During the class period, which ran from February 15, 2004, through November 8, 2010, Defendants attempted 15 price increases, and with one exception, all Defendants joined each one, at roughly the same time (11 out of 15 times within the same month). Twelve times out of 15 they increased prices by identical amounts; the remaining times the increases of different firms varied by less than 2% of the average price.

Capacity in the industry over this period was declining in North America, though increasing elsewhere; meanwhile, demand was constant or increasing. Defendants increased prices at least once during the recession of 2008 and 2009, and they raised prices again twice in 2010. Inventory levels were decreasing, because of several steps they took: they closed many mills; they indefinitely idled some; they temporarily idled others; and they slowed down production. In 2005, they announced mill closures representing 931,000 tons of capacity, and shortly thereafter they raised prices $30/ton. They did much the same thing in 2009. Communication among the Defendants was easy, thanks to trade associations.

These and other facts spurred the Purchasers to bring this suit and to structure it as a class action. They filed their motion for class certification only after extensive discovery. In that motion, they relied on the type of industry facts we have just mentioned, as well as on reports from two experts, Michael J. Harris and Mark Joseph Dwyer. Defendants countered with reports from two other experts, Dennis Carlton and Janusz Ordover. Harris concluded that the structure of the containerboard industry made it likely that a conspiracy among the Defendants could succeed in increasing prices for all or nearly all purchasers; he also opined that Defendants' strategy would not have made sense if it had been undertaken unilaterally by each company. Carlton and Ordover disagreed, contending that Defendants' pricing behavior could be explained by oligopolistic interdependence (that is, by parallel but independent behavior undertaken by firms in a concentrated market). They suggested ways in which the supply restrictions might have been rational under the circumstances. Tellingly, however, they never said that there might have been a cartel with respect to some purchasers and not with respect to others.

On the subject of damages, Purchasers' expert Dwyer examined price movements. For example, he compared the actual prices paid by a sample of class members before and after the Defendants' price increases and found that in 92% of cases those prices increased. He also constructed a regression model to estimate the overcharges made possible by the conspiracy. That model indicated that the class paid overcharges of approximately 3.08%, or in dollar terms, approximately $3.8 billion too much. Defendants' experts criticized the sample size that Harris had used, and they asserted that Purchasers' experts had failed adequately to account for external factors influencing price and capacity.

B

The district court began its analysis of predominance—the central disputed issue in the case—by recalling the Supreme Court's statement in Amchem Products, Inc. v. Windsor , 521 U.S. 591, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997), that “[t]he Rule 23(b)(3) predominance inquiry tests whether proposed classes are sufficiently cohesive to warrant adjudication by representation.” Id. at 623, 117 S.Ct. 2231. It also acknowledged that, as the Supreme Court puts it, “Rule 23(b)(3)'s predominance criterion is even more demanding than Rule 23(a).” Comcast Corp. v. Behrend , ––– U.S. ––––, 133 S.Ct. 1426, 1432, 185 L.Ed.2d 515 (2013). Predominance is satisfied when “common questions represent a significant aspect of a case and ... can be resolved for all members of a class in a single adjudication.” Messner , 669 F.3d at 815 (internal quotation marks omitted); see also Wal–Mart , 564 U.S. at 350, 131 S.Ct. 2541 (a common contention for Rule 23(a)(2) purposes “must be of such a nature that it is capable of classwide resolution—which means that determination of its truth or falsity will resolve an issue that is central to the validity of each one of the claims in one stroke”). With those principles in mind, the court evaluated the two central elements of the Purchasers' case: the alleged violation of the antitrust laws, and the causal link between that violation and their alleged injury. It set the question of damages to one side, noting that “it is well established that the presence of individualized questions regarding damages does not prevent certification under Rule 23(b)(3).” Messner , 669 F.3d at 815 (citing Wal–Mart , 564 U.S. at 362, 131 S.Ct. 2541 (“individualized monetary claims belong in Rule 23(b)(3) ”)).

With respect to proof of liability, the court had this to say:

To prove each element of a conspiracy, virtually all class members would be relying on the same evidence that Plaintiffs have submitted in support of class certification—namely, the documents, emails, phone records, and other indirect evidence necessary to prove that Defendants conspired in violation of antitrust laws.... [I]t is much more efficient to have a single trial on the alleged conspiracy rather than thousands of identical trials all alleging identical conspiracies based on identical evidence.

While acknowledging that Defendants hotly contested the conspiracy allegation, the court found that their arguments went to the merits, not to the suitability of the case for class treatment.

Turning to causation, to which it also referred as “antitrust impact,” the court rejected the Defendants' effort to equate this case to Comcast, where the Supreme Court found a mismatch between the plaintiffs' damages theory and the evidence they presented to show predominance. First, on the question of impact, defined as whether Purchasers were harmed, the court found that at the class-certification stage the plaintiffs needed to demonstrate that the element of impact is capable of class-wide proof at trial, through evidence common to all class members. Looking at all the evidence, the court found this element satisfied. For example, the Defendants' price increases were not tailored to each individual purchaser; this was a commodity market with a structure conducive to collusion; communications took place at a high level; the common use of the PPW index affected all market participants; and the Defendants lacked any other reasonable explanation for the tight correlation between the index and their announcements of price increases.

With respect to damages, the court found that the Purchasers had the burden of producing a reliable method of measuring classwide damages based on common proof. It rejected the Defendants' argument that the eventual need to examine each individual purchaser's damages was enough to defeat a finding of predominance. Nothing in Comcast, the court said, requires a different outcome. As this court noted in In re IKO Roofing Shingle Products Liability Litigation , 757 F.3d 599 (7th Cir. 2014), the plaintiffs' damages expert in Comcast had estimated harm based on the assumption that all four theories of liability that plaintiffs offered had been established. The class certified by the court, however, was limited to only one of those theories. This, we explained, is what the Supreme Court said, “made class treatment inappropriate: without a theory of loss that matched the theory of liability, the class could not get anywhere.” Id. at 602. With that point established, the court assessed Dwyer's report, concluded that both the methodology and the data were reliable, and concluded that it could be used to demonstrate class-wide damages.

Finally, the court held that Purchasers had shown the superiority of proceeding under Rule 23(b)(3). The fact that some class members had signed releases as a part of a settlement of an earlier class action (dealing with an alleged linerboard conspiracy that took place between 1993 and 1995) did not require a contrary finding. As the court said,

[t]he conduct at issue in the prior litigation was Defendants' allegedly collusive behavior in the mid-nineties. The actions at issue here are coordinated market manipulation and price-increase announcements that occurred nearly a decade later.... Under Defendants' argument, they are free to keep colluding in violation of antitrust laws so long as they conspire in the same way as they were alleged to have behaved in a prior settled case. The Court is unaware of any case supporting this argument; indeed, several cases are to the contrary.

The court also rejected similar arguments based on particular contractual provisions, and it decided that retaining defendant Rock–Tenn in the case would not violate its bankruptcy discharge.

C

1

We follow the same general outline that the district court used, looking first at predominance and then at superiority. Within predominance, we consider two points: whether common methods of proof can be used to demonstrate the existence of the alleged collusion and its effect on prices in the containerboard market; and whether the existence and impact of any such collusion predominate over other factors that may affect an individual plaintiff's damages. These inquiries apply to all defendants. Defendant RockTenn raises some additional arguments related to its bankruptcy; we address these at the close of the opinion.

In order to secure class certification, the Purchasers had to demonstrate (not merely allege) that there is proof common to all class members, and that this proof would show that they suffered “injuries that reflect the anticompetitive effect of either the violation or the anticompetitive acts made possible by the violation.” James Cape & Sons Co. v. PCC Const. Co. , 453 F.3d 396, 399 (7th Cir. 2006) ; see Brunswick Corp. v. Pueblo Bowl–O–Mat, Inc. , 429 U.S. 477, 97 S.Ct. 690, 50 L.Ed.2d 701 (1977).Purchasers tendered extensive evidence that, if believed, would be enough to prove the existence of the alleged conspiracy. Not surprisingly, it is largely circumstantial. But they offered voluminous written materials of various types, which in the aggregate pointed to the existence of both agreement and actions to violate the antitrust laws. Indeed, Defendants do not contest that the existence of the conspiracy could be (perhaps had to be) proven by evidence common to the class.

The more difficult question (though not too difficult in the end) is whether the common evidence could show the fact of injury on a classwide basis. See Messner , 669 F.3d at 819 (“The ability to use such common evidence and common methodology to prove a class's claims is sufficient to support a finding of predominance on the issue of antitrust impact for certification under Rule 23(b)(3).”). At base, Defendants argue that it is not enough for Purchasers to prove aggregate injury and one aggregate overcharge, without allocating how much of that overcharge was paid by each individual class member. They urge that Purchasers have the burden of showing that every class member must prove at least some impact from the alleged violation. For that proposition, they rely on In re Hydrogen Peroxide Antitrust Litigation , 552 F.3d 305, 311 (3d Cir. 2008), and In re Rail Freight Fuel Surcharge Antitrust Litigation , 725 F.3d 244, 252 (D.C. Cir. 2013).

While we have no quarrel with the proposition that each and every class member would need to make such a showing in order ultimately to recover, we have not insisted on this level of proof at the class certification stage. To the contrary, we said in Suchanek v. Sturm Foods, Inc. , 764 F.3d 750 (7th Cir. 2014), that “[i]f the [district] court thought that no class can be certified until proof exists that every member has been harmed, it was wrong.” Id. at 757 ; see also Parko v. Shell Oil Co. , 739 F.3d 1083, 1084–85 (7th Cir. 2014) ; McReynolds v. Merrill Lynch, Pierce, Fenner & Smith, Inc. , 672 F.3d 482, 491 (7th Cir. 2012). There is no evidence to make us think that the class defined by the district court either excludes too many purchasers or contains troublesome internal conflicts, either of which would indicate it should be rejected. We therefore move on to the adequacy of the Purchasers' showing that the conspiracy had an effect on the prices they paid.

The parties have jousted over the need for some kind of “but-for” analysis, by which Defendants mean an expert construction of a hypothetical market free of any anticompetitive restraint, to which the actual market can be compared. See Blades v. Monsanto Co. , 400 F.3d 562, 569 (8th Cir. 2005). That might be one way in which a plaintiff could satisfy its burden, but we think that the formulation is too narrow. What is essential is whether the class can point to common proof that will establish antitrust injury (in the form of cartel pricing here) on a classwide basis. Like the district court, we are satisfied that Purchasers have done so.

The Purchasers built up their case with several types of evidence. First, expert Harris's report showed that the structure of the containerboard market was conducive to successful collusion. He pointed to the concentration of manufacturers; the vertical integration of the market; the capital-intensive manufacturing process (which affected the pace and likelihood of new entry); weak competition from imported containerboard; no good substitutes for the product; a low elasticity of demand; and a standardized, commodity product. These are all well accepted characteristics of a market that is subject to cartelization. See, e.g., In re Text Messaging Antitrust Litig. , 782 F.3d 867, 872 (7th Cir. 2015) ; Minn–Chem, Inc. v. Agrium, Inc. , 683 F.3d 845, 859–60 (7th Cir. 2012) (en banc ); In re High Fructose Corn Syrup Litig. , 295 F.3d 651, 657 (7th Cir. 2002) ; Jack Walters & Sons Corp. v. Morton Bldg., Inc. , 737 F.2d 698, 710–11 (7th Cir. 1984).

Defendants pooh-pooh these cases as examples of the discredited structure-conduct-performance (SCP) paradigm that ruled antitrust from the 1950s until the mid-1970s. See, e.g. , United States v. Von's Grocery Co. , 384 U.S. 270, 86 S.Ct. 1478, 16 L.Ed.2d 555 (1966) (striking down a merger between a firm with 4.7% of the market and a firm with 4.2%). We put to one side the fact that the SCP paradigm was used during that era primarily in merger cases and this is a cartel case alleging hard-core price-fixing—the kind of case in which lack of market power or reasonableness of price is no defense. The evidence here goes well beyond the structural. The flaw in the old SCP notion was the thought that it was enough to know the structure of a market in order to predict what kind of conduct would ensue, and how competitively that market would perform. No such chain of assumptions taints the Purchasers' proof. They have shown actual price increases, a mechanism for those increases, the communication channels the conspirators used, and factors suggesting that cartel discipline can be maintained. We are not saying that any of these points have been proven, of course, but we are saying that this evidence is enough to support class treatment of the merits.

Defendants also object to the Purchasers' definition of the market. The Purchasers, they say, have conflated the market for containerboard (the material) with the market for finished corrugated products. The district court responded that the uniform vertical integration found in this industry makes it appropriate to look to the finished products. That is correct: Purchasers (and we) have no reason to dig inside the defendant companies to evaluate their internal pricing of the raw materials they use in producing the boxes and other products they sell.

Next, Defendants criticize Dwyer's examination of the 15 price increases they announced and his use of the PPW index in that connection. He analyzed “industry-wide reflections of price and actual prices paid by class members before and after” the price-increase announcements, and he found that nine of the 15 efforts succeeded (i.e. resulted in a durable price increase). He also performed a regression analysis comparing classwide aggregate prices to the PPW index and found that “more than 97% of variation in aggregate prices is explained by changes in the index.” He reviewed 738 contracts (those the Defendants had produced) and found that 96% of them “contained provisions that tied pricing to the PPW index.” The Defendants protest that the Purchasers have shown only correlation, not causation, but we think, taking into account the rest of the evidence, Purchasers have not fallen into that trap.

Defendants also argue that Dwyer's approach is the same kind of “trial-by-formula” that the Supreme Court rejected in Wal–Mart. But in that case the Court disapproved the plaintiff's attempt to take a sample of the class members, who alleged employment discrimination, to determine what percentage of that sample had actually experienced discrimination, and then to extrapolate that percentage for the whole class. The Purchasers here are doing nothing of the sort: they assert that every person or entity in North America paid the overcharges that resulted from Defendants' collusive practices. Even for transactions where prices were negotiated individually or a longer term contract existed, the district court found, reasonably, that the “starting point for those negotiations would be higher if the market price for the product was artificially inflated.”

We have already discussed the Purchasers' common proof of damages, but we add a few more words here to respond to the Defendants' Comcast arguments. Defendants understand Comcast to hold that “individualized damages do foreclose predominance if plaintiffs present no classwide method to adjudicate damages tethered to their theory of antitrust violations and if resolving those individualized damages issues would ‘overwhelm questions common to the class.’ ” Brief for Appellants at 36 (quoting 133 S.Ct. at 1433 ). We agree with Defendants that Comcast insists that the damages theory must correspond to the theory of liability, but that is all Comcast said that is pertinent to our case. We must see if there is a classwide method for proving damages, and if not, whether individual damage determinations will overwhelm the common questions on liability and impact.

Dwyer conducted a preliminary analysis to demonstrate the feasibility of estimating damages on a classwide basis. He created two categories of products, intermediate and final, and he used two benchmark periods (before and after the class period) to compare prices. He also accounted for many other variables, such as downstream demand, production and delivery, inflation, and seasonal factors, in order to control for other influences on price and to isolate the impact of the conspiracy. Using a “dummy variable,” he calculated an average overcharge of 2.92% for the final products category and 3.81% for the intermediate products category. He then multiplied the average overcharges by the dollar amount of purchases by class members, subtracting purchases that had taken place under previously contracted prices. He found that the class members paid $801.27 million more for intermediate products and $2.991 billion more for final products than they would have absent the conspiracy.

Defendants complain that it is wrong to calculate aggregate rather than individual damages for the class. The district court rejected that position as a matter of law, as do we. We held in Loeb Indus., Inc. v. Sumitomo Corp. , 306 F.3d 469 (7th Cir. 2002), that plaintiffs are permitted to use estimates and analysis to calculate a reasonable approximation of their damages. Id. at 493. And we already have confirmed that at the class certification stage, plaintiffs are not obliged to drill down and estimate each individual class member's damages. The determination of the aggregate classwide damages is something that can be handled most efficiently as a class action, and the allocation of that total sum among the class members can be managed individually, should the case ever reach that point. If in the end the Defendants win on the merits, this entire matter will be over in “one fell swoop.” (See WILLIAM SHAKESPEARE, MACBETH , act 4, sc. 3, l. 220 (David Bevington ed., Pearson Longman 6th ed. 2009.)) If Purchasers prevail on the common issues, both liability and aggregate damages will be resolved. The district court did not commit reversible error when it concluded that the class issues predominated.

2

Everything we have said thus far also points to the superiority of the class device for this case. We need to address only two potential flies in the ointment that Defendants see: first, the significance (if any) of certain releases that some class members signed; and second, the relevance of contract defenses that might apply.

Some class members settled claims in an earlier lawsuit against the same companies, dealing with the same industry. Defendants represent that there are 39 relevant settlement agreements implicating almost 10,000 of the individual claims at issue. The Purchasers respond that these numbers are wrong, because they involve double-counting and give an exaggerated impression of the real number of affected class members, since most people who signed releases did so with multiple defendants. More importantly, Purchasers also note that the Defendants' numbers imply that most people who signed releases did so after the events giving rise to the present case, whereas in reality the releases are heavily distributed toward the beginning of the class period or earlier. Purchasers suggest the simple expedient of limiting the recovery period for any class member who signed a release to purchases made after that release was signed. That strikes us as an easy and effective way to handle this problem. Moreover, as the district court observed, the fact that some plaintiffs released the defendants from further liability for their actions in the mid-1990s is not a life-time inoculation against antitrust liability in the same industry.

The other contract defenses to which Defendants point involve such provisions as mandatory arbitration and mediation clauses, forum-selection clauses, jury waivers, provisions shortening the statute of limitations, and clauses eliminating remedies such as treble damages. Taking these limitations into account, they say, will destroy the cohesion of the class. The problem is that Defendants are relying on a case that involved a class-action waiver: Lozano v. AT&T Wireless Services, Inc. , 504 F.3d 718, 728 (9th Cir. 2007), and there is no such waiver here. The Purchasers point out that Defendants have identified only 190 class members affected by this group of limitations, out of over 100,000 notices that were sent out pursuant to Rule 23(c)(2)(B). As the record stands, this smattering of individual contract defenses does not undermine the superiority of the (b)(3) class action.

III

We noted earlier that defendant RockTenn is in a different position from the other defendants, because it filed for bankruptcy and received a discharge on June 30, 2010, approximately four months before the end of the class period. The district court refused to dismiss RockTenn on that basis because it found evidence that RockTenn re-joined the conspiracy after the discharge. (For example, on the very evening of the day when the discharge order was entered, RockTenn's president sent an email stating “I assume we are announcing tomorrow,” after three other defendants announced a simultaneous price increase.) The court also found that RockTenn might be jointly and severally liable for actions undertaken by its co-conspirators before the discharge, based on its post-discharge participation. See Havoco of Am., Ltd. v. Shell Oil Co. , 626 F.2d 549, 554 (7th Cir. 1980) (“[A] co-conspirator who joins a conspiracy with knowledge of what has gone on before and with an intent to pursue the same objectives may, in the antitrust context, be charged with the preceding acts of its co-conspirators.”).

The district court's reasoning was sound. RockTenn is free to argue at trial that it did not re-join the conspiracy. There is no conflict with bankruptcy law, however, if it did so, because in that case its liability would be predicated on post-discharge conduct. To the extent that these nuances need to be brought to the jury's attention, we are confident that the district court can do so through proper instructions.

IV

We conclude by noting again the basis of our ruling. First, with respect to the central issue of class certification under Federal Rule of Civil Procedure 23(a) and (b)(3), the only contested points relate to predominance and superiority. Defendants did not challenge Purchasers' experts under Daubert and Federal Rule of Evidence 702, and so we accept their reports for what they are worth at this stage. We did not discuss the opposing views expressed by Defendants' experts because they did not undermine the class certification decision. Defendants' experts' reports will be important, we assume, at the merits stage, but the fact that class certification decisions must be supported by evidence does not mean that certification is possible only for a party who can demonstrate that it will win on the merits.

We AFFIRM the class-certification order of the district court.