POSNER, Circuit Judge.

The plaintiffs in this class action suit on behalf of more than 500 female employees of a Rolls-Royce plant in Indiana that manufactures aircraft, industrial, and marine engines appeal from the denial of class certification and the subsequent grant of Rolls-Royce's motion for summary judgment. (We refer to the defendants, all of which are affiliated corporations, collectively as "Rolls-Royce.") The plaintiffs charge Rolls-Royce with sex discrimination, in violation of Title VII and the Equal Pay Act, in paying the members of the class less than comparable male employees by setting the base pay of women employees in the class members' compensation categories below that of male employees in the same categories, and in denying them promotions they would have received had they been men. There are other claims, which we'll not discuss, instead relying on the district judge's cogent analysis of them in three opinions: 2010 WL 987484 (S.D.Ind. Mar. 12, 2010); 2010 WL 1948222 (S.D.Ind. May 13, 2010); 742 F.Supp.2d 974 (S.D.Ind.2010).

To appeal a district court's denial of class certification, as the plaintiffs are doing in this case, is a risky strategy, especially when, as in this case, the class is proposed to be certified under Rule 23(b)(2) of the civil rules. Under that rule, which governs class actions in which "final injunctive relief or corresponding declaratory relief is appropriate respecting the class as a whole," notice to unnamed class members is optional. Rule 23(c)(2)(A). The consequence is that if the denial of certification is reversed but the decision on the merits, adverse to the class, is affirmed, the claims of the unnamed members, as of the named members, will be barred unless (see Cooper v. Federal Reserve Bank, 467 U.S. 867, 878-80, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984)) their claims are dissimilar to those of the named plaintiffs. Bolin v. Sears, Roebuck & Co., 231 F.3d 970, 975-76 (5th Cir.2000); Baby Neal ex rel. Kanter v. Casey, 43 F.3d 48, 58-59 (3d Cir.1994); Greene v. Los Angeles Unified School Dist., 246 F.3d 674 (9th Cir.2000) (unpublished). Even an unnamed class member who has a much stronger claim than the named plaintiffs may be hurt by certification, because a subsequent court may assume that certification would have been denied had the named's claims not been typical of those of all, or at least the vast majority, of the unnamed class members. In contrast, when the class is certified under Rule 23(b)(3), which governs class actions in which monetary relief is the primary relief sought, the unnamed class members must be notified and allowed to opt out of the class action, Rule 23(c)(2)(B); Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 176, 94 S.Ct. 2140, 40 L.Ed.2d 732 (1974), which gives them a chance to litigate their claims in a new suit. Yet those who do not opt out will be bound by the judgment in the class action. Nagel v. ADM Investor Services, Inc., 217 F.3d 436, 442 (7th Cir. 2000); Amati v. City of Woodstock, 176 F.3d 952, 957 (7th Cir.1999).

Conversely, a defendant confident of prevailing on the merits will often be well advised not to oppose certification, though there is some risk in doing so (so perhaps we should say a defendant utterly confident of winning on the merits would be well advised not to oppose certification). Rolls-Royce is confident of prevailing on the merits, and rightly so as we'll see, but follows the lawyer's reflexive strategy of denying whatever the opponent asserts.

Certification and merits cannot always be separated. For example, certification may be denied because the named plaintiff's claim is atypical of the claims of the other members of the class, and it may be a plaintiff typical because of a possibly complete defense to his claim that may not apply to claims of the other class members, as in CE Design Limited v. King Architectural Metals, Inc., 637 F.3d 721, 725-28 (7th Cir.2011). And then the only effect if the denial of certification is upheld may be the substitution, in a new class action suit, of another class member for the named plaintiff in the old suit, and in that event the defendant's victory will be Pyrrhic; substitution is an issue in this case, as we'll see.

But a plaintiff's victory in overturning the denial of certification may be equally Pyrrhic if he prevails only by occluding significant differences between his claim and that of other class members by insisting on its typicality, thus making it more difficult for unnamed class members to convince a court that their own claims are stronger than his (implying that his is atypical) and so should not be barred by a judgment against him.

We'll discuss the merits and then certification.

Rolls-Royce determines the compensation of its employees (all its employees, but this case concerns just those exempt from the minimum-wage and maximum-hours provisions of the Fair Labor Standards Act) in two steps. The first is to establish a broad pay range for each class of employees whom it deems of equal value to the company. We'll call these broad ranges "compensation categories." The class is spread over five of these categories. The second step, which is based on Rolls-Royce's recognition that it must meet competition from other employers for the employees it wants to hire or retain, is to create within each broad range a narrower range based on prevailing market wages for each of the jobs in question— "prevailing market wages" meaning wages offered by competing employers. Because of these ranges within ranges, the class that the plaintiffs want certified sprawls over twenty different compensation grades, including supervisory and nonsupervisory positions and encompassing starting salaries ranging from $40,050 to $190,750.

Thus, while in theory the jobs within each compensation category are of equal value to the company (we imagine that Rolls-Royce's motive for saying this— thereby unwittingly arming its adversaries in this case—is to improve employee morale by reassuring each employee that he or she is as good as others in the same compensation category even if paid less than they), the jobs are not equally valued by the market. Recognizing that it therefore must pay some employees in each category more than others, Rolls-Royce specifies different levels of base pay for different jobs within a category and (further complicating comparison across jobs) authorizes supervisors to make ad hoc pay adjustments; notably, each employee is eligible to obtain a percentage of his base pay as additional compensation, the percentage being based on an evaluation of the employee's performance by his superior.

In 2003, the year before the beginning of the complaint period, the average base pay (that is, the base pay before the performance add-on just noted) of male employees in the twenty compensation grades was about 5 percent higher than that of the women in those grades. That differential persisted throughout the complaint period. And because the performance adjustments were calculated as percentages of base pay, base pay influenced total pay throughout the period, though other adjustments may have diluted that influence or for that matter eliminated it. Of course if the women outperformed the men, they might catch up and even exceed them in pay, just by virtue of the performance adjustment. Yet they would exceed them by less than if their base pay had been equal to the men's at the outset. Suppose that in year one W's pay (after performance adjustment) is $90,000, and so this becomes her base pay in year two. M's pay is $100,000 in year one. In year two W receives a 20-percent performance bonus and M only a 5-percent bonus. As a result W's pay now exceeds M's—it is $108,000 to his $105,000. But if W's base pay in year two had been equal to M's, her second-year pay would have been $120,000, and so she was hurt by having started from a lower base—the difference in year-one base pay being attributable, according to the plaintiffs, to sex discrimination.

If the difference was attributable to sex discrimination, Rolls-Royce's failure to eliminate the difference would, by perpetuating discrimination, violate Title VII. Bazemore v. Friday, 478 U.S. 385, 394-96, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986) (concurring opinion—joined, however, by all the Justices); Hildebrandt v. Illinois Dep't of Natural Resources, 347 F.3d 1014, 1025-29 (7th Cir.2003); Goodwin v. General Motors Corp., 275 F.3d 1005, 1009-10 (10th Cir.2002). It is true that the prima facie case for a violation of the Equal Pay Act, which the plaintiffs also allege, does not require proof of discrimination, but only of unequal pay for "equal work on jobs the performance of which requires equal skill, effort, and responsibility, and which are performed under similar working conditions." 29 U.S.C. § 206(d)(1); see Fallon v. Illinois, 882 F.2d 1206, 1213-14 (7th Cir.1989). But the plaintiffs have been unable to identify any male worker who satisfied the stringent statutory requirement of equality of job skills, etc., and so the district judge was right to grant summary judgment for Rolls-Royce on the Equal Pay Act claim.

Rolls-Royce's expert, Bernard R. Siskin, shot down the plaintiff's theory of discrimination in base pay under Title VII by showing that once differences in the jobs performed by male and female employees in each compensation category are corrected for, the sex-correlated difference in base pay disappears. Adjusting base pay in response to market competition (which is different from other adjustments, such as those based on favorable evaluation of an employee's performance) takes place within a range that allows for considerable variance. The range is between 25 percent below and 25 percent above the median market wage for the jobs in the category. Remember that jobs are placed in the same compensation category because they are deemed by Rolls-Royce to be of equal value to the company, but since it cannot pay less (and will not pay more) than the market wage for a particular job, the base pay for the category is a range that permits differentiation because the market wage for a category of different jobs is also a range. A personnel officer might be as valuable to Rolls-Royce as an aeronautical engineer, but if the latter commands a higher wage in the market for aeronautical engineers, Rolls-Royce will have to pay him or her more; and if, as Siskin found, there were at the outset of the complaint period more male than female employees in jobs that command a higher market wage, the average compensation of male employees would exceed that of female employees in the same job category for a reason unrelated to sex discrimination. If cardiologists command a higher market wage than internists, they will be paid more even if the clinic that employs both types of physician regards them as equally valuable. Maybe workers in different jobs that are in some sense of comparable value, though the market thinks otherwise, should be paid the same as a moral matter; but "comparable worth" is not recognized as a theory on which to base a federal discrimination suit. E.g., Lang v. Kohl's Food Stores, Inc., 217 F.3d 919, 923 (7th Cir.2000); American Nurses' Ass'n v. Illinois, 783 F.2d 716, 719-20 (7th Cir.1986); Mikula v. Allegheny County, 583 F.3d 181, 183, 185 (3d Cir.2009) (per curiam); United Auto. Workers v. Michigan, 886 F.2d 766, 768-69 (6th Cir.1989). Anyway it is not urged by the plaintiffs in this case.

In concluding that the base-pay difference was attributable to discrimination, the plaintiffs' expert, Richard Drogin, made errors besides failing to adjust for differences in the jobs occupied by male and female employees. We'll mention only one of these errors: he included in the comparison employees hired after the beginning of the complaint period. That made no sense without an inquiry, which he did not attempt, into the reasons for the different starting salaries of male and female hires. Remember that the claim is that Rolls-Royce discriminated against women by failing to erase a disparity in base pay that existed at the outset of the complaint period; for all we know it did erase it, and the reason for the apparent persistence of the disparity is that new female hires were, for reasons unknown but not contended to be discriminatory, paid less than new male hires.

Having failed to rebut Siskin's key finding, either with Drogin's defective report or anything else, the plaintiffs' complaint about base-pay discrimination fails. We add (it bears on the issue of class certification, discussed below) that in several of the years in question the named plaintiffs' base pay exceeded, with only a few exceptions, that of the male employees in the plaintiffs' compensation grades who the plaintiffs claimed were comparable to them.

The named plaintiffs are more concerned with promotions they failed to get than they are with the largely nonexistent (for them at least) base-pay differentials. Yet Siskin's study found that women in the class members' five compensation categories are promoted on average more rapidly than men. Furthermore, while many promotions in a firm or other institution are more or less routine and even automatic, this is not true at the level of our plaintiffs, both of whom are in the highest of the five compensation categories, earning well over $100,000. Rolls-Royce has relatively few employees in this rarefied stratum and their work is not fungible. They do different jobs involving different skills and experience. The fact that some of the male employees who the plaintiffs contend were promoted ahead of them are, like them, called "Director of Operations" has no significance; the title covers a multitude of positions differing in authority (such as number of employees supervised) and responsibility.

In beginning to speak of facts peculiar to the two named plaintiffs, we are veering from merits issues to the certification issue. Because the district judge denied class certification, thus extruding the unnamed class members from the case, her grant of summary judgment spelled dismissal on the merits only of the named plaintiffs' claims. Both their pay claims and their promotion claims may well be weaker than those of class members in lower compensation grades than theirs. If we reverse the denial of class certification, we would, as explained earlier, jeopardize the ability of unnamed class members to obtain relief in individual suits or in a subsequent class action.

Fortunately for the class, the plaintiffs' challenge to the denial of class certification fails. Their claims are, as we just noted, significantly weaker than those of some (perhaps many) other class members; and as explained in CE Design Limited v. King Architectural Metals, Inc., supra, 637 F.3d at 725-28, named plaintiffs who are subject to a defense that would not defeat unnamed class members are not adequate class representatives, and adequacy of representation is one of the requirements for class certification. Fed. R.Civ.P. 23(a)(4); Amchem Products, Inc. v. Windsor, 521 U.S. 591, 625-27, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997). The district judge said that the plaintiffs' claims were not "typical of the claims or defenses of the class," also a requirement (Rule 23(a)(3)), though the usual practical significance of lack of typicality, as again explained in CE Design, is that it undermines the adequacy of the named plaintiff as a representative of the entire class.

The adequacy of the plaintiffs' representation is further undermined by the existence of a conflict of interest, beyond that implicit in their having weaker claims than some of the unnamed class members, between them and unnamed class members. Amchem Products, Inc. v. Windsor, supra, 521 U.S. at 625, 117 S.Ct. 2231; Gilpin v. American Federation of State, County & Municipal Employees, 875 F.2d 1310, 1313 (7th Cir.1989); Hines v. Widnall, 334 F.3d 1253, 1258 (11th Cir. 2003) (per curiam). The plaintiffs have authority within the company with regard to the compensation of some, and maybe many, of the unnamed class members and, as worrisome, over male employees in the same job categories as the class members. Although we doubt that the plaintiffs would deliberately depress the salary of female employees whom they supervise, or increase the salary of male employees whom they supervise, in order to create evidence of discrimination, the possibility of such strategic conduct (which might be unconscious) creates a conflict of interest between the plaintiffs and unnamed members of the class, (as well as with Rolls-Royce, if the plaintiffs raised the salaries of male employees in the class members' compensation categories in order to create evidence of sex discrimination). A class representative's conflict of interest is an independent ground for denial of class certification. Wagner v. Taylor, 836 F.2d 578, 595-96 (D.C.Cir.1987); Wells v. Ramsay, Scarlett & Co., 506 F.2d 436, 437-38 (5th Cir.1975). There is even evidence that the plaintiffs participated in decisions concerning female employees' compensation that, on their theory of the case, were discriminatory.

The plaintiffs made two attempts in the district court to avoid a finding that they are inadequate class representatives. The first was to cast this as an injunction class action suit, which is to say a class action suit governed by Rule 23(b)(2). It is true that Rule 23(b) (captioned "Types of Class Actions") is explicit that the requirements set forth in Rule 23(a) (captioned "Prerequisites [to Class Actions"]), such as the requirement that a named plaintiff be an adequate class representative, apply to all types of class action, including therefore class action suits seeking injunctive relief. But depending on the precise terms of the relief sought, an injunction suit might avoid adequacy issues that a class action suit for damages, which would be governed by Rule 23(b)(3), would present. It's easier for a named plaintiff to prove he's an adequate class representative in an injunctive action because usually there is less variance in injunctive relief sought for members of the class than in damages sought—imagine if the plaintiffs in this case were just seeking an injunction commanding base-pay equalization between male and female employees.

But that's not what they're seeking, exclusively or even mainly; and indeed this isn't a proper Rule 23(b)(2) suit. Class action lawyers like to sue under that provision because it is less demanding, in a variety of ways, than Rule 23(b)(3) suits, which usually are the only available alternative. Mark A. Perry & Rachel S. Brass, "Rule 23(b)(2) Certification of Employment Class Actions: A Return to First Principles," 65 N.Y.U. Annual Survey of Am. Law 681, 689-92 (2010); Roger H. Trangsrud, "The Adversary System and Modern Class Action Practice," 76 Geo. Wash. L.Rev. 181, 186-87 (2008). Of particular significance, "plaintiffs may attempt to shoehorn damages actions into the Rule 23(b)(2) framework, depriving class members of notice and opt-out protections. The incentives to do so are large. Plaintiffs' counsel effectively gathers clients— often thousands of clients—by a certification under (b)(2). Defendants attempting to purchase res judicata may prefer certification under (b)(2) over (b)(3)." Bolin v. Sears, Roebuck & Co., supra, 231 F.3d at 976. How far Rule 23(b)(2) can be stretched is the issue in the gigantic class action against Wal-Mart, Dukes v. Wal-Mart Stores, Inc., 603 F.3d 571, 619 (9th Cir.) (en banc), cert. granted, ___ U.S. ___, 131 S.Ct. 795, 178 L.Ed.2d 530 (2010), now before the Supreme Court. The present case is not as big a stretch, but it is big enough.

True, the only monetary relief sought is back pay; true, too—contrary to the common but erroneous notion that courts of equity can't award monetary relief—they can do so if the award is merely incidental to the grant of an injunction or declaratory relief: "incidental" in the sense of requiring only a mechanical computation. That is the "clean-up" doctrine of equity. Reich v. Continental Casualty Co., 33 F.3d 754, 756 (7th Cir.1994); Medtronic, Inc. v. Intermedics, Inc., 725 F.2d 440, 442-43 (7th Cir.1984); Mowbray v. Moseley, Hallgarten, Estabrook & Weeden, Inc., 795 F.2d 1111, 1113-14 (1st Cir.1986). In such a case, to make the class representative bring a second suit, for damages, on top of his injunctive action would create pointless redundancy. In re Allstate Ins. Co., 400 F.3d 505, 507 (7th Cir.2005); see also Lemon v. International Union of Operating Engineers, 216 F.3d 577, 580-81 (7th Cir. 2000), and cases cited there.

The plaintiffs argue that if only equitable relief is sought, a class action suit may be maintained under Rule 23(b)(2) even if the equitable relief is mainly monetary. We disagree. See Thorn v. Jefferson-Pilot Life Ins. Co., 445 F.3d 311, 331-32 (4th Cir.2006). To read "injunctive" in the rule to mean "equitable" is to become mired in sticky questions of differentiating between "legal" and "equitable" actions—and such questions abound. See, e.g., Medtronic, Inc. v. Intermedics, Inc., supra. We can avoid the mire by recognizing that Rule 23(b)(2) class actions are limited to cases in which "final injunctive relief or corresponding declaratory relief" is appropriate, rather than extending to all cases in which any kind of equitable relief is sought. Hohider v. United Parcel Service, Inc., 574 F.3d 169, 202 (3d Cir.2009). The monetary relief sought in a case, whether denominated legal or equitable, may make the case unsuitable for Rule 23(b)(2) treatment. Kartman v. State Farm Mutual Auto. Ins. Co., 634 F.3d 883, 894-95 (7th Cir.2011); In re Allstate Ins. Co., supra, 400 F.3d at 507-08; Reeb v. Ohio Dep't of Rehabilitation & Correction, 435 F.3d 639, 651 (6th Cir.2006). As this case illustrates: calculating the amount of back pay to which the members of the class would be entitled if the plaintiffs prevailed would require 500 separate hearings. The monetary tail would be wagging the injunction dog. An injunction thus "would not provide `final' relief as required by Rule 23(b)(2). An injunction is not a final remedy if it would merely lay an evidentiary foundation for subsequent determinations of liability." Kartman v. State Farm Mutual Auto. Ins. Co., supra, 634 F.3d at 893.

It would not be enough, for example, to award all members of the class 5 percent of their earnings during the complaint period, to erase the allegedly discriminatory differential in pay between male and women employees; for if the women's salaries had been 5 percent higher from the outset, they might have received lower performance or other pay raises above their base pay. Remember that compensation is influenced by the labor market: women underpayed because of the base-pay differential would be more likely to receive a compensatory pay adjustment than if their base pay had been higher.

The claim of discrimination in promotions presents a further complication. Because Rolls-Royce does not have a fixed compensation schedule for employees in the compensation categories at issue, individualized hearings would be required to determine how much higher an employee's pay would have been had she received a promotion denied her on the ground of her sex.

The proper approach in this case would thus have been for the plaintiffs to seek class certification under Rule 23(b)(3)—which requires full notice so that class members can opt out if they want to bring an independent suit for damages or other monetary relief—but to ask for injunctive as well as monetary relief. In re Allstate Ins. Co., supra, 400 F.3d at 508; see Laura J. Hines, "Challenging the Issue Class Action End-Run," 52 Emory L.J. 709, 716-17, 741-43 (2003). It is only when the primary relief sought is injunctive, with monetary relief if sought at all mechanically computable, that elaborate notice is not required and so Rule 23(b)(2) is applicable because the claims of the class members are uniform (or as the cases sometimes say, "cohesive"). Jefferson v. Ingersoll Int'l, Inc., 195 F.3d 894, 897-99 (7th Cir.1999); Thorn v. Jefferson-Pilot Life Ins. Co., supra, 445 F.3d at 331-32; Coleman v. General Motors Acceptance Corp., 296 F.3d 443, 447-48 (6th Cir.2002); Murray v. Auslander, 244 F.3d 807, 812-13 (11th Cir.2001); Allison v. Citgo Petroleum Corp., 151 F.3d 402, 411 (5th Cir. 1998).

The plaintiffs' other attempted end run around the district judge's denial of certification is to ask us to reverse her denial of their motion to substitute two other class members for the original named plaintiffs—substitutes who might have a more typical (and, not incidentally, a stronger) claim than the original plaintiffs. Such substitution (via permissive intervention by an unnamed plaintiff, who if intervention is allowed becomes the named plaintiff and thus the class representative) is possible. See Fed.R.Civ.P. 23(d)(1)(B)(iii), 24(b); Champ v. Siegel Trading Co., 55 F.3d 269, 272-74 (7th Cir. 1995); Birmingham Steel Corp. v. TVA, 353 F.3d 1331, 1339 (11th Cir.2003); McKowan Lowe & Co. v. Jasmine, Ltd., 295 F.3d 380, 383, 389 (3d Cir.2002). But it's not automatic, and the district judge was on sound ground in ruling that the motion, filed on March 26, 2010, came too late. See Fed.R.Civ.P. 24(b)(3) ("in exercising its discretion [in deciding whether to permit intervention], the court must consider whether the intervention will unduly delay or prejudice the adjudication of the original parties' rights").

The motion was not filed until after the judge had denied class certification—and that was almost four years after the suit had begun and long after it was plain that there were substantial doubts about the typicality of the named plaintiffs' claims and the adequacy of their representation of the class. As the district judge explained, "until [the plaintiffs] secured the assistance of additional, more experienced counsel, this case progressed at an almost imperceptible pace, with Plaintiffs seeking and receiving numerous extensions of the deadlines for filing their class certification motion, to the point that the Court finally had to admonish counsel regarding their duty of diligence and to voice our concerns over the apparent limited resources being devoted to the case." 2010 WL 987484, at *13. Things sped up for a time when the plaintiffs retained a firm "with apparently much needed class action expertise and additional resources"—but the firm soon withdrew, citing irreconcilable differences with the plaintiffs' original lawyers. Id. The judge remarked that "local counsel has been in the `driver's seat' throughout the case, and has set, at best, a plodding pace." 2010 WL 1948222, at *3.

It would go too far to suggest that unless substitution for the original named plaintiffs is sought as soon as a substantial challenge to certification is made, the district judge is justified in denying it. Such a rule might involve constant interruptions of the proceeding—procedural hiccups—as nervous class action counsel tried to add new class representatives every time the defendants raised an objection to certification. But it was obvious from the outset that these named plaintiffs faced a serious challenge to their status as class representatives. And with the entire class in one location (a single plant in Indiana), class counsel had ample opportunity to sift through potential named plaintiffs before deciding on Randall and Pepmeier. Intervention shouldn't be allowed just to give class action lawyers multiple bites at the certification apple, when they have chosen, as should have been obvious from the start, patently inappropriate candidates to be the class representatives. Griffin v. Singletary, 17 F.3d 356, 359-60 (11th Cir. 1994); see also Sanford v. MemberWorks, Inc., 625 F.3d 550, 560-61 (9th Cir.2010). The judge was justified in denying the motion to intervene.

AFFIRMED.