
504 F.3d 665 (2007)
James T. SULLIVAN, et al., Plaintiffs-Appellants,
v.
WILLIAM A. RANDOLPH, INC., Defendant-Appellee.
Nos. 06-1581, 06-2994.
United States Court of Appeals, Seventh Circuit.
Argued April 6, 2007.
Decided October 5, 2007.
*666 *667 John W. Loseman (argued), Lewis, Overbeck & Furman, Chicago, IL, for Plaintiffs-Appellants.
Renee Legrand Koehler (argued), Leslie J. Johnson, Andrews, Koehler & Passarelli, Lisle, IL, for Defendant-Appellee.
Before POSNER, FLAUM, and EVANS, Circuit Judges.
POSNER, Circuit Judge.
This is a suit under ERISA and the Taft-Hartley Act by the trustees of a multiemployer pension plan for an accounting and damages. Section 515 of ERISA, 29 U.S.C. § 1145, requires an employer to make contributions to a multiemployer plan that are called for "under the terms of the plan or under the terms of a collectively bargained agreement," and section 502(g)(2) makes the employer's obligation enforceable by a suit in federal court. Since the breach of a contract between a union and an employer is actionable under section 301 of the Taft-Hartley Act, 29 U.S.C. § 185(a), the trustees were able to base their claim on this section as well as on ERISA. (The remedies under the two statutes differ somewhat. See, e.g., Laborers Health & Welfare Trust Fund for Northern California v. Advanced Lightweight Concrete Co., 484 U.S. 539, 549 n. 16, 108 S.Ct. 830, 98 L.Ed.2d 936 (1988); Zielinski v. Pabst Brewing Co., 463 F.3d 615, 617 (7th Cir.2006). That is the usual *668 incentive to claim under both. An illustration of the remedial differences is the attorneys' fee provision of ERISA, discussed later in this opinion.) The district judge granted summary judgment for the defendant and also awarded it some $56,000 in attorney's fees.
The defendant, a construction company, was surprised to be sued in respect of contributions that it was alleged to owe under a collective bargaining agreement made in 2000 between local 130 of the technical engineers' union and the Lake County Contractors Association, to which the defendant belongs. The defendant had not employed any workers represented by the union since 1997, and while it had subcontracted some work to such workers, the collective bargaining agreement states that subcontractors are not employees for whom contributions to the multi-employer pension fund must be made.
Although the contractors association bargains collectively on behalf of its members with the various construction unions, the agreements it negotiates must be accepted by a member to be enforceable against him. Moriarty v. Pepper, 256 F.3d 554, 556-59 (7th Cir.2001); Trustees of UIU Health & Welfare Fund v. New York Flame Proofing Co., 828 F.2d 79, 82-83 (2d Cir.1987); Bennion v. NLRB, 764 F.2d 739, 742 (10th Cir.1985). Since the defendant had rarely employed workers represented by the union in 1997, none since, and before that none since a four-month period in 1977, it had little incentive to sign the 2000 agreement, and it did not sign it. The plaintiffs argue that it manifested acceptance by a "course of conduct." If you behave in a way that you would not have done had you not thought you were bound on a contractsuch as by making the payments called for by itthe fact that you omitted to sign it will not allow you to deny that you are bound. Bricklayers Local 21 of Illinois Apprenticeship & Training Program v. Banner Restoration, Inc., 385 F.3d 761, 766-69 (7th Cir.2004); Moriarty v. Larry G. Lewis Funeral Directors Ltd., 150 F.3d 773, 777 (7th Cir. 1998); Southern California Painters & Allied Trade Dist. Council No. 36 v. Best Interiors, Inc., 359 F.3d 1127, 1133 (9th Cir.2004); Brown v. C. Volante Corp., 194 F.3d 351, 355 (2d Cir.1999); NLRB v. Haberman Construction Co., 641 F.2d 351, 356 (5th Cir.1981). Actions can speak as loud as words. That is a general principle of contract law rather than anything special to collective bargaining agreements. "An agreement implied in fact is `founded upon a meeting of minds, which, although not embodied in an express contract, is inferred, as a fact, from conduct of the parties showing, in the light of the surrounding circumstances, their tacit understanding.'" Hercules Inc. v. United States, 516 U.S. 417, 424, 116 S.Ct. 981, 134 L.Ed.2d 47 (1996), quoting Baltimore & Ohio R.R. v. United States, 261 U.S. 592, 597, 58 Ct.Cl. 709, 43 S.Ct. 425, 67 L.Ed. 816 (1923).
But the only "course of conduct" evidence in this case is that after 1997, though no longer employing anyone represented by the union, the defendant continued filing the monthly contribution reports required by the collective bargaining agreements negotiated by the contractors association. Of course in each report it put "0" in the space for the amount of contributions due. There is no evidence to contradict its contention that the continued filing of the reports was a clerical oversight rather than a manifestation of consent to be bound by successor agreements. There is no contention that the filing of the monthly reports induced reliance on the part of the pension fund that might estop the defendant to deny that it was a party to the 2000 agreement or that the filing of *669 the reports conferred any benefit on the defendant. It would be different if instead of just filing a report the defendant had made contributions. Paying money over a period of years is less likely to be the result of a mistake than filing a report that denies any obligation to pay.
The only complication is that in its initial answer to the complaint the defendant admitted that it was bound by the 2000 agreement. It was later permitted by the district court to file an amended answer in which it withdrew the concession. An admission made in a pleading is a "judicial admission," and ordinarily is binding. Murrey v. United States, 73 F.3d 1448, 1455 (7th Cir.1996); Higgins v. Mississippi, 217 F.3d 951, 954-55 (7th Cir. 2000); Bright v. QSP, Inc., 20 F.3d 1300, 1305 (4th Cir.1994). But the fact that it is binding unless withdrawn does not prevent its being withdrawn, if the judge allows the filing of an amended pleading, Fed. R.Civ.P. 15(a), unless withdrawal would work a hardship on the opposing party. E.g., Quintanilla v. Texas Television Inc., 139 F.3d 494 (5th Cir.1998). There is nothing to suggest that the initial admission was anything other than an error, like the filing of the monthly contribution forms. If the error put the plaintiffs to additional expense, they would be entitled to compensation, Mid Valley Bank v. North Valley Bank, 764 F.Supp. 1377, 1390-91 (E.D.Cal.1991), or perhaps other relief, but they did not seek any.
The plaintiffs argue that the withdrawal of the admission caught them unawares and as a result they were unable to complete discovery to determine whether the defendant was bound by the 2000 agreement before the judge ruled on summary judgment. They had asked the judge to extend the deadline for completion of discovery, but he had refused. If that was an error, it was harmless. For by the time the plaintiffs filed their summary-judgment brief, they had discovered that the defendant had since 2000 employed as subcontractors workers represented by the union and that if contributions were due for them the defendant owed the pension fund some $31,000. The defendant denied liability not only because it was not a party to the agreement but also because of the agreement's exclusion of subcontractors. If the judge was correct that even if the defendant was a party to the 2000 agreement it was nevertheless sheltered from having to make contributions by the subcontractor exclusion, it is irrelevant whether the defendant was a party to the agreement. And the judge was correct, because subcontractors are excluded. The plaintiffs contend, it is true, that another agreement between the union and the contractors association (they call this the Standard Agreement) narrowed the subcontractor exclusion. But since the defendant did not sign or even know of the Standard Agreement, it was not bound by that agreement either.
The plaintiffs complain that the defendant failed to produce the documents they needed in order to be able to determine the subcontractors' status. If the defendant refused a proper discovery request, the plaintiffs could have moved the district judge for an order compelling production, and they didn't do that.
They also argue that the investigation which they conducted after filing their complaint to determine what the defendant owed placed on the defendant the burden of proving that the subcontractors were not covered by the multiemployer plan. We do not understand the argument. The "postcomplaint audit" as they call it was premised on their belief that the Standard Agreement had brought subcontractors under the plan, and we have seen that the *670 defendant was not bound by that agreement.
So the appeal has no merit. But the postcomplaint audit remains pertinent to whether the district judge committed a reversible error in awarding attorneys' fees to the defendant. The plaintiffs argue that they had to sue just to be able to discover whether the defendant owed contributions, because the defendant had refused to cooperate in their request for a precomplaint audit; so if the suit lacked a substantial justification, it is the defendant's fault.
One cannot sue, without courting sanctions, unless one has grounds to believe that one has been injured by a wrong committed by the person one wants to sue. So what is a prospective plaintiff to do when the prospective defendant takes steps to thwart a precomplaint investigation essential to determining whether there are grounds? We need not worry the question in this case, because both the collective bargaining agreement that the plaintiffs think the defendant a party to, and ERISA itself, authorize the pension plan to examine the books of an employer claimed to be a signatory. Central States, Southeast & Southwest Areas Pension Fund v. Central Transport, Inc., 472 U.S. 559, 572, 105 S.Ct. 2833, 86 L.Ed.2d 447 (1985). If an employer refuses, the plan can seek an order from a federal district court under the same provisions of ERISA and Taft-Hartley that authorize a suit for contributions. Id. at 563-64 and n. 4, 105 S.Ct. 2833; Northwestern Ohio Administrators, Inc. v. Walcher & Fox, Inc., 270 F.3d 1018, 1023 (6th Cir.2001). The plaintiffs did not follow that route. But more fundamentally, they presented no evidence that the defendant refused to permit a precomplaint audit. They have confused assertion with evidence.
ERISA authorizes the award of a reasonable attorney's fee to the prevailing party. 29 U.S.C. § 1132(g)(2). In Bittner v. Sadoff & Rudoy Industries, 728 F.2d 820, 828-30 (7th Cir.1984), we held that either partyplaintiff or defendantwho prevails is entitled to such an award unless the loser's position, though unsuccessful, had substantial justification. This is a departure from the common approach to the interpretation of fee-shifting statutes, which creates a presumption in favor of awarding fees to a prevailing plaintiff but allows fees to be awarded to a prevailing defendant only if the suit was frivolous. Independent Federation of Flight Attendants v. Zipes, 491 U.S. 754, 760, 109 S.Ct. 2732, 105 L.Ed.2d 639 (1989); Hensley v. Eckerhart, 461 U.S. 424, 429 and n. 2, 103 S.Ct. 1933, 76 L.Ed.2d 40 (1983). That asymmetry, emphasized in civil rights cases, is defended by reference to the disparity in resources in the typical litigation governed by a fee-shifting statute and to a belief that the usual purpose of fee shifting is to make it easier for plaintiffs to obtain relief. Id. at 429, 103 S.Ct. 1933; Newman v. Piggie Park Enterprises, Inc., 390 U.S. 400, 401-02, 88 S.Ct. 964, 19 L.Ed.2d 1263 (1968) (per curiam). Neither consideration is present when a pension or welfare fund is suing an employer without substantial justification, in this case because of the fund's failure to conduct an adequate precomplaint investigation. The presumption of the civil rights cases has therefore been rejected for ERISA by most courts (see the helpful summary in Martin v. Arkansas Blue Cross and Blue Shield, 299 F.3d 966, 969-72 (8th Cir. 2002); see also Carolina Care Plan Inc. v. McKenzie, 467 F.3d 383, 390 (4th Cir. 2006); Moore v. LaFayette Life Ins. Co., 458 F.3d 416, 440-41 (6th Cir.2006); Janeiro v. Urological Surgery Professional Ass'n, 457 F.3d 130, 143-44 (1st Cir.2006); Brown v. Aventis Pharmaceuticals, Inc., *671 341 F.3d 822, 828 (8th Cir.2003))  including, of course, ours. E.g., Lowe v. McGraw-Hill Cos., 361 F.3d 335, 339 (7th Cir.2004); Perlman v. Swiss Bank Corp. Comprehensive Disability Protection Plan, 195 F.3d 975, 980 (7th Cir.1999); Bittner v. Sadoff & Rudoy Industries, supra, 728 F.2d at 829.
Bittner's simple test of substantial justification was offered as an alternative to, rather than a substitute for, the "five factor" test theretofore applied to fee-shifting issues under ERISA and described in Bittner as follows:

Janowski v. International Brotherhood of Teamsters, 673 F.2d 931, 940 (7th Cir.1982), vacated on other grounds, is illustrative of a number of cases that list five factors for a district judge to consider in evaluating a fee request under section 1132(g)(1): "(1) the degree of the offending parties' culpability or bad faith; (2) the degree of the ability of the offending parties to satisfy personally an award of attorneys' fees; (3) whether or not an award of attorneys' fees against the offending parties would deter other persons acting under similar circumstances; (4) the amount of benefit conferred on members of the pension plan as a whole; and (5) the relative merits of the parties' positions."
728 F.2d at 828-29. The five-factor test continues to be intoned in this circuit, often in conjunction with the Bittner test. E.g., Lowe v. McGraw-Hill Cos., supra, 361 F.3d at 339. Two tests to govern the same issue might well seemeven though they are not inconsistentone too many, Eddy v. Colonial Life Ins. Co. of America, 59 F.3d 201, 210 (D.C.Cir.1995) (dissenting opinion), especially when one is a multifactor test; such tests tend to be "redundant, incomplete, and unclear." Palmer v. City of Chicago, 806 F.2d 1316, 1318 (7th Cir. 1986); see also Exacto Spring Corp. v. Commissioner, 196 F.3d 833, 834 (7th Cir. 1999); Stevens v. Tillman, 855 F.2d 394, 399-400 (7th Cir.1988). Consider: Factor 1 (bad faith) identifies a basis for awarding (or refusing to award) attorneys' fees that owes nothing to the fee-shifting provision of ERISA, because, as we noted in Bittner v. Sadoff & Rudoy Industries, supra, 728 F.2d at 828, courts have inherent authority to award attorney's fees as a sanction for conducting litigation in bad faith. Chambers v. NASCO, Inc., 501 U.S. 32, 46-47, 50, 111 S.Ct. 2123, 115 L.Ed.2d 27 (1991); Stive v. United States, 366 F.3d 520, 521 (7th Cir.2004); Brown v. Aventis Pharmaceuticals, Inc., 341 F.3d 822, 828 (8th Cir. 2003). Factor 2 (ability to pay) is a general point about sanctions rather than anything specific to awarding attorneys' fees; there is not much use trying to squeeze water out of a stone. And since there is federal insurance (though capped at a fairly modest level) of vested pension benefits, Nachman Corp. v. Pension Benefit Guaranty Corp., 446 U.S. 359, 375 and n. 23, 100 S.Ct. 1723, 64 L.Ed.2d 354 (1980); Lowe v. McGraw-Hill Cos., supra, 361 F.3d at 339, and since an award of attorneys' fees will rarely be big enough to affect a pension plan's solvency, rarely will there be cause for concern that an award of attorneys' fees may reduce the benefits of the innocent participants and beneficiaries of the plan.
Factor 3 (deterrence) is empty because while a practice of awarding fees to a winning party will tend to deter the filing of groundless suits and the interposing of groundless defenses to meritorious suits, whether the award of fees in a particular case will have a deterrent effect cannot be determined.
Factors 4 and 5 go to the merits of the claim or defense, and thus to the issue of substantial justification flagged by Bittner. If the ERISA plaintiff prevails, but obtains *672 meager relief, this either indicates that the defendant had a substantial justification for opposing the suit (the defendant was successful in getting the amount sought by the plaintiff cut down), or disentitles the plaintiff to a generous award because attorneys' fee awards should be proportional to the degree of success that the suit achieves. Finally, the "relative merits of the parties' positions" is an oblique way of asking whether the losing party was substantially justified in contesting his opponent's claim or defense.
At most the five-factor test is a checklist of factors for the district judge to consider to make sure he hasn't overlooked anything that might be relevant to the appropriateness or size of the award. As we put it in Lowe v. McGraw-Hill Cos., supra, 361 F.3d at 339, "the factors in the [five-factor] test are used to structure or implement, rather than to contradict, the `substantially justified' standard, described in Little v. Cox's Supermarkets, 71 F.3d 637, 644 (7th Cir.1995), as the `bottom-line' question to be answered even when the more elaborate test is used." See also Bowerman v. Wal-Mart Stores, Inc., 226 F.3d 574, 592-93 (7th Cir.2000). It adds little, though, to the simpler test, and perhaps has outlived its usefulness. American law is needlessly complex, and occasions for simplification should be embraced.
The present suit was not substantially justified, and so the judge was right to award a reasonable attorney's fee to the defendant. The plaintiffs do not contest the amount of the fee. The defendant asks us to award fees for its defense of the appeal. Although the issues discussed in this opinion are sufficiently uncertain to have justified the plaintiffs in seeking appellate review, affirmance entitles an appellee who has properly been awarded an attorney's fee in the district court to an attorney's fee for successfully defending the district court's judgment in the court of appeals. Helfrich v. Carle Clinic Ass'n, P.C., 328 F.3d 915, 919 (7th Cir.2003). Otherwise the purpose of the initial awardto shift the cost of litigation to the losing partywould be imperfectly achieved. Rickels v. City of South Bend, 33 F.3d 785, 787 (7th Cir.1994).
So the defendant is awarded his reasonable attorney's fees for defending the appeal; and the judgment for the defendant, and the award of attorneys' fees by the district court, are affirmed.
