This case presents a variety of appeals and cross-appeals arising out of a hybrid breach of contract/unfair representation action brought by Fletcher L. Allen (Allen) under section 301(a) of the Labor Management Relations Act, 29 U.S.C. § 185.1 Allen sought reinstatement, back pay, damages and attorney fees against his employer, Allied Plant Maintenance Company of Tennessee (Allied), his collective bargaining agent, Local 912, International Union of Operating Engineers (Local 912), and Local 912’s parent organization, the International Union of Operating Engineers, AFL-CIO (International).2
The case was tried on March 23-25,1987, without the intervention of a jury. The district court found that Allied and International had conspired to cause Allen’s discharge without just cause and to deny him fair representation by International because of his leadership in an effort to remove Local 912 and to substitute another union as bargaining agent for Allied’s employees. In particular, the court found that Allied and International agreed that Allied would fire Allen on spurious charges and then with International’s help select an arbitrator who they believed would uphold the discharge. The district court found, however, that Local 912 was only an unknowing instrument in this conspiracy and that it did not breach its duty to Allen in its handling of the grievance including the arbitration. The court then vacated the arbitration decision upholding Allen’s discharge and decided the grievance on the merits. Finding that Allied had breached the collective bargaining agreement by firing Allen without just cause and that International had breached its duty of fair representation, the court ordered Allen’s reinstatement without loss of seniority and ultimately entered judgment, jointly and severally, against Allied and International for $98,-845.60 in back pay. Allen was also awarded $26,007.25 in attorney fees and ex*294penses, jointly and severally, after the court had adjusted the hourly rate and then reduced the amount of such fees by 35%.
The parties raise several issues on appeal. Allied and International contend that the district court clearly erred in finding a conspiracy against Allen. Further, Allied and International contend that, even assuming there was such a conspiracy, the court as a matter of law should not have vacated the arbitration decision because there was no evidence and the court did not find that the arbitrator’s decision was affected by bias. International contends that the court’s finding that it breached its duty of fair representation was improper because Local 912, not International, had the primary responsibility to represent Allen in the grievance procedure including the arbitration. Allied argues that the court erred in awarding the back pay damages and attorney fees jointly and severally against Allied and International. Allen cross-appeals the district court’s finding that Local 912 was not a part of the conspiracy and that it did not breach its duty in the handling of the arbitration. Allen also appeals the court’s disallowance of punitive damages and the reduction in attorney fees.
Concluding that the district court’s findings are supported by the record and that it made no errors of law, we AFFIRM.
I. Factual Background
A summary of the district court’s findings, which are supported by substantial evidence, are as follows.
Allen was an employee of Allied from 1975 until his discharge on July 11, 1984. Allied performed maintenance and janitorial services for Bridgestone Tire and Rubber Company at its plant at LaVergne, Tennessee. Local 912 was the collective bargaining representative of the maintenance and janitorial employees under a contract with Allied. Allen was a member of International and Local 912, as well as chairman of the Allied Workers Committee (AWC), a group of Allied employees who were dissatisfied with the allegedly meek representation by Local 912 and sought to replace Local 912 as the collective bargaining representative for Allied’s employees at Bridgestone’s plant. It was Allen’s hope that AWC would become a local of United Rubber Workers which represented the production workers at Bridgestone. AWC’s decertification activities culminated on June 5, 1984, with the filing of a section 301 action against Local 912 and Allied, in which Allen was the first named plaintiff.
On July 11, 1984, Allied discharged Allen for the theft of company property and insubordination for allegedly using a Bridge-stone photocopying machine in disregard of previous warnings not to use the machine. This discharge was done pursuant to the conspiracy between Allied and International to get rid of Allen. Allen claimed that the photocopying machine, which he had used previously for AWC business, not only belonged to Bridgestone but that he had Bridgestone’s permission to use it. He contended that he had not actually used it on the day he was discharged for doing so. He further claimed that other employees had previously used the photocopier. Finally, Allen contended that Allied discharged him, as it had conspired with International to do, in retaliation for his decerti-fication activities with AWC. It was stipulated that there was no prior adverse action or information in Allen’s file.
Local 912 thereafter instituted grievance proceedings as provided for in the collective bargaining agreement. The agreement provided for a four step grievance process followed by a final step of arbitration. International’s participation was called for only at the fourth step of the process. The first two steps of Allen’s grievance did not resolve the dispute. The third step then took place on August 9, 1984 without resolution. Prior to the fourth step of the grievance procedure, Bennie Splain, field representative of the International, and Charles King, a labor relations official of Allied’s parent corporation, had agreed that N.L. Scanlon would be chosen as arbitrator because of King’s information that Scanlon would likely dismiss the grievance and decide in favor of Allied. To this end King, in his letter to the Federal Mediation and Conciliation Ser*295vice (FMCS), a show copy of which was received by Splain, requested that Scanlon be included on the list of five possible arbitrators since “both sides” had so agreed.
At the fourth step meeting on September 19, 1984, Allied refused to change its decision as to Allen’s discharge. Thereupon, a list of arbitrators supplied by FMCS, which included Scanlon, was already available in that it had been received by King and Splain as had been requested by King. Representatives of Allied struck two names from the list and left the room. Then Splain and representatives of Local 912 considered the remaining three names. Splain gave adverse information about the two persons remaining on the list other than Scanlon so that representatives of Local 912 struck these two names. As a result, Scanlon was chosen as arbitrator. Thus King, with the cooperation of Splain, was allowed to have Scanlon, whom King considered (as he testified) to be a “ringer,” to arbitrate Allen’s discharge.
Representatives of Local 912 were not a part of the conspiracy to get rid of Allen and to select an arbitrator who would be favorable to Allied’s position. Nor did Local 912 breach its duty of fair representation in the manner in which it prepared for and conducted the arbitration proceeding in Allen’s behalf.
The arbitration hearing was then conducted. In upholding Allen’s discharge, arbitrator Scanlon found that Allen had been willfully insubordinate and had committed theft of company property by his use of the Bridgestone photocopier for personal business.
II. Conspiracy to fire Allen and select a biased arbitrator
Allied and International first contend that the district court’s finding of a conspiracy between them for Allied to fire Allen and then to select an arbitrator perceived as biased against Allen is clearly erroneous.
As Allied and International are contesting the district court’s finding of fact, we must apply the standard of review mandated by Fed.R.Civ.P. 52(a). Pursuant to Fed. R.Civ.P. 52(a), findings of fact by a district judge should not be reversed unless “clearly erroneous.” A finding of fact will only be clearly erroneous when, although there is evidence to support it, “the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.” Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985) (quoting United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 541-542, 92 L.Ed. 746 (1948)). When the findings rest on credibility determinations, Rule 52 demands “even greater deference to the trial court’s findings; for only the trial judge can be aware of the variations in demeanor and tone of voice that bear so heavily on the listener’s understanding of and belief in what is said.” Anderson, 470 U.S. at 575, 105 S.Ct. at 1512. The Supreme Court has stated that courts of appeal can find clear error, even in findings based on credibility determinations, in instances where documents or objective evidence contradict testimony or when a witness’ story is so internally inconsistent or implausible that it would not be believed by a reasonable factfinder. “But when a trial judge’s finding is based on his decision to credit the testimony of one of two or more witnesses, each of whom has told a coherent and facially plausible story that is not contradicted by extrinsic evidence, that finding, if not internally inconsistent, can virtually never be clear error.” Id.
Viewing the record in its entirety, we conclude that the district court did not clearly err in finding that Allied and International conspired to get rid of Allen on trumped-up charges and then to select an arbitrator perceived to be biased.3 Undis-*296putably, International and Local 912 officials were concerned about the decertification activities of AWC, the group led by Allen. Support for Allen’s effort among Local 912’s rank and file was very strong. It was not in the interest of Local 912 officials or International for Allen to succeed in AWC’s effort to displace them. In response, International dispatched field representative Splain to monitor the situation. King, labor relations representative for Allied, testified that, on the occasion of the third step in the grievance process, he met with Splain on August 9 and 10, 1984, to discuss the “employee activities” at the LaVergne plant. At trial, Splain denied that he, or any other official from International, had played any role or had any conversations concerning Allen’s grievance before International’s participation in the fourth step of the grievance process. Nonetheless, soon after his meeting with Splain, King wrote a letter to the FMCS and requested a panel of five arbitrators for the arbitration of Allen’s grievance. Significantly, the letter stated that “both sides” wished to have N.L. Scanlon of Port Arthur, Texas included on the panel of arbitrators. The letter shows that a copy was sent to Splain. Splain testified that he never saw the letter and that it was sent to the wrong address, but there was evidence that, by the fourth step meeting, Splain and the Local 912 representatives had a copy of the list of five arbitrators sent by FMCS. The court concluded that Splain had received his copy of King’s letter to FMCS and that he had been sent the list by FMCS as a result of King’s letter to FMCS.4 Upon questioning by the court, King testified that Scanlon was chosen because King had reason to believe that Scan-lon would rule against Allen in the case. King had selected Scanlon in five previous cases and had won three out of the five. Further, King agreed with the court that Scanlon was a “ringer” and that the outcome of events was that Allied succeeded in getting its “ringer.” Tony Beckelheimer, a Local 912 official, testified that, before the fourth step, he telephoned Tony Petrolonis, an Allied official in New York, who said that both sides had met and already agreed on Scanlon as arbitrator. Beekelheimér also testified that Splain was present at the official selection of Scanlon and influenced Local 912’s decision by giving unfavorable information to Local 912 representatives about the other potential arbitrators. Splain denied these allegations.
We therefore find there was ample evidence to support the finding that Allied and International conspired to get rid of Allen and to choose an arbitrator who would likely dismiss Allen’s grievance.
III. Local 912 as not part of the conspiracy
Allen cross-appeals the district court’s finding to the extent that Local 912 was not included as a co-conspirator with Allied and International. The district court did not believe that Local 912’s involvement rose to the level of a co-conspirator. As the court stated, “LOCAL was an instrumentality of the INTERNATIONAL but *297not a conscious member of the conspiracy, because the evidence indicates that KIN-CADE and WRIGHT [business managers of the Local] were not aware of the full implications of SPLAIN’s activities [on behalf of International] (footnote omitted).” JA at 55-56. Again, we affirm the court’s factual finding concerning the existence of a conspiracy and the reach of that conspiracy. While this is a close call, we believe the court should be affirmed as not being clearly erroneous.
IV. Local 912 as not breaching its duty of fair representation
Allen also cross-appeals the district court’s finding that Local 912 did not violate its duty of fair representation in preparing for and presenting Allen’s case at the arbitration hearing. A breach of a union’s duty of fair representation occurs when its conduct toward a member of the collective bargaining unit it represents is arbitrary, discriminatory, or in bad faith. Vaca v. Sipes, 386 U.S. 171, 190, 87 S.Ct. 903, 916, 17 L.Ed.2d 842 (1967); Ruzicka v. General Motors Corp., 523 F.2d 306, 309 (6th Cir.1975). Mere negligence or mistaken judgment does not breach a union’s duty of fair representation. Poole v. Budd Co., 706 F.2d 181, 183 (6th Cir.1983). The district court found that, on the whole, Local 912’s representation of Allen was at most negligent and represented bad judgment. In its view, however, the evidence was not sufficient to show that Local 912 acted arbitrarily or in bad faith. JA at 50. Upon review, while again this is a close call, we do not believe this finding is clearly erroneous.
V. International’s breach of its duty of fair representation
International contends that it could not be guilty of a breach of duty of fair representation of Allen since, as the district court found, Local 912 did not breach its duty of fair representation. This would be true if International played no part in the grievance procedure. Ruzicka v. General Motors Corp., 523 F.2d 306, 309 (6th Cir.1975). Here, however, under the terms of the collective bargaining contract, International participated at the fourth step of the grievance procedure; and, through Splain, it actually participated in the selection of the arbitrator. Moreover, the denial of fair representation to Allen was not in the preparation for and the representation of Allen at the arbitration hearing but was in the selection of the arbitrator. Accordingly, we believe the district court was correct in its determination that International could be guilty of violating its duty of fair representation of Allen even though it found that Local 912 was not guilty.
VI.Vacating the arbitrator’s award and deciding de novo on merits.
Allied and International contend that, even if they did carry out a conspiracy the purpose of which was the discharge of Allen on spurious grounds and the selection of an arbitrator who they believed would likely sustain the discharge, the district court erred in setting aside the arbi-tral decision because there was no evidence and the court did not find that the decision of the arbitrator was actually affected by bias.5
In Hines v. Anchor Motor Freight, Inc., 424 U.S. 554, 96 S.Ct. 1048, 47 L.Ed.2d 231 (1976), the Court held that where a union breaches its duty of fair representation of an employee in an arbitration, a court may set aside the arbitral decision if it determines that the union’s breach of duty contributed to the erroneous outcome of the arbitration. As the Court stated: “[W]here the union actually utilizes the grievance and arbitration procedures on behalf of the employee, the focus is no longer on the reasons for the union’s failure to act but on whether, contrary to the arbitrator’s decision, the employer breached the contract and whether there is substantial reason to believe that a union breach of duty contributed to the erroneous outcome of *298the contractual proceedings.” 424 U.S. at 568, 96 S.Ct. at 1058 (emphasis added).
Following Hines, this court decided Wood v. International Brotherhood of Teamsters, 807 F.2d 493 (6th Cir.1986), cert. denied., 483 U.S. 1006, 107 S.Ct. 3232, 97 L.Ed.2d 738 (1987), in which a district court decision setting aside an arbitration ruling was reversed on the ground that the evidence did not show that any failure by the union to fairly represent the employees at the arbitration hearing affected the outcome of the proceeding. At the arbitral hearing, the employees were represented by their own counsel as well as by their union representatives. Thus, this court said, the arbitration decision must stand because the employees had not shown that the decision was “tainted” by the conduct of the union representatives at the hearing. Relying primarily on Wood, Allied and International contend that, in the absence of proof that the arbitral decision was affected by bias of the arbitrator, the decision must stand.
We do not agree. Implicit in the doctrine of Hines and Wood — that the arbitral decision should not be set aside unless the breach of duty of fair representation by the union affected the outcome — is the assumption that the employer is innocent of wrongdoing. For if the employer is innocent, it would simply be unfair to the employer to set aside the arbitral decision, even if erroneous, unless the union’s breach of duty affected the outcome. But where, as here, the proof showed that Allied and International acted jointly to procure an arbitrator who they thought would be biased against Allen, it is simple fairness to set aside the arbitration decision even in the absence of a finding of bias of the arbitrator. Here it can fairly be concluded that International’s joining with Allied to defeat the claim of International’s dues-paying member “tainted” the arbitral proceeding whether or not they were successful in obtaining a biased arbitrator.
Accordingly, we conclude that the district court did not err in its determination that the arbitral decision should be set aside. Moreover, Allied and International do not contend that, having set aside that decision, the district court did not have the discretion to make the plenary decision on the issue of unjust discharge of Allen de novo rather than order another arbitration. Furthermore, they do not contend that the court’s decision that Allen was unjustly discharged is not based on substantial evidence.
VII. Joint and Several Apportionment of Damages and Attorney Fees
Allied challenges the court’s determination that it should be jointly and severally liable along with International for damages and attorney fees. It asserts that the usual practice in section 301 cases is to apportion liability between the employer and the union according to the damage caused by the wrongdoing of each. In addition, Allied argues that only International should be responsible for Allen’s attorney fees, as such fees are directly associated with a union’s failure to fairly represent the grievant in arbitration.
The district court recognized the usual apportionment of damages as argued by Allied in section 301 cases but emphasized the difference from the usual facts involved here. As it reasoned:
Ordinarily, joint and several liability would not be appropriate. But when, as here, an employer and a union have colluded to effect a firing in violation of the collective bargaining agreement and to attempt to prevent the employee from receiving an impartial arbitration of his grievance, it is appropriate to impose joint and several liability upon both for damages the employee suffers both before and after the point when an impartial arbitration proceeding would have cured the breach of contract that resulted from the firing.
JA at 58. Similarly, it reasoned that joint and several liability for attorney fees was proper since these parties conspired to have Allen fired on spurious grounds and sought to deny him a fair hearing.
On review, we agree with the district court’s apportionment of damages and attorney fees in this case. See Bowen v. *299United States Postal Serv., 459 U.S. 212, 223 n. 11, 103 S.Ct. 588, 595 n. 11, 74 L.Ed.2d 402 (1983) (In discussing the usual allocation of damages in section 301 actions, the Court noted “that this is not a situation in which either the union or the employer has participated in the other’s breach.”); Vaca v. Sipes, 386 U.S. 171, 197 n. 18, 87 S.Ct. 903, 920 n. 18, 17 L.Ed.2d 842 (1967) (“Since the Union played no part in Swift’s alleged breach of contract and since Swift took no part in the Union’s alleged breach of duty, joint liability for either wrong would be unwarranted.”) Because this case presents the unusual situation in which an employer has participated in the union’s breach of duty, we believe joint and several liability is proper.
VIII. Punitive Damages; Dismissal of 42 U.S.C. § 1985(2) and 29 U.S.C. § 411 claims
On cross-appeal, Allen contends that the district court erred in not allowing him to recover punitive damages. We believe the district court correctly refused to award punitive damages to Allen, considering the Supreme Court’s strong statement against awarding punitive damages in unfair representation actions. International Bhd. of Elec. Workers v. Foust, 442 U.S. 42, 99 5.Ct. 2121, 60 L.Ed.2d 698 (1979).
Hoping to find some other predicate to justify an award of punitive damages, Allen attempts on appeal to resurrect his 42 U.S.C. § 1985(2) and 29 U.S.C. § 411 claims. The district court dismissed both of these claims early on in the process at the summary judgment stage, and the two claims were not presented at trial. Allen v. Allied Plant Maintenance Co., 636 F.Supp. 1090, 1092-95, 1096-97 (M.D.Tenn.1986). It would appear that, to award punitive damages under these statutes, it would require a reversal of the grant of the motion to dismiss/summary judgment and a further taking of proof in support of these claims. In any event we believe the district court’s reasoning in dismissing both of these claims is persuasive and should be affirmed.
IX. Reduction in Attorney Pees
The district court denied Allen’s request for a fee enhancement and reduced the hourly rate to rates the district court deemed reasonable. In addition, the court reduced the amount of the award of attorney fees by 35%, reasoning that Allen was only partially successful in the case and that the amount of fees should be reduced accordingly. On cross-appeal, Allen questions the court’s 35% fee reduction.
As a general matter, the Supreme Court has emphasized that a plaintiff’s success is a critical factor in determining the proper amount of attorney fees. Hensley v. Eckerhart, 461 U.S. 424, 440, 103 S.Ct. 1933, 1943, 76 L.Ed.2d 40 (1983). As the Court observed, “Where a plaintiff has failed to prevail on a claim that is distinct in all respects from his successful claims, the hours spent on the unsuccessful claim should be excluded in considering the amount of a reasonable fee. Where a lawsuit consists of related claims, a plaintiff who has won substantial relief should not have his attorney’s fee reduced simply because the district court did not adopt each contention raised. But where the plaintiff achieved only limited success, the district court should award only that amount of fees that is reasonable in relation to the results obtained." Id. (emphasis added).
We believe that the district court in this case properly took into account Allen’s “limited success” in pursuing his many claims. The court noted that much of the services performed by Allen’s attorneys were unsuccessful. The original complaint filed by Allen included ten defendants, five causes of action,6 and a prayer for punitive damages. Allen recovered against only two defendants and only on one cause of action. Moreover, his request for punitive damages was denied.
We believe that each of the district court’s asserted reasons for reduction of *300attorney fees was proper under the Supreme Court’s decision in Hensley. See Cabrales v. County of Los Angeles, 864 F.2d 1454, 1466 (9th Cir.1988), vac’d on other grounds, — U.S. -, 109 S.Ct. 2425, 104 L.Ed.2d 982 (1989) (25% reduction in attorney fees not abuse of discretion based on plaintiffs lack of success in its claims against 20 or more individual sheriff’s deputies, even though those claims were related to plaintiff’s successful claims against the county and jail commander); Popham v. City of Kennesaw, 820 F.2d 1570, 1578-82 (11th Cir.1987) (66.7% reduction in attorney fees not an abuse of discretion under Hensley where plaintiff only recovered on one out of eight related claims against the individual defendants and did not recover at all against city; plaintiff’s lack of success as to punitive damages also a relevant factor); Spanish Action Comm. of Chicago v. City of Chicago, 811 F.2d 1129, 1135 (7th Cir.1987) (plaintiff’s failure to prevail on punitive damage claims was “important” factor to be considered in determining whether total number of attorney hours expended was reasonable). Accordingly, we affirm the district court’s 35% reduction as not being an abuse of discretion.
X. Conclusion
After reviewing the many issues presented in this case, we are convinced that the district court made the correct decision on all contested issues. Finding no reason to reverse its decision in this case, we AFFIRM.
. In a hybrid suit under section 301 of the Labor Management Relations Act, 29 U.S.C. § 185, to recover against either the company or the union, an employee must show that the company breached the collective bargaining agreement and that the union breached its duty of fair representation. Hines v. Anchor Motor Freight, Inc., 424 U.S. 554, 570-71, 96 S.Ct. 1048, 1059, 47 L.Ed.2d 231 (1976). Unless the employee demonstrates both violations, he cannot succeed against either party.
. Allen also brought actions under 42 U.S.C. § 1985(2), section 7 of the National Labor Relations Act, 29 U.S.C. § 157, section 101 of the Labor Management Reporting and Disclosure Act, 29 U.S.C. § 411, and for treble damages under Tenn.Code Ann. § 47-50-109. All claims except the section 301 claim were dismissed by the district court prior to trial. See Allen v. Allied Plant Maintenance Co., 636 F.Supp. 1090 (M.D.Tenn.1986).
. International contests the burden of proof employed by the district court in finding a conspiracy in this case. International argues that United Mine Workers v. Gibbs, 383 U.S. 715, 86 S.Ct. 1130, 16 L.Ed.2d 218 (1966), requires that evidence of a conspiracy involving unions must be established by "clear proof,” which the Supreme Court has construed to require at least "clear, unequivocal, and convincing proof of participation, authorization, or ratification of the con*296spiracy." Id. at 737, 86 S.Ct. at 1144. The district court held that the Gibbs rule was inapplicable and instead applied the usual preponderance of the evidence standard in determining whether there was a conspiracy. In its view, the application of the higher “clear proof” standard was limited to cases involving an “association or organization participating or interested in a ‘labor dispute.'" 29 U.S.C. § 106 (emphasis added). The court questioned whether this case fell within the statutory definition of “labor dispute.” Alternatively, it interpreted Gibbs as being "limited to the issue of whether a principal in a labor dispute is to be liable for the acts of its agent, not to the issue of whether the alleged conspiratorial acts occurred.” JA at 56 n. 1.
We agree with the district court’s analysis as to the scope of Gibbs. See Ramsey v. United Mine Workers, 401 U.S. 302, 311, 91 S.Ct. 658, 664, 28 L.Ed.2d 64 (1971); Fleming Bldg. Co. v. Northeastern Okla. Bldg. & Const. Trades Council, 532 F.2d 162, 164 (10th Cir.1976). As a result, we believe that the district court used the correct burden of proof by requiring that Allen prove the alleged conspiratorial acts by a preponderance of the evidence.
. Allied decries the district court’s use of this letter as a "smoking gun” in light of Splain’s testimony that he never saw it. We refuse to find fault with the inferences that the district court drew from this letter.
. While the district court did not find that the decision of the arbitrator was affected by bias, upon review of the decision it appears to us that it can hardly be said to be thorough and professional.
. See supra note 2. As indicated there, Allen also sued, inter alia, for treble damages for inducing a breach of contract under state law and for damages for conspiracy to obstruct justice under 42 U.S.C. § 1985(2).