Bowne of New York City, Inc. (BNY), Pandick Press, Inc. (Pandick), and Chas. P. Young Co. (CPY), appeal from a judgment of the United States District Court for the Southern District of New York, Owen, J., confirming an arbitrator’s award implementing Article 14, Section 7 of a collective bargaining contract, effective January 1, 1983 to October 3, 1989 (the “Contract”), between New York Typographical Union No. 6 (the “Union,”) and the Printers League Section of the Association of Graphic Arts (the “League”), a trade association representing printing employers.
We agree with the District Court that the Arbitration Award granting the Union’s request for relief was in keeping with the terms of the Contract as agreed to by the employers. The arbitrator’s explanations set forth in his fully reasoned decision rejecting appellants’ contentions as to the unfairness of the arbitration procedure was “far more than ‘a barely colorable justification for the outcome reached.’ ” Advance Publications, Inc. v. Newspaper Guild of New York Local 3, TNG, AFL-CIO, 616 F.2d 614, 618 (2d Cir.1980) (quoting Andros Compania Maritima, S.A. v. Marc Rich & Co., 579 F.2d 691, 704 (2d Cir.1978)). Contrary to appellants’ contention, appellants received notice, the arbitrator was not par*58tial, and appellants are bound by the arbitrator’s award. For reasons set forth below, we affirm the District Court’s judgment confirming the Arbitration Award.
BACKGROUND
The Union, a collective bargaining representative of employees employed in composing room work in the New York City area, and the League, the collective bargaining representative of employers in the printing and typographical industry, have engaged in a series of collective bargaining agreements, the most current of which is the one effective January 1983-October 1989. The collective bargaining agreement specifically provides that in the event a member of the League resigns from League membership, such member shall remain bound by the terms of the Contract. Although they withdrew their membership in 1987, appellants BNY, Pandick, and CPY were members of the League when the current Contract was entered into. The Contract thus covers League employers, non-League employers, as well as employers who were never members but who nonetheless agreed to be bound by its terms.
Article 14 of the Contract, entitled “Settlement of Issues,” establishes a procedure for dispute resolution. All disputes, controversies or grievances arising out of any provision in the Contract are to be settled by arbitration before a Designated Arbitrator or an Alternate Designated Arbitrator selected by mutual agreement between the League and the Union.
Sections 6 and 7 of Article 14 set forth the manner in which administrative expenses incurred during arbitration are to be handled. Administrative expenses contemplated under Section 6(A) are expenses incurred “in the form of fees and expenses in the selection of a Designated Arbitrator and in the form of the fees and expenses of the Designated Arbitrator.” Under Section 6(B), these expenses are to be “shared equally” between the Union and the League. With regard to employers who are not League members, Section 7 provides that they are to pay seven dollars per employee per month into a special joint account, entitled the “Typographical Union No. 6 — Printers League Joint Administrative Account,” to be used to defray the Section 6(A) expenses for which the League and the Union would otherwise be liable.
However, because the Union and the non-League employers who engaged in arbitration effectively ignored payment provisions set forth in Section 7 and instead simply paid their half of the cost of arbitration, the joint account was never established. This practice occurred from 1983 until 1987, during which time appellants were League members.1
In or about October 1987, BNY, no longer a League member, together with another non-League employer, became embroiled in lengthy arbitration proceedings with the Union. BNY refused to accede to the Union’s demand that, in accordance with consistent past practice, it pays its pro-rata share in fees and expenses incurred during arbitration. BNY, instead, contended that Section 7 of Article 14 of the Contract established the exclusive means by which a non-League employer could be made responsible for arbitration-related payments, that is, its obligation as a non-League employer consisted solely of contributions into a joint account of deposits of seven dollars per employee per month. By letter dated November 19, 1987, BNY informed the Designated Arbitrator that, subject to acceptance of its proposal by both the League and the Union, arbitration-related fees and expenses incurred subsequent to its withdrawal from the League would be paid by it directly, so long as such expenses are capped by its own Section 7 share of costs.
Because of BNY’s rejection of past practice and because of the League’s refusal to pay for the cost of arbitrations which do not involve its members, the Designated Arbitrator suspended completion of arbitration hearings or commencement of addi*59tional hearings until such time as payment was received. By letter dated March 11, 1988, the Union, which had paid its shares of the fees, moved for arbitration before the Alternate Designated Arbitrator, Thomas Knowlton, to implement and enforce Section 7, as set forth in its collective bargaining agreement with the League. The Union also sent a copy of the March 11 letter to all non-League employers inviting them to attend the hearing.
The Arbitration Hearing
At the arbitration hearing, the Union sought an order requiring full payment to the fund from all non-League members, including BNY, Pandick and CPY. The Union also waived its entitlement to joint control of these monies, and proposed that the Section 7 fund be used solely to defray non-League employers’ arbitration costs.2
All three appellants were present at the hearing, which was held on March 21, 1988. Pandick and CPY requested an adjournment of the hearing, citing short notice and lack of adequate time to prepare a response to the issues raised. Their requests were denied. In addition, Pandick objected to implementing Section 7 and instead urged continued adherence to the past practice of direct payment to the arbitrator of each non-League employers’ respective share. BNY, by contrast, continued to argue that its obligation could not exceed the level of contribution delineated in Section 7. The League stated that while it would not cover non-League employers’ arbitration expenses, it would not object to establishing a Section 7 fund for that purpose if so ordered by the arbitrator. After the hearing, BNY, Pandick and the Union submitted briefs to the arbitrator, setting forth in writing the respective positions they had espoused at the hearing.
On May 16, 1988, Arbitrator Knowlton issued his Opinion and Award. The arbitrator noted the various objections raised by appellants, for example, CPY’s objection of inadequate notice and BNY’s contention that arbitration was not justified because no dispute existed between the League and the Union. The arbitrator then proceeded to reject appellants’ objections, finding that the Union’s proposed “modifications” were appropriate because the Union was entitled to request a waiver of its full rights as set forth in the collective bargaining agreement. On that basis, the arbitrator issued his Arbitration Award requiring the establishment of a Special Bank Account under the administration of the League for the purpose of covering non-League employers’ shares of fees and expenses incurred in arbitration.
District Court Proceedings
The non-League employers’ failure to fully comply with the Arbitration Award caused the Union to file a verified petition with the District Court on or about July 18, 1988. Pandick and BNY opposed the petition on the grounds that the Arbitration Award was inappropriate because it modified the Contract, that because there had been no dispute between the Union and the League, the Arbitration Award was in essence a product of a sham arbitration, and thereby violated 29 U.S.C. § 158(b)(1)(B) of the National Labor Relations Act. Further objections concerning the adequacy of notice and the alleged partiality of the arbitrator were also raised. BNY in particular contended that the Arbitration Award should not be confirmed because of “evident partiality,” 9 U.S.C. § 10(b), on the part of Arbitrator Knowlton, whom BNY contended had a personal financial stake in the matter before him.
On October 26, 1988, the District Court issued an endorsed memorandum confirming the Arbitration Award, stating that “[respondents’ objections to this ruling do not come within the very narrow statutory grounds for refusing to confirm an award: fraud, partiality, or fundamental defect in the arbitration procedure.” New York Typographical Union No. 6 v. Printers League, et al., 88 Civ. 5001 (S.D.N.Y. October 26, 1988). The court also found that “any defect in notice to the employers was inconsequential,” that “the employers’ obligations arise not from any arbitration *60award, but from the terms of the Agreement that each employer signed,” and finally that “the employers’ objection to the alleged ‘modification,’ which lets the League alone administer the fund, seems nothing more than a strange strategy to force the Union to commit an unfair labor practice, when it is clear that the Union has no desire to do so.” Id.
DISCUSSION
Alleged Modifications of the Contract
It is well-settled that “[a]n arbitrator’s decision is entitled to substantial deference, and the arbitrator need only explicate his reasoning under the contract ‘in terms that offer even a barely colorable justification for the outcome reached’ in order to withstand judicial scrutiny.” In re Marine Pollution Service, Inc., 857 F.2d 91, 94 (2d Cir.1988) (citation omitted). However, where “it is clear that the arbitrator ‘must have based his award on some body of thought, or feeling, or policy, or law that is outside the contract (and not incorporated in it by reference, either ...),’ the arbitrator has failed to draw the award from the essence of the collective bargaining agreement.” Id. (quoting Ethyl Corp. v. United Steelworkers, 768 F.2d 180, 184-85 (7th Cir.1985), cert. denied, 475 U.S. 1010, 106 S.Ct. 1184, 89 L.Ed.2d 300 (1986)) (emphasis in original) (citation omitted).
In the instant case, the Arbitration Award is clearly in keeping with the objective underlying Section 7 of the Contract mandating the creation of a fund for the payment of non-League employers’ fees and costs of arbitration. Confronted with the facts as set forth before him — that is, with BNY’s refusal to adhere to the past practice of directly paying for its portion of his fee, as well as the League’s disclaimer of liability for non-League employers’ expenses — the arbitrator deemed that a genuine dispute existed which required prompt resolution. Although he recognized some merit in appellant Pandick’s argument against deviation from established past practice, he also took note of Section 67 of Part VI of the Contract, which explicitly stated that “[n]o precedents or previous conditions, rules or agreements shall be recognized in any way, or affect or modify this Contract.”
The Arbitration Award has not altered the rights and responsibilities of appellants as set forth in the collective bargaining agreement. Under the Arbitration Award, non-League employers’ obligations consisted of pooling monthly contributions into a fund from which they could draw to offset fees and expenses incurred in arbitration. The only difference is that the Union has waived its right to use such fund to reduce its own obligations under Section 6(B) so that the Union will now be entirely responsible for its own share of arbitration expenses. Non-League employers who will suffer no financial impact other than that originally contemplated by a contract to which they themselves were signatories are simply not in a position to object to the illegality of a provision which has been waived by the Union. Having waived the provision entitling it to draw from the fund’s monies, it is no longer necessary for the account to be jointly held by the Union and the League, as originally provided under Section 7. Because the “arbitrator’s decision concerns construction of the contract,” United Steelworkers of America v. Enterprise Wheel and Car Corp., 363 U.S. 593, 599, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960), the “arbitration award will not be vacated ... even if the arbitrator’s interpretation of the contract is clearly erroneous ...,” Meyers v. Parex, Inc., 689 F.2d 17, 18 (2d Cir.1982) (citation omitted), so long as such award is explained “in terms that offer even a barely colorable justification for the outcome reached.” Andros Compania Maritima, S.A. v. Marc Rich & Co., 579 F.2d 691, 704 (2d Cir.1978).
Moreover, the Union’s proposal was designed to prevent any possible violation of Section 302 of the Taft-Hartley Act, 29 U.S.C. § 186, which prohibits an employer from paying “any money or other thing of value,” 29 U.S.C. § 186(a), to “any labor organization,” 29 U.S.C. § 186(a)(2), unless excepted by specific provisions in the statute. “[M]oney or other thing of value paid to a trust fund,” 29 U.S.C. § 186(c)(5), is *61statutorily permissible provided that such fund is used for “the sole and exclusive benefit of the employees” for one or more of the purposes specified in the statute. Id. Because Section 7 as originally written contemplated the establishment of a joint account to reduce both League and Union Section 6 arbitration expenses, it ran the risk of violating 29 U.S.C. § 186. The Union’s proposal, therefore, would not only correct this possible illegality but would also be in accordance with explicit terms provided in the collective bargaining agreement. Section 77, Part VI of the Contract specifically states as follows:
To the best knowledge and belief of the League and the Union this Contract now contains no provision which is contrary to federal or state law. Should, however, any provision of this Contract, at any time during its life, be held by a court of competent jurisdiction to be in conflict with federal or state law then such provision shall continue in effect only to the extent permitted. In event of any provision of this Contract thus being held inoperative, the remaining provisions of the Contract, shall, nevertheless, remain in full force and effect.
In light of the Severance Clause contained in the Contract, and in light of Section 67 of the same Contract stating that “[n]o precedents or previous conditions ... shall modify this Contract,” we find that the District Court’s confirmance of the Arbitration Award, essentially reinstating Section 7 and discontinuing past practice, was sensible and proper.
Notice to Non-League Employers
Appellants attack the Arbitration Award by contending that they were deprived of adequate notice. The record, however, reveals that all three appellants had notice of the grievance and all three participated, or at least had the opportunity to participate, in the arbitration. BNY and Pandick even submitted post-hearing briefs to the arbitrator, and CPY, though afforded the same opportunity, chose not to file any post-hearing submissions. The mere fact that they were not officially named as parties did not prevent any of the appellants from participating in the proceedings as though they in fact were parties to the hearing. “Our review is restricted to determining whether the procedure was fundamentally unfair.” Teamsters, Chauffeurs, Warehousemen, Helpers and Food Processors, Local Union 657 v. Stanley Structures, Inc., 735 F.2d 903, 906 (5th Cir.1984). Appellants were given notice by letter dated March 11,1988. On March 21, 1988, the hearing was held. Appellants were provided with adequate “notice of the grievances ... and an opportunity to be heard. [They] thus received industrial due process.” Id. Appellants are therefore bound by the Arbitration Award interpreting the terms of the Contract.
Arbitrator Knowlton’s Alleged Partiality
Appellants’ argument that the arbitrator should have recused himself is equally without merit. The only issue was the method by which the arbitrator would be paid. The arbitrator had no personal stake in whether or not the Section 7 fund would be implemented or whether or not past practice should be continued. His decision one way or another in no way affects the amount of his fee in these or any other proceedings nor his term of employment. Cf. Pitta v. Hotel Ass’n. of New York City, Inc., 806 F.2d 419, 423 (2d Cir.1986) (“Because the subject of the arbitrable grievance directly concerns the arbitrator’s own employment for what may be an extended period of time, impermissible self-interest requires his disqualification.”). The Arbitration Award in this case does not affect whether or how much the arbitrator is to be paid but only in what manner he is to be paid under the terms of the collective bargaining agreement. There simply is no “evident partiality,” Morelite Const. Corp. v. New York City District Council Carpenters Benefit Funds, 748 F.2d 79, 84 (2d Cir.1984), that would require judicial reversal of the Arbitration Award.
CONCLUSION
For the reasons set forth above, the judgment of the District Court is affirmed.
. Appellant Pandick was a member of the League until February 17, 1987 when it withdrew by notice of withdrawal. Appellant BNY withdrew on February 9, 1987, and appellant CPY withdrew in September 1987.
. This proposal was apparently motivated by concern on the Union’s part that a joint fund would violate § 302 of the Labor Management Relations (Taft-Hartley) Act, 29 U.S.C. § 186.