Neal Stevens appeals from the district court’s enforcement of an arbitration award for $4706.26 in favor of Carpenters’ Local Union No. 1478 (the union). Stevens contends that the arbitrator’s award is inconsistent with earlier findings made by the National Labor Relations Board (the Board) in an election proceeding. We agree, and because the arbitrator’s award is contrary to applicable principles of labor law, we reverse.

I.

FACTS AND PROCEEDINGS BELOW

This case arises out of the operation of two entities: EOS Enterprises, Inc. (EOS) and Neal Stevens Contracting (NSC), a sole proprietorship. EOS commenced operations in 1975 and is engaged in the concrete construction business. It is wholly owned by Neal Stevens and his wife, Jean Stevens, and employs an average of four to seven carpenters. The union and EOS have never entered into a collective bargaining agreement. NSC also is involved in the construction business. When NSC began operations in 1977 Stevens signed a memorandum agreement with the union on behalf of NSC that incorporated the master labor agreement between the Southern California General Contractors and the United Brotherhood of Carpenters and Joiners. Apparently this was done to assure that an *1274 individual whom EOS wished to hire as a superintendent would continue to receive union fringe benefits. E.R. 45. In 1980, Stevens executed a second memorandum agreement that incorporated the 1980-83 master labor agreement. The other party to the memorandum agreements was the Southern California Conference of Carpenters, which represents the district councils and local unions of the United Brotherhood of Carpenters and Joiners in eleven southern California counties.

The memorandum agreements generally obligated NSC to comply with the terms of the master labor agreement. Paragraph 9 of the 1980-83 memorandum agreement, about which the parties in this case vigorously dispute, provides:

The master labor agreement required NSC to pay union wages and benefits to its carpenter employees and to employ union carpenters for all work performed by NSC.

On March 2, 1982, the union filed a grievance with a contract adjustment board alleging that NSC had violated provisions of the labor agreements. The grievance arose because EOS, not NSC, had employed non-union carpenters at a jobsite. However, NSC, the union’s grievance alleged, “is the alter-ego, single employer, and/or joint venture of EOS.” That is, allegedly what EOS had done was done by NSC and vice versa. The Conference of Carpenters on March 11, 1982, sent NSC a letter that noted the pending arbitration regarding “the application of the master labor agreement to EOS, a non-union entity, which is failing to comply with the terms and conditions of the master labor agreement.” This letter sought information from NSC pursuant to the National Labor Relations Act in order to proceed to arbitration on the grievance.

In response, EOS filed a petition with the Board on April 2, 1982, seeking a representation election among its carpentry employees. The Conference of Carpenters responded by filing a disclaimer of interest stating that it did not wish to represent the employees of EOS. The Regional Director, however, noted that the union had not withdrawn its March 2, 1982, grievance, and concluded that this action was tantamount to a claim that it represented a majority of the EOS employees. On September 22, 1982, the Regional Director issued his decision directing an election among the carpenters employed by EOS. Two findings underlying this decision are particularly relevant. First, he found that the carpentry workers of EOS were a separate bargaining unit from which he specifically excluded NSC’s employees. Second, he found that NSC and EOS were neither alter egos nor joint employers. The union did not seek review of these two findings. 1

Thereafter, the arbitrator, on February 18,1983, announced her decision and award in which she concluded that her jurisdiction was not affected by the earlier Board pro *1275 ceedings. She reasoned that the Regional Director “did not decide whether NSC, by virtue of its alleged relationship with EOS, violated any provisions of the Agreement between NSC and the Union.” E.R. 11 (emphasis added). Notwithstanding the previous findings of the Regional Director, the arbitrator held that NSC and EOS “have single employer, alter ego, and joint venture status vis-a-vis each other” and EOS was therefore bound to the terms of the labor agreement. E.R. 12. The failure of EOS to pay union wages and benefits to its employees was therefore equivalent to non-payment by NSC in violation of the 1980-83 memorandum agreement. The arbitrator accordingly awarded damages to-talling $4,706.26. The union sought an order in district court pursuant to section 301 of the Labor Management. Relations Act, 29 U.S.C. § 185 (a), to confirm the award. Stevens filed a complaint under section 301 to vacate the award. These actions were consolidated and the district court confirmed the award. Stevens filed a timely notice of appeal.

II.

DISCUSSION

At the outset we acknowledge that an arbitrator’s factual determinations and legal conclusions generally receive deferential review by the courts, and an award will be upheld so long as it draws its essence from the collective bargaining agreement. E.g., Broadway Cab Cooperative v. Teamsters & Chauffeurs Local Union No. 281, 710 F.2d 1379, 1382 (9th Cir.1983). Nonetheless, an arbitrator’s decision forfeits this deference if it violates law or an explicit, well-defined and dominant public policy. George Day Construction Co. v. United Brotherhood of Carpenters and Joiners, 722 F.2d 1471, 1477 (9th Cir.1984); see Broadway Cab, 710 F.2d at 1382-85 (reversing award that contradicted Supreme Court precedent and applied incorrect legal standard). Here the arbitrator’s award is inconsistent with previous Board findings involving the same parties. Under these circumstances we need not defer and we hold that the district court erred in confirming the award.

A. “Double-Breasted” Operations In General.

This case concerns the circumstances in which the terms of a labor agreement with a signatory company can be applied to employees of a nonsignatory company. This issue frequently arises where, as in this case, a contractor operates one company that is party to a labor agreement and a second company that is non-union. Such “double-breasted” operations allow a contractor to compete for both union and nonunion work. 2 The non-union company can bid competitively on jobs that do not require union contractors, while the union company continues to bid on jobs requiring union contractors. This type of operation is not inherently illegal. Moreover, in particular cases the Board has refused either to require the non-union and nonsignatory company to recognize the bargaining representative of the signatory company’s employees or to apply the labor agreement to the employees of the non-union, nonsignatory company. See, e.g., Local 627, International Union of Operating Engineers v. NLRB, 595 F.2d 844 (D.C.Cir.1979); A-1 Fire Protection, Inc., 250 N.L.R.B. 217 , 220 (1980), aff'd on this issue sub nom. Road Sprinkler Fitters Local Union No. 669 v. NLRB, 676 F.2d 826 (D.C.Cir.1982); Frank N. Smith Associates, 194 N.L.R.B. 212 (1971); Gerace Construction, Inc., 193 N.L.R.B. 645 (1971). 3

*1276 Unions have resisted the use of double-breasted operations in the construction industry. 4 Understandably, they would prefer to have the industry completely unionized. One response by unions has been to bring unfair labor practice charges that seek to extend the labor agreement to the employer’s non-union operations. Thus, a union will allege that the employer’s refusal to apply the agreement to the non-union company violates sections 8(a)(1) and 8(a)(5) of the National Labor Relations Act. 5

B. The “Single Employer” and “Alter Ego ” Doctrines.

In evaluating unfair labor practice charges against double-breasted operations, the Board has employed the “single employer” and the “alter ego” doctrines. E.g., NLRB v. Al Bryant, Inc., 711 F.2d 543 (3d Cir.1983), cert. denied, —— U.S. -, 104 S.Ct. 699 , 79 L.Ed.2d 165 (1984). Under the single employer doctrine, two companies may be bound by a union contract signed by one of them if they are a “single employer” and the employees of each constitute a single bargaining unit. See, e.g., Brotherhood of Teamsters, Local No. 70 v. California Consolidators, Inc., 693 F.2d 81, 82-83 (9th Cir.1982). The following factors are considered in determining whether two or more business entities are a single employer: (1) interrelation of operations, (2) common management, (3) centralized control of labor relations, and (4) common ownership. E.g., NLRB v. Don Burgess Construction Corp., 596 F.2d 378 , 384 (9th Cir.), cert. denied, 444 U.S. 940 , 100 S.Ct. 293 , 62 L.Ed.2d 306 (1979). No factor is controlling and all need not be present. Id. Similar factors are considered in applying the “alter ego” doctrine. See NLRB v. Big Bear Supermarkets #3, 640 F.2d 924 , 928 n. 5 (9th Cir.), cert. denied, 449 U.S. 919 , 101 S.Ct. 318 , 66 L.Ed.2d 147 (1980).

The single employer and alter ego doctrines function differently, however. 6 To impose a labor agreement on a nonsignatory company under the single employer doctrine, the employees of both companies must be shown to constitute a single bargaining unit. 7 Such a showing is not re *1277 quired under the alter ego doctrine, focuses on whether there is an attempt to avoid the obligations of a collective bargaining agreement through a sham transaction or a technical change in operation. See NLRB v. Al Bryant, 711 F.2d at 550, 553 ; Carpenters Local Union No. 1846 v. Pratt-Farnsworth, Inc., 690 F.2d 489 , 507-09 (5th Cir.1982), cert. denied, — U.S. -, 104 S.Ct. 335 , 78 L.Ed.2d 305 (1983); Comment, Dual Companies — When Does a Union Have the Right to Expanded Representation, 12 U.S.F.L.Rev. 89, 94-95 (1977). The alter ego doctrine applies in circumstances in which the bargaining unit of the signatory company is effectively the same as that of the nonsignatory company. Thus, when the alter ego doctrine is applicable we have enforced Board orders applying a labor agreement to a nonsignatory company without requiring a determination regarding the appropriate bargaining unit. See J.M. Tanaka Construction, Inc. v. NLRB, 675 F.2d 1029, 1033-35 (9th Cir.1982). It

C. The Inconsistency Between the Decisions of the Regional Director and the Arbitrator.

These observations demonstrate the significance of the Regional Director’s findings in this case. Because the carpentry employees of EOS and NSC do not constitute a single bargaining unit, the single employer doctrine cannot serve to impose terms of the memorandum agreement and the master labor agreement on EOS. And the Regional Director’s express finding that NSC and EOS were not alter egos precludes application of the labor agreement to EOS under the alter ego doctrine.

Notwithstanding these findings, the arbitrator concluded that EOS must adhere to the terms of the labor agreement signed by NSC. E.R. 12. The arbitrator found that the evidence submitted by the union established that “NSC and EOS have single employer, alter ego, and joint venture status vis-a-vis each other.” It followed that the labor agreement had been violated because EOS had failed to pay union wages and benefits to its carpentry employees. 8

The decisions of the Regional Director and the arbitrator are patently inconsistent. To avoid this conclusion, the union argues that the arbitration award rests on a contractual basis. It is here that the importance of the aforementioned Paragraph 9 emerges. The union maintains that it merely seeks contractual damages for NSC’s breach of the labor agreement. It does not seek to represent the employees of EOS or to bind EOS to a labor agreement. This contention ignores the fact that the arbitrator explicitly based the award on the conclusion that EOS was bound by the labor agreement. Moreover, the failure to pay union wages and benefits with respect to EOS employees is wrongful only if the labor agreement applies to EOS, and it is applicable only if NSC and EOS are a single employer or EOS is the alter ego of NSC. According to the Regional Director neither is the case. We therefore decline to uphold an arbitration award premised on the application of the labor agreement to EOS when previous Board proceedings establish that EOS is not bound by the agreement. 9 In so doing we *1278 reject explicitly the proposition that in a double-breasted situation, where neither the alter ego nor the single employer doctrine is applicable, the union business can unilaterally contract to apply the terms of the agreement to the employees of the non-union, nonsignatory business.

D. The Primacy of the Regional Director’s Decision.

It is obvious that in this case the arbitrator’s award impinges on the Board’s authority under section 9 of the National Labor Relations Act, 29 U.S.C. § 159 . Section 9(b) provides that “[t]he Board shall decide in each case whether, in order to assure to employees the fullest freedom in exercising the rights guaranteed by this subchapter, the unit appropriate for purposes of collective bargaining shall be the employer unit, craft unit, plant unit or subdivision thereof.” 29 U.S.C. § 159 (b). This section confers broad discretion on the Board to determine appropriate bargaining units, and a reviewing court will defer to the Board’s determination unless it is arbitrary or capricious. See, e.g., Pacific Southwest Airlines v. NLRB, 587 F.2d 1032, 1037 (9th Cir.1978). Because the bargaining unit determination is a representational question reserved in the first instance to the Board, we have held that a district court does not have jurisdiction to address this question in a section 301 suit. California Consolidators, 693 F.2d at 84 . 10

Notwithstanding section 9(b)’s delegation of authority to the Board, certain representational issues can be the subject of arbitration. In Carey v. Westinghouse Electric Corp., 375 U.S. 261 , 84 S.Ct. 401 , 11 L.Ed.2d 320 (1964), for example, a union sued to compel arbitration of a claim that the employer was improperly allocating work to members of another union. The employer refused to arbitrate on the grounds that the controversy involved a representation matter within the exclusive jurisdiction of the Board. Id. at 262 , 84 S.Ct. at 404 . The Court held that although the dispute involved representational issues, it could be the subject of arbitration. Id. at 268, 272 , 84 S.Ct. at 407, 409 . Arbitration “is proper, even though an alternative remedy before the Board is available, which, if invoked by the employee will protect him.” Id. at 268 , 84 S.Ct. at 407 . More importantly for our purposes, the Court observed that if the Board subsequently disagreed with the arbitrator’s decision, “the Board’s ruling would, of course, take precedence ...” and “[t]he superior authority of the Board may be invoked at any time.” Id. at 272 , 84 S.Ct. at 409 .

Thus, Carey indicates that, while the possibility of a subsequent decision by the Board does not prevent arbitration of certain representational issues in a section 301 *1279 proceeding, 11 where the findings of the Board and an arbitrator conflict on a particular issue, the Board’s decision must take precedence. We so held in Cannery Warehousemen, Food Processors, Drivers and Helpers v. Haig Berberian, Inc., 623 F.2d 77 (9th Cir.1980). There an arbitrator found that a new processing plant was subject to a labor agreement that applied to the employer’s other facilities. The Board subsequently found, however, that, the new plant was not covered by the existing labor agreement, and the employees at that plant later voted against unionization. Relying on Carey , we affirmed the district court’s refusal to affirm the award by noting that the Board’s decision takes precedence over the arbitrator’s decision. Id. at 81. See also Local 7-210, Oil, Chemical and Atomic Workers v. Union Tank Car Co., 475 F.2d 194, 199 (7th Cir.), cert. denied, 414 U.S. 875 , 94 S.Ct. 68 , 38 L.Ed.2d 120 (1973); New Orleans Typographical Union No. 17 v. NLRB, 368 F.2d 755, 767-68 (5th Cir.1966). The same must be true here. The Regional Director’s findings must take precedence over the arbitrator’s decision.

This conclusion precludes a variance in the employer’s obligations under the labor agreement merely because the arbitrator’s decision arises in the context of a section 301 proceeding instead of a Board proceeding. The primacy of the latter type of proceeding is suggested by Howard Johnson Co. v. Detroit Local Joint Executive Board, 417 U.S. 249 , 94 S.Ct. 2236 , 41 L.Ed.2d 46 (1974). There a union, in a suit under section 301 seeking to bind a successor employer to a labor agreement signed by the predecessor employer, argued that the successor was bound to arbitrate concerning its obligations under the previous employer’s labor agreement. The Court held that the successor was not required to arbitrate because it had not explicitly or implicitly assumed the agreement to arbitrate and because there was no substantial continuity of identity in the workforce. Id. at 264-65 , 94 S.Ct. at 2244-2245 . Howard Johnson relied on the earlier decision in NLRB v. Burns International Security Services, 406 U.S. 272 , 92 S.Ct. 1571 , 32 L.Ed.2d 61 (1972), in which the Court rejected the Board’s position that national labor policies require a nonsignatory successor employer to assume its predecessor’s collective bargaining agreement. The important point for our purposes is that the Court expressly noted that even though Burns arose in the context of an unfair labor practice case, the principles it recognized must be taken into account in the section 301 context. 417 U.S. at 256 , 94 S.Ct. at 2240 . Cf. Pratt-Farnsworth, 690 F.2d at 510-11 (substantive law developed by Board and federal appellate courts in unfair labor practices cases should apply in section 301 suit against related employers). In this case we conform to the principles of Howard Johnson by refusing “to permit the rights and obligations of the parties to vary with the forum.” Id. at 513; cf. Howard Johnson, 417 U.S. at 262 , 94 S.Ct. at 2243 (“The union’s effort to circumvent [the Burns ] holding by asserting its claims in a § 301 suit to compel arbitration rather than in an unfair labor practice context cannot be permitted.”).

E. Protection of Rights of Employees of EOS.

Finally, our holding prevents an infringement upon the rights of the employees of EOS. The clear effect of the arbitrator’s decision would be to apply the terms of the *1280 NSC labor agreement to the EOS carpenters. Section 7 of the National Labor Relations Act provides:

29 U.S.C. § 157 . '

The rights guaranteed employees by section 7 cannot be limited by contract between a union and an employer. See, e.g., Local 3-193, International Woodworkers v. Ketchikan Pulp Co., 611 F.2d 1295, 1301 (9th Cir.1980); Sheraton-Kauai Corp. v. NLRB, 429 F.2d 1352 , 1357 (9th Cir.1970). Paragraph 9 of the agreement signed by NSC cannot be permitted to limit the rights of the EOS employees. This position is supported by Florida Marble Polishers Health & Welfare Trust Fund v. Edwin M. Green, Inc., 653 F.2d 972 (5th Cir.1981), cert. denied, 456 U.S. 973 , 102 S.Ct. 2235 , 72 L.Ed.2d 846 (1982). There a union brought suit under section 301 seeking to recover benefit contributions on the grounds that a labor agreement applied to a nonsignatory, non-union operation. Id. at 974-75. The Fifth Circuit rejected this argument by noting that the parties to the labor agreement could not usurp the self-determination rights of the non-union entity’s employees. Id. at 976-77. Consequently, the court refused to require either the union or the non-union business to pay damages for the failure to make benefit contributions for the employees of the non-signatory operation. Id. at 977.

The strength of this position is enhanced when it is recognized that to hold otherwise would confront employers in Stevens’ position with a serious dilemma. 12 Should he refuse to apply the terms of the labor agreement to the non-union carpenters, he would be liable for damages under an approach that accorded primacy to the arbitrator’s decision. On the other hand, should he insist on applying the agreement to those workers in the face of the Board’s findings in the election proceedings, the employer would be liable for having committed an unfair labor practice. See Sheraton-Kauai Corp., 429 F.2d at 1354 (employer committed unfair labor practice by extending labor agreement to bargaining unit Board identified as distinct); Welch Scientific Co. v. NLRB, 340 F.2d 199, 203 (2d Cir.1965) (unfair labor practice for employer to apply agreement covering Chicago plants to employees in New York).

Our approach avoids this dilemma and protects the section 7 rights of employees in the position of those of EOS. Enforcement of the award would not serve these ends. Therefore, we reverse the district court and remand the case with instructions to vacate the arbitrator’s award.

REVERSED and REMANDED.

. On April 16, 1982, the union filed unfair labor practice charges alleging that Neal Stevens had violated §§ 8(a)(1) and (5), see infra note 5, by refusing to furnish the information requested in the March 11 letter and by refusing to bargain with respect to the employees of EOS. The Regional Director dismissed these charges on June 10, 1982, after he concluded that "the evidence is insufficient to establish that the Employer has' any obligation to bargain with respect to the employees of EOS.” The General Counsel of the Board denied the union's appeal from the dismissal of the unfair labor practice charges on September 27, 1982.

On September 30, 1982, the union requested Board review of the Regional Director’s decision directing an election among the carpenters employed by EOS. The union only sought review of the Regional Director’s determination that the union’s grievance action was inconsistent with its disclaimer. On October 20, 1982, the Board granted the union’s request. However, EOS's petition for a representation election was withdrawn on August 10, 1984 and the case was closed.

. See, e.g., Local 627, Int’l Union of Operating Eng’rs v. NLRB, 595 F.2d 844 , 845 n. 1 (D.C.Cir.1979); Comment, Double-Breasted Operations in the Construction Industry: A Search for Concrete Guidelines, 6 U.Dayton L.Rev. 45 (1981).

. Some commentators have criticized the Board’s early decisions concerning double-breasted operations for indifference to an employer’s intent of avoiding contract obligations under a labor agreement. See King & LaVante, Current Trends in Construction Industry Labor Relations — The Double-Breasted Contractor and the Prehire Contract, 29 Syracuse L.Rev. 901, 902-28 (1978). This concern may be addressed by the Board's recent use of the "alter ego” *1276 doctrine in unfair labor practice cases involving double-breasted operations. See infra pp. 3344-45.

. Carpenters Local Union No. 1846 v. Pratt-Farnsworth, Inc., 690 F.2d 489 (5th Cir.1982), illustrates the different means by which unions have opposed double-breasted operations. In what the court characterized as an "all-out assault,” id. at 497, unions brought claims under section 301; the Employee Retirement Income Security Act, 29 U.S.C. §§ 1001-1461 ; and the Sherman and Clayton Antitrust Acts, 15 U.S.C. §§ 1-7 , 12-27.

Antitrust claims apparently no longer offer an effective weapon, because in Associated General Contractors v. California State Council of Carpenters, 459 U.S. 519 , 103 S.Ct. 897 , 74 L.Ed.2d 723 (1983), the Supreme Court rejected an antitrust challenge to double-breasted operations on the grounds that the union was not a "person injured" under § 4 of the Clayton Act. Id. at 913.

. Section 8(a)(1), 29 U.S.C. § 158 (a)(1), provides that "[i]t shall be an unfair labor practice for an employer ... to interfere with, restrain, or coerce employees in the exercise of the rights guaranteed in [section 7] of this title.”

Section 8(a)(5), 29 U.S.C. § 158 (a)(5), provides that "[i]t shall be an unfair labor practice for an employer ... to refuse to bargain collectively with the representative of his employees

. In Big Bear Supermarkets, we observed that the same factors are relevant in determining whether the "single employer” or "alter ego" doctrines apply.

We do not read that case as suggesting that the two doctrines are identical with regard to the application of a labor agreement to a non-signatory business. As explained infra, the alter ego doctrine does not require independent determination of the appropriate bargaining unit, because this doctrine applies in cases in which the non-union entity is a sham attempt to avoid the employer's obligations under a labor agreement. See also Anderson, Suits to Bind Nonsig-natories to Collective Bargaining Agreements Under Section 301: The Emerging Federal Law, 1983 B.Y.U.L.Rev. 241, 248-49 (discussing alter ego doctrine).

. We have held that § 301 grants a district court jurisdiction to decide whether employers constitute a single employer, but the bargaining unit determination is a representational question reserved in the first instance to the Board. California Consolidators, 693 F.2d at 83-84 . In contrast, the Fifth Circuit has held that where the *1277 bargaining unit issue is essential to the disposition of contractual rights in a § 301 action, the district court may decide that issue, at least in the absence of a pending or previous decision by the Board. See Pratt-Farnsworth, 690 F.2d at 521.

. There is no suggestion in the arbitrator’s decision or in the union’s grievance that Stevens violated the labor agreement because EOS, rather than NSC, performed work on a particular jobsite. The gravamen of the union’s complaint is that Stevens has breached the agreement by not applying its terms to the employees of EOS. Cf. Road Sprinkler Fitters Local Union No. 669 v. NLRB, 676 F.2d 826 , 830-31 (D.C.Cir.1982) (distinguishing claim that labor agreement applied to nonsignatory business from claim that work was illegally transferred to such a business).

. The union did not challenge the Regional Director’s finding that NSC and EOS were neither alter egos nor joint employers. The union cannot relitigate this issue in any related subsequent unfair labor practice proceeding. See 29 C.F.R. § 102.67 (f) (1983).

The district court relied on different arguments than those now advanced by the union in *1278 upholding the award. First, the district court maintained that the arbitrator was not required to give collateral estoppel effect to the Board findings because the election proceeding involved the Conference of Carpenters, a "wholly distinct party” from the union involved in the arbitration. This contention is belied by the fact that the Conference was the representative of the union. Indeed, the union’s § 301 claim was based on the labor agreement signed by the Conference on behalf of the union. The district court also stated that the Board findings were not supported by substantial evidence. However, neither the union nor the Conference of Carpenters appealed the Regional Director's decision, and the district court had no jurisdiction to review that decision in a subsequent § 301 suit. See Local # 1547, Int'l Bhd. of Elec. Workers v. Local # 959, Int’l Bhd. of Teamsters, 507 F.2d 872, 874-75 (9th Cir.1975).

The district court’s final argument was that "the arbitrator’s decision was not inconsistent with the NLRB’s bargaining unit determination in that the arbitrator was not called upon to determine the ultimate validity or invalidity of the relevant terms of the collective bargaining agreement, but merely was asked to apply and interpret said terms with regard to the grievance filed.” E.R. 239. This statement does not alter the fact that the arbitrator's conclusion that the terms of the labor agreement apply to EOS is fundamentally inconsistent with the Board’s findings. Cf. Associated Gen. Contractors v. International Union of Operating Eng’rs, 529 F.2d 1395 , 1397-98 (9th Cir.) (§ 301 action not precluded by Board ruling where former not inconsistent with latter), cert. denied, 429 U.S. 822 , 97 S.Ct. 72 , 50 L.Ed.2d 84 (1976).

. See supra note 7.

. This fact may seem anomalous inasmuch as district courts lack jurisdiction over representational issues under the Board’s jurisdiction in § 301 cases in which the labor agreement does not provide for arbitration. The anomaly results, however, from our need to reconcile Carey with the Supreme Court’s holding in South Prairie Constr. Co. v. Local 627, Int'l Union of Operating Engr’s, 425 U.S. 800 , 96 S.Ct. 1842 , 48 L.Ed.2d 382 (1976) (per curiam), that courts may not foreclose the Board from deciding the appropriate bargaining unit in the first instance. See Ketchikan, 611 F.2d at 1298-1300 . A persuasive argument can be made that it is even less appropriate for arbitrators than for courts to decide representational issues within the Board’s primary jurisdiction. See Comment, Arbitration of Representational Issues: A Critique of Carey, 1983 B.Y.U.L.Rev. 349.

. In Carey , the Supreme Court suggested in dicta that this outcome would not occur even though certain representational issues are subject to arbitration. After noting that a subsequent Board decision would take precedence over a conflicting ruling by an arbitrator, the Court added: "if the employer's action had been in accord with [the Board’s] ruling, it would not be liable for damages under § 301." 375 U.S. at 272 , 84 S.Ct. at 409 . The Courts of Appeals have followed the suggestion in Carey. See, e.g., Pilot Freight Carriers v. International Bhd. of Teamsters, 659 F.2d 1252, 1258 (4th Cir.1981) (subsequent Board decision protected employer from enforcement of arbitration awards in accretion controversy); Local 7-210, Oil, Chemical and Atomic Workers v. Union Tank Car Co., 475 F.2d 194, 197-99 (7th Cir.) (refusing to enforce arbitrator's damage award that was inconsistent with subsequent Board determination), cert. denied, 414 U.S. 875 , 94 S.Ct. 68 , 38 L.Ed.2d 120 (1973); cf. International Union of Operating Eng'rs v. Sullivan Transfer, Inc., 650 F.2d 669, 677 (5th Cir.1981) (union may not recover damages in § 301 suit to extent award is repugnant to Board's § 10(k) jurisdictional determination).