
656 F.3d 860 (2011)
INTERNATIONAL UNION OF PAINTER AND ALLIED TRADES, DISTRICT 15, LOCAL 159, Petitioner-Appellant,
v.
J & R FLOORING, INC., dba J. Picini Flooring; Freeman's Carpet Service, Inc.; FCS Flooring, Inc.; Flooring Solutions of Nevada, Inc., dba FSI, Respondents-Appellees.
International Union of Painter and Allied Trades, District 15, Local 159, Petitioner,
J & R Flooring, Inc., Intervenor,
v.
National Labor Relations Board, Respondent.
Flooring Solutions of Nevada, Inc., DBA FSI, Petitioner,
District Council of Painters No. 16, Intervenor-Pending,
v.
National Labor Relations Board, Respondent.
National Labor Relations Board, Petitioner,
v.
Flooring Solutions of Nevada, Inc., DBA FSI, Respondent.
Nos. 08-17089, 10-72727, 10-73383, 10-73561.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted July 14, 2011.
Filed August 29, 2011.
*862 David A. Rosenfeld, Alameda, CA, for petitioner-appellant International Union of Painter & Allied Trades, District, Council 15, Local 159.
Thomas A. Lenz, Cerritos, CA, for respondent-appellee Flooring Solutions of Nevada, Inc., dba FSI.
Gregory E. Smith, Las Vegas, NV, for respondents-appellees J & R Flooring, Inc., et al.
Steven B. Goldstein, NLRB, Washington, D.C., for respondent-petitioner National Labor Relations Board.
Before: MARY M. SCHROEDER and CONSUELO M. CALLAHAN, Circuit Judges, and BARBARA M.G. LYNN, District Judge.[*]

OPINION
SCHROEDER, Circuit Judge:
These consolidated cases arise out of a 2007 labor dispute between the Painters Union and Nevada contractors over whether the Union's card check established its majority status under the terms of the collective bargaining agreement ("CBA"), thereby requiring the contractors to bargain with the Union pursuant to Section 9(a) of the National Labor Relations Act ("NLRA"). One set of cases arises from the Union's charges before the National Labor Relations Board ("Board") that the contractors failed to bargain in good faith during and following the card check. The other case arises from the district court, where the Union sought an order to arbitrate whether the card check established the Union's majority status under the terms of the CBA. We have seen the appeal from the district court before when the district court declined to order arbitration. See Int'l Union of Painter and Allied Trades, Dist. 15, Local 159 v. J & R Flooring, Inc., 616 F.3d 953 (9th Cir.2010). We have now ordered the appeal reheard.
When we originally decided the district court appeal, the Union's unfair labor practice charges had been pending before the Board for more than two years, a delay resulting from the Board's inability to function because it lacked a third member. In our opinion, we considered Ninth Circuit precedent and the manner in which the dispute had been characterized by the Union. We concluded that the dispute was primarily representational and properly *863 belonged before the Board. Int'l Union of Painter, 616 F.3d at 962. We therefore affirmed the district court's dismissal of the Union's petition to compel arbitration. The Union petitioned for rehearing of our decision.
Soon after our opinion issued, the Board decided the unfair labor practice charges. J & R Flooring, Inc., 355 NLRB No. 123 (Aug. 26, 2010). In a bifurcated decision, the Board held that one of the employers, Flooring Solutions of Nevada, Inc. ("FSI"), had refused in bad faith to bargain with the Union, and ordered FSI to bargain. Id. at *8. As for the other employers, collectively known as the J & R Flooring Employers, the Board held they were not guilty of unfair labor practices because they had acted in good faith by relying on a reasonable interpretation of the CBA in disputing the card check. Id. at *7. The Board declined to consider which of the parties' contract interpretations was correct, and whether the Union was entitled to majority recognition, because the resolution of the dispute was immaterial to whether the employers acted in good faith in relying on their interpretation of the CBA to dispute the card check. Id. at *22 n. 17.
FSI did not ask the Board to reconsider its decision. Instead, FSI petitioned this court for review of the Board's decision and bargaining order; the Board cross-petitioned for enforcement of the bargaining order; and the Union petitioned for review of the Board's ruling in favor of the J & R Flooring Employers. We ordered the Board petitions calendared before this panel, granted the Union's petition for panel rehearing of the district court appeal, and consolidated all of the matters for argument and decision together.
Rehearing of the district court appeal was required because one of the practical effects of the Board's decision, when coupled with our decision denying arbitration, was to leave the Union without any forum to determine whether it had established majority status under the CBA. This would have been an unfortunate result given the parties' contractual agreement to determine majority status through a card check, and the CBA's specific clause requiring expedited arbitration of any disputes concerning the card-check provision.
We now have the benefit of the Board's decision, the petitions to this court emanating from it, and the rearguments of the parties. In the petitions for review from the Board's decision, we enforce the Board's order, and deny the Union's and FSI's petitions for review. In the appeal from the district court, we conclude that the dispute over whether the Union established majority status pursuant to the CBA's card-check provision is primarily contractual and subject to arbitration. The parties contractually agreed to determine majority status through a card check, and to arbitrate any dispute concerning the card-check provision. We therefore withdraw our prior decision, Int'l Union of Painter and Allied Trades, Dist. 15, Local 159 v. J & R Flooring, Inc., 616 F.3d 953 (9th Cir.2010), and replace it with this opinion reversing the district court's order denying arbitration. We remand for the district court to order all parties to arbitrate whether, under the CBA's card-check provision, the Union established majority status. Any remedies fashioned in arbitration must be consistent with the Board's bargaining order against FSI.

FACTUAL AND PROCEDURAL BACKGROUND
The background of this dispute is familiar to the parties and is set forth in the Board's decision. J & R Flooring, 355 NLRB No. 123, at *2-8. We recount only those facts that are necessary to explain our decision.
*864 The employers are four Nevada contractors engaged in commercial and industrial flooring: FSI, J & R Flooring, Freeman's Carpet Service, and FCS Flooring. The latter three employers are referred to collectively as the J & R Flooring Employers. The International Union of Painter and Allied Trades, Local 159, entered into a collective bargaining agreement with all of the employers, which was in effect from February 1, 2004, through January 31, 2007. Article 4 of the CBA provides that the employers will recognize the Union as a majority representative of their employees if the Union establishes majority status through a third-party card check. Article 4 further requires the parties to submit any disputes concerning that provision to expedited arbitration.
Before the CBA was due to expire, the Union notified the employers that it wished to bargain for a new contract and announced its intention to conduct a third-party card check, in accordance with Article 4, to determine whether it represented a majority of the employees. The J & R Flooring Employers met with the Union several times but failed to reach an agreement. On January 31, 2007, the day the contract was set to expire, the Union, for the first time, announced that it was conducting a card check. The J & R Flooring Employers objected to the card check on the grounds that the remittance reports that the Union intended to use were not current; that the J & R Flooring Employers were not involved in selecting the third party and were not assured of the third party's neutrality; and that at least two employees had complained about the Union misinforming them of the purpose of the cards. Despite J & R Flooring Employers' objections to the card-check procedures, the Union nevertheless conducted the card check. The J & R Flooring Employers then refused to accept the card-check results and refused to recognize the Union as the majority representative of their employees.
With respect to FSI, the Union requested that the parties hold a card check on January 23, 2007. FSI responded that it was not available on that date or any other dates suggested by the Union. The Union then informed FSI that it was conducting a card check on January 30, 2007, but FSI did not appear at the card check. FSI subsequently refused to recognize the Union as the majority representative of its employees and maintained that it had no duty to bargain with the Union following the expiration of the CBA.
In February 2007, the Union filed unfair labor practice charges against the employers, alleging that the Union had established that it represented a majority of the employees, but that the employers had wrongfully refused to bargain with the Union. The ALJ recommended dismissing the charges in September 2007. The Union filed exceptions to the ALJ's decision before the Board in October 2007.
While the unfair labor charges were still pending before the Board, the Union asked the employers to arbitrate the dispute over whether the Union had established majority status under the terms of the CBA, but the employers refused. In December 2007, the Union filed a petition to compel arbitration in the district court. The district court dismissed the Union's petition for lack of jurisdiction, concluding that the issue the Union sought to arbitrate was primarily representational and, thus, within the Board's primary jurisdiction. We affirmed. Int'l Union of Painter, 616 F.3d at 962.
The Union then petitioned for rehearing of our decision, and while that petition was pending, the Board, in August 2010, decided the unfair labor practice charges. It agreed with the ALJ that the J & R Flooring Employers acted in good faith in *865 relying on their interpretation of Article 4 of the CBA to refuse the card-check results. The Board, however, noted that it was not the proper forum to decide which of the parties' "equally plausible interpretations of art. 4" of the CBA was correct. J & R Flooring, 355 NLRB No. 123, at *9 n. 16. As for FSI, the Board found that FSI's unreasoned refusal both to participate in, and then accept the results of, the card check was motivated by bad faith, and not by a bona fide dispute over the interpretation of Article 4. Id. at *8. It therefore ordered FSI to recognize the Union as the majority representative and to bargain with the Union. FSI did not seek reconsideration from the Board. Instead, FSI petitioned for review of the Board's bargaining order; the Board cross-petitioned for enforcement of its order; and the Union petitioned for review of the Board's decision dismissing the charges against the J & R Flooring Employers.
In April 2011, this panel granted the Union's petition for rehearing of the appeal from the district court's judgment dismissing the arbitration petition, and we consolidated that appeal for argument and decision with the petitions for review and enforcement of the Board's decision on the unfair labor practice charges.

ANALYSIS

I. The Union's Petition for Review of the Board's Order Dismissing the Charges Against J & R Flooring Employers
The Union argues that the J & R Flooring Employers acted in bad faith by refusing to recognize the Union as the majority representative even though the Union had obtained authorization cards from the majority of the employees. The Board, however, found that the Union and the J & R Flooring Employers disagreed as to how the card check should be conducted. The J & R Flooring Employers refused to participate in the card check because they were not involved in the selection of the third party, they were not assured of the third party's neutrality, and the remittance reports were not current. The Union, however, interpreted Article 4 of the CBA as allowing it unilaterally to select its own third party to conduct the card check.
The Board noted that Article 4 is silent as to how the card check should be conducted. The Board then concluded that J & R Flooring Employers' interpretation, requiring both parties to mutually agree on the procedures of the card check, was reasonable and that the J & R Flooring Employers did not act in bad faith in refusing to honor the card check results.
We must decide whether the Board's conclusion of good faith is supported by substantial evidence in the record as a whole. See Allentown Mack Sales & Serv., Inc. v. NLRB, 522 U.S. 359, 366, 118 S.Ct. 818, 139 L.Ed.2d 797 (1998). We conclude that it is. The Union did not inform the J & R Flooring Employers of its intention to conduct a card check until January 31, 2007, at which time the J & R Flooring Employers immediately objected on the ground that they disagreed with the manner in which the card check was conducted. The CBA is silent as to the procedures to be used in conducting a card check, and the J & R Flooring Employers relied on a permissible interpretation of the card-check provision in raising their objections. Thus, the Board reasonably concluded that the J & R Flooring Employers did not act in bad faith when they objected to the Union's unilateral imposition of the card-check procedures.
The Board's decision to dismiss the unfair labor charges against the J & R Flooring Employers is consistent with the Board's precedent. The Board has previously held that it will dismiss an unfair labor practice charge against an *866 employer for failing to comply with its collective bargaining agreement if the employer has a sound arguable basis for its interpretation. See Phelps Dodge Magnet Wire Corp., 346 NLRB 949, 951-52 (2006) (dismissing charges against the employer because, although the employer's "construction of[the agreement] may have been erroneous, its interpretation had a sound arguable basis"); NCR Corp., 271 NLRB 1212, 1213 (1984) ("[W]hen `an employer has a sound arguable basis for ascribing a particular meaning to his contract and his action is in accordance with the terms of the contract as he construes it,' the Board will not enter the dispute to serve the function of arbitrator in determining which party's interpretation is correct." (citation omitted)).
The Board's conclusion, that the J & R Flooring Employers acted in good faith because their refusal to accept the card-check results was done in reliance on a reasonable interpretation of Article 4, is supported by the record as well as in accordance with the Board's precedent. We therefore deny the Union's petition for review of the dismissal of the unfair labor charges against the J & R Flooring Employers.

II. FSI's Petition for Review, and the Board's Cross-Petition for Enforcement of, the Board's Bargaining Order Against FSI
The Board concluded that FSI acted in bad faith in refusing to accept the card-check results, because it did not rely on its own interpretation of the card-check provision. This conclusion is supported by substantial evidence in the record. Even though FSI had ample notice of the Union's demands for a card check, and how it would be conducted, FSI failed to object to the card-check procedures until after the Union had conducted the card check. Indeed, FSI deliberately dodged the Union's requests to meet and did not participate in the card check.
On January 17, 2007, the Union informed FSI that it had obtained authorization cards from a majority of FSI's employees and that it intended to conduct a card check pursuant to Article 4 to establish its majority status. The Union proposed that the card check be conducted on January 23, but FSI responded that it was unavailable to meet that day. When the Union requested that FSI provide dates and times when it would be available to meet, FSI did not respond. On January 25, the Union provided FSI with copies of signed authorization cards from nineteen of FSI's twenty-two unit employees and again asked FSI to meet to negotiate. FSI responded that it was unavailable to meet. On January 30, the Union informed FSI that it would conduct a card check that day and requested FSI's presence. FSI did not respond, and did not attend the card check. After the card check was conducted, the Union sent FSI the authorization cards and FSI admitted that it had "no doubt" that a majority of its employees signed the cards. Later, FSI indicated its belief that a Board election, rather than a card check, was the fairest and only method for determining majority status. This evidence supports the Board's determination that FSI's refusal to honor the card check results was not based on a disagreement over the procedures or results and therefore constituted bad faith.
Having concluded that FSI engaged in an unfair labor practice by acting in bad faith, the Board ordered FSI to recognize the Union as the majority representative and to bargain with the Union. In addition to challenging the Board's findings, FSI asks us to undo the Board's bargaining order, arguing that even if FSI did act in bad faith, requiring FSI to bargain was too extraordinary a remedy. *867 FSI, however, did not seek reconsideration of the Board's bargaining order and, thus, did not give the Board the opportunity to consider its objection. Therefore, we lack jurisdiction to consider the Board's choice of remedies.
Section 10(e) of the NLRA provides that "[n]o objection that has not been urged before the Board ... shall be considered by the court, unless the failure or neglect to urge such objection shall be excused because of extraordinary circumstances." 29 U.S.C. § 160(e). FSI contends that it could not have raised objections to the Board's bargaining order because the ALJ had recommended dismissal of the charges against FSI and, therefore, FSI could not have known that the Board would sua sponte order FSI to bargain. We have, however, applied the § 10(e) bar in cases where a party could have asked the Board to reconsider its sua sponte remedial order, but failed to do so. See NLRB v. Sambo's Rest., Inc., 641 F.2d 794, 796 (9th Cir.1981) (holding that "because of the availability of a rehearing before the Board, the Board's sua sponte adoption of an unargued remedy is not a statutory extraordinary circumstance under section 10(e) that would allow the Company to assert an objection for the first time on appeal"). We explained that the Board should have the first opportunity to apply its labor relations expertise to address a party's arguments, so that we may have the benefit of the Board's opinion when we review its decision. Id. A year later, the Supreme Court held that appellate courts lack jurisdiction to consider an objection raised by a party for the first time on appeal when that party had the opportunity to ask the Board for rehearing but failed to do so. See Woelke & Romero Framing, Inc. v. NLRB, 456 U.S. 645, 666, 102 S.Ct. 2071, 72 L.Ed.2d 398 (1982) (stating that when a party "could have objected to the Board's decision in a petition for reconsideration or rehearing," its "failure to do so prevents consideration of the question by the courts"). Accordingly, we may not consider FSI's objection to the Board's bargaining order, because FSI failed to seek rehearing.
When § 10(e) bars our consideration of a party's objection to the Board's order, the Board is entitled to enforcement unless the Board has "patently traveled outside the orbit of its authority." NLRB v. Cheney Cal. Lumber Co., 327 U.S. 385, 388, 66 S.Ct. 553, 90 L.Ed. 739 (1946). In such a case, there would be "legally speaking no order to enforce." Id. The Supreme Court has held that the Board has broad discretion to fashion remedies, including ordering parties to bargain. See NLRB v. Gissel Packing Co., 395 U.S. 575, 610-12, 89 S.Ct. 1918, 23 L.Ed.2d 547 (1969). The Board did not err in ordering FSI to bargain on the basis of its findings, which are supported by substantial evidence in the record. Thus, the Board is entitled to enforcement of its order.

III. The Union's Appeal of the District Court's Dismissal for Lack of Jurisdiction
In the district court proceedings, the Union sought to compel the employers to arbitrate whether the Union had established majority status under the card-check provision. The Union claimed the employers' refusal to bargain or arbitrate was a breach of the CBA. Section 301 of the Labor Management Relations Act ("LMRA") creates a cause of action, enforceable in either state or federal court, for violation of collective bargaining contracts. 29 U.S.C. § 185(a); Charles Dowd Box Co. v. Courtney, 368 U.S. 502, 506, 82 S.Ct. 519, 7 L.Ed.2d 483 (1962). "All that is required for jurisdiction to be proper under § 301(a) is that the suit be based on an alleged breach of contract between an employer and a labor organization and that *868 the resolution of the lawsuit be focused upon and governed by the terms of the contract." Painting & Decorating Contractors Ass'n v. Painters & Decorators Joint Comm., 707 F.2d 1067, 1071 (9th Cir.1983). Because the parties contractually agreed to determine the Union's majority status through a card check, and to arbitrate any disputes concerning the card-check provision, we conclude that the district court has jurisdiction under § 301 to compel arbitration.
All of the parties to the dispute, including the Union, FSI, and the J & R Flooring Employers, were signatories to the CBA. Article 4 of the CBA provides:
The Employer hereby recognizes the Union as the sole and exclusive bargaining agent of employees classified herein.... The Employer agrees that if a majority of its employees authorize the Union to represent them in collective bargaining, the Employer will recognize the Union as the NLRA Section 9(a) majority collective bargaining agent for all employees performing work within the jurisdiction of this Agreement. The Employer agrees furthermore upon demand by the Union to submit to a third party card check to determine the majority status of the Union. Any disputes concerning this provision shall be resolved by expedited arbitration under the terms of this Agreement (emphasis added).
Pursuant to Article 4, the Union sought to establish its majority status through a card check, but the employers refused to participate. The J & R Flooring Employers disagreed with the Union over the procedures of the card check, including the unilateral selection of a third party, the accuracy of the remittance reports for determining eligibility to vote, and whether adherence to the Board's Daniel-Steiny eligibility formula was required. When the Union demanded arbitration to resolve this dispute and to determine whether the Union was entitled to majority status, the employers refused. The Union then requested the district court to compel arbitration, stating that the employers breached the CBA by refusing to arbitrate the dispute, as required by Article 4 of the CBA. Because the parties expressly agreed to arbitrate any disputes concerning the card-check provision, we conclude that the employers' refusal to do so was in violation of the CBA and the Union is entitled to arbitration.
We note that the Board has already ordered FSI to bargain with the Union as a remedy for its labor violation, which presumably overlaps with the contractual remedies that the Union seeks in arbitration. However, the Union argues, with considerable force, that FSI should be included in arbitration because there is a separate value in whatever decision the arbitrator reaches and there may be additional remedies available for any breach of contract. We agree. Thus, if an arbitrator were to find that the card check was valid, the arbitrator could fashion a contractual remedy in addition to the existing bargaining order. Alternatively, if an arbitrator finds that the card check was invalid, FSI would nonetheless have to comply with the bargaining order.
Were we to separate FSI from the other employers in the arbitration, it could have the unfortunate effect of fragmenting the resolution of the dispute into bargaining and arbitration proceedings. This would be a less than comprehensive resolution of all the issues. The Supreme Court has recognized the importance of avoiding such fragmentation and achieving conciliation through comprehensive arbitration. See Carey v. Westinghouse Elec. Corp., 375 U.S. 261, 272, 84 S.Ct. 401, 11 L.Ed.2d 320 (1964) ("By allowing the dispute to go to arbitration its fragmentation is avoided to *869 a substantial extent; and those conciliatory measures which Congress deemed vital to `industrial peace' ... and which may be dispositive of the entire dispute, are encouraged." (citing Textile Workers v. Lincoln Mills, 353 U.S. 448, 455, 77 S.Ct. 912, 1 L.Ed.2d 972 (1957))). Including all of the parties in the arbitration therefore avoids such fragmentation.
Our holding that all parties should proceed to arbitration of the contractual dispute is consistent with the Board's decision and our precedent. The Board declined to reach the contractual dispute, explaining that it was "not the proper forum for determining which of the parties' equally plausible interpretations of art. 4 is more appropriate." See J & R Flooring, 355 NLRB No. 123, at *9 n. 16. Arbitration is the appropriate forum to resolve the parties' dispute. Similarly, while we have recognized that courts generally lack jurisdiction over claims involving representational issues that are reserved for the Board, we have held that courts have jurisdiction over representational issues that the parties themselves have purported to resolve by contract. Hotel Emps., Rest. Emps. Union, Local 2 v. Marriott Corp., 961 F.2d 1464, 1468 (9th Cir.1992). We also note that the Second Circuit has recognized that courts may order arbitration of representational issues where, as here, a clause in the collective bargaining agreement authorizes it. See N.Y. Health and Human Serv. Union v. NYU Hosps. Ctr., 343 F.3d 117, 119 (2d Cir.2003); Hotel & Rest. Emps. Union, Local 217 v. JP Morgan Hotel, 996 F.2d 561, 566-67 (2d Cir.1993).
Our decision is also supported by longstanding Supreme Court precedent encouraging the use of contractual arbitration provisions to resolve labor disputes. See United Steelworkers v. Am. Mfg. Co., 363 U.S. 564, 567-68, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960) (holding that, when the parties have negotiated an arbitration clause, the function of the enforcing court is limited to determining "whether the party seeking arbitration is making a claim which on its face is governed by the contract"); United Steelworkers v. Warrior & Gulf Navigation Co., 363 U.S. 574, 581-83, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960) (holding that all questions on which parties disagree come within the scope of arbitration unless specifically excluded, instructing that "[d]oubts should be resolved in favor of coverage"); United Steelworkers v. Enter. Wheel & Car Corp., 363 U.S. 593, 597-99, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960) (holding that a reviewing court should not refuse to enforce an arbitral award merely because it would read the collective bargaining agreement differently than the arbitrator).
Accordingly, we conclude that the district court has jurisdiction to compel arbitration, and that the Union is entitled to arbitration among all the parties. We remand to the district court for further proceedings consistent with this opinion.

CONCLUSION
In appeal Nos. 10-72727, 10-73383, and 10-73561, the Board's petition for enforcement of the order requiring FSI to bargain is GRANTED, and FSI's and the Union's petitions for review are DENIED.
In appeal No. 08-17089, the judgment of the district court dismissing the Union's petition to compel arbitration is REVERSED, and the matter is REMANDED to the district court to order all parties to arbitrate for resolution of the dispute consistent with the Board's order requiring FSI to bargain.
Each party shall bear its own costs on appeal.
NOTES
[*]  The Honorable Barbara M.G. Lynn, District Judge for the United States District Court for the Northern District of Texas, sitting by designation.
