This appeal presents unusual labor arbitration issues. When an employer and employee enter into a last chance agreement (“LCA”) enforcing the employer’s drug policy without the union’s participation, the employer subsequently invokes the LCA provision mandating discharge in the event of a violation, and the union claims this discipline was contrary to the “just cause” limitation in the grievance and arbitration provisions of the collective bargaining agreement (“CBA”), what is the appropriate standard of review (i) for the arbitrator, and (ii) for this court in reviewing the arbitrator’s award? Here, the employer is Associated Electric Cooperative, Inc. (“AECI”), the union is Local 53 of the International Brotherhood of Electrical Workers (the “Union”), and the discharged employee is grievant Leo Johnson. The arbitrator upheld the grievance, awarding Johnson reinstatement and back pay, concluding the LCA did not provide Associated just cause to terminate Johnson. The *900district court vacated the award, concluding that the arbitrator overstepped his authority by refusing to enforce the LCA’s mandatory discharge clause. The Union appeals. We reverse and enforce all but a portion of the award.

I.

AECI operates the Thomas Hill Power Plant, which generates electricity for rural electric cooperatives that own AECI. At the time in question, approximately. 175 AECI employees were represented by the Union and covered by a fíve-year CBA between the Union and AECI. Article I, Section 6(a), was a broad “Management Rights” clause, subject to a proviso in Section 6(c) that “discipline and/or discharge of employees shall be for just cause only, and such action shall be subject to the grievance and arbitration procedure.” Article XII set forth detailed grievance and arbitration procedures. Article XII, Section 4(a)(4), provided that the “decision of the Arbitrator shall be final and binding on all parties.” Section 4(b) provided that the Arbitrator “shall have no authority to add to, detract from or in any way modify the terms of this Agreement.” Article XII did not include agreed procedures for the use of progressive discipline or LCAs. Compare Bureau of Engraving, Inc. v. Graphic Commc’n Int'l Union, Local 1B, 284 F.3d 821, 823 (8th Cir. 2002).

On April 18, 2011, AECI subjected employees at work that day to random drug testing, a practice AECI instituted in 2008 after discussions with the Union. Leo Johnson was a heating, ventilation, air conditioning, and refrigeration mechanic who had worked for AECI for over 28 years. He provided a urine sample and then informed the Plant Manager that he would test positive because he had recently smoked marijuana with family members while on leave to attend his brother’s funeral. AECI offered Johnson Union representation for a disciplinary proceeding. He declined, signed AECI’s standard form LCA, and AECI suspended him without pay. The LCA specifically provided: “I understand and agree that if I report to work under the influence, test positive, or I am in the possession of alcohol, drugs, or controlled substances on Cooperative property, my employment with AECI will be terminated.”

One week later, AECI advised Johnson by letter that he would likely qualify for “FMLA sick leave” when he began the chemical dependency treatment required by the LCA, and that his return to work “will be contingent on ... successful completion of a treatment program, and a negative drug screen result.” The next day, AECI informed Johnson that the test report of his April 18 urine sample was negative (did not reveal marijuana use). Johnson nonetheless remained on suspension and continued treatment under the terms of the LCA.

While suspended, Johnson submitted to two drug tests that showed trace amounts of THC (marijuana), which prevented his return to work under AECI’s drug policy, and the presence of a benzodiazepine drug. Johnson had a valid prescription for clonazepam, a benzodiazepine (brand name Klonopin). On June 3, the treatment counsel- or advised AECI that Johnson needed no further treatment and was clear to return to work. AECI instructed Johnson to appear for a return-to-work drug screen. Laboratory analysis of Johnson’s urine sample revealed the presence of a different benzodiazepine, diazepam (brand name Valium), for which Johnson did not have a prescription. AE Cl’s drug testing Guidelines provide that taking a non-prescribed medication results in a positive test. By letter dated June 16, AECI terminated Johnson’s employment for violating the LCA by testing positive “for a controlled substance that had not been prescribed for *901your medical history.” The Union and Johnson timely filed a grievance asserting there was not “just cause for termination.” AECI denied the grievance because, “[b]y violating the [LCA] Leo Johnson left [AECI] no other alternative but to terminate his employment.” The Union submitted the dispute to arbitration, stating as the issue to be decided by the arbitrator: “Was the grievant discharged for just cause, and if not, what is the appropriate remedy.”

Following an evidentiary hearing, the arbitrator issued a lengthy decision sustaining the grievance “in full” and ordering AECI to reinstate Johnson with back pay “for all lost wages from the time he was forced to clock out on the date of the random drug test.” The arbitrator acknowledged AECI’s strong interest in a drug-free workplace, and noted that LCAs are “commonly used” as substitutes for the just cause provision of the CBA. But he ruled that this LCA was “unconscionable” because Johnson’s negative April 18 urine sample established that he had not broken any work rule. Continuing the suspension after learning Johnson passed the random test was “simply indefensible.” Then, before Johnson returned to work, AECI fired him for taking the wrong prescription medication, without considering his explanation (that he inadvertently had taken a family member’s similar prescribed medication), and without further delaying his return to work until he passed the return-to-work screen. In these circumstances, the arbitrator concluded, and taking into account Johnson’s long and largely positive tenure with AECI, Johnson was first suspended and then terminated without just cause.

AECI commenced this action against the Union seeking to vacate the arbitrator’s award; the Union counterclaimed to enforce the award. In granting AECI’s cross-motion for summary judgment, the district court properly noted that a reviewing court is ordinarily “obligated to defer to an arbitrator’s conclusion, even where it believes serious error was committed.” The court nonetheless vacated the award. Relying on this court’s decision in Coca-Cola Bottling Co. v. Teamsters Local Union No. 688, 959 F.2d 1438 (8th Cir.), cert. denied, 506 U.S. 1013, 113 S.Ct. 635, 121 L.Ed.2d 566 (1992), the district court ruled that the LCA “superseded the collective bargaining agreement” and therefore, when “the arbitrator ignored the clear and unambiguous terms of the LCA,” he “imposed his personal standards of industrial justice.” The Union appeals. We review the district court’s grant of summary judgement de novo. Electrolux Home Prods. v. UAW, Local No. 442, 416 F.3d 848, 853 (8th Cir. 2005).

II.

As the district court recognized, we give decisions by labor arbitrators substantial deference. The federal labor laws “reflect a decided preference for private settlement of labor disputes.” United Paperworkers Int’l Union v. Misco, Inc., 484 U.S. 29, 37, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987). Therefore, “as long as the arbitrator is even arguably construing or applying the [CBA] and acting within the scope of his authority, that a court is convinced he committed serious error does not suffice to overturn his decision.” Id. at 38, 108 S.Ct. 364. But an arbitrator’s authority is limited. His award must “draw[ ] its essence” from the CBA, not merely reflect “his own brand of industrial justice.” United Steelworkers of Am. v. Enter. Wheel & Car Corp., 363 U.S. 593, 597, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960).

In this case, the district court understandably disagreed with the arbitrator’s decision to declare the LCA “unconscionable.” The Management Rights clause of *902the CBA unambiguously confirmed AECI’s right to adopt plant rules, such as a drug policy with random drug testing. It also confirmed AECI’s right to discipline employees, which includes the discretion to enter into LCAs and other types of agreements with one or more employees, individually, to resolve particular performance or disciplinary issues. The LCA was not “unconscionable” when Johnson and AECI entered into it after Johnson predicted he would fail the drug test, even though that prediction proved to be wrong.

However, in concluding that the arbitrator was obligated to enforce a mandatory termination provision in the LCA, the district court read our decision in Coca-Cola Bottling too broadly. In Coca-Cola Bottling, we noted that “normally last chance agreements are binding in arbitration.” 959 F.2d at 1441 (emphasis added), quoting Ohio Edison Co. v. Ohio Edison Joint Council, 947 F.2d 786, 787 (6th Cir. 1991). There, the employer and the union resolved disciplinary proceedings that would likely have led to termination by entering into an LCA that gave the employee “another opportunity to correct the deficiencies in his job performance [and] provided for his discharge in the event he did not.” 959 F.2d at 1440. The union grieved the employee’s subsequent discharge for violating the LCA, and the arbitrator ruled there was no just cause for the discharge. Id. at 1439. We vacated the award, concluding that the “bargained-for” LCA “superseded” the CBA’s just cause provision and therefore the arbitrator “did not have authority” to disregard the plain meaning of the LCA’s mandatory termination provision. Id. at 1440-42; accord Boise Cascade Corp. v. Paper Allied-Indus., Chemical and Energy Workers, Local 7-0159, 309 F.3d 1075, 1078, 1085 (8th Cir. 2002), and cases cited. In all of these cases, the bargaining that resulted in an LCA (1) involved the union, and (2) resolved pending disciplinary proceedings governed by the grievance and arbitration provisions of the applicable CBAs.

Here, on the other hand, the Union did not agree to the LCA between Johnson and AECI, and the LCA was the result of a mutual mistake — that Johnson had violated AECI’s drug policy — not the result of pending disciplinary proceedings. The relevant agreement between the Union and AECI was the CBA. It provided that “discharge of employees shall be for just cause,” Art. I, § 6(c); that disputes “over the interpretation or application of [the CBA], or other agreements made between Management and employees ... shall be settled through the grievance procedure,” Art. XII, § 2(a); and that the Union and AECI may submit unresolved grievances to arbitration, Art. XII, § 4(a). Those were the contractual provisions that defined the arbitrator’s authority. Thus, the Union and AECI acted in accordance with the CBA in submitting to the arbitrator whether there was just cause for Johnson’s termination,1 and the arbitrator correctly focused his decision on the just cause issue. This focus did not permit the arbitrator to ignore the LCA, but it did mean he was not contractually bound to apply the LCA’s mandatory termination clause if the evidence persuaded him there was not just cause to do so. See Alvey, Inc. v. Teamsters Local Union No. 688, 132 F.3d 1209, *9031211-13 (8th Cir. 1997); cf. United Steelworkers of Am,., Local No. 1165 v. Lukens Steel Co., 969 F.2d 1468, 1478 (3d Cir. 1992). The situation here is analogous to that in Shop ’N Save Warehouse Foods, Inc. v. United Food & Commercial Workers Int’l Union, Local No. 88, 61 F.3d 632, 634-35 (8th Cir. 1995), cert. denied, 516 U.S. 1113, 116 S.Ct. 912, 133 L.Ed.2d 843 (1996), where the arbitrator did not find that an LCA had been consummated and therefore based his decision “on the limited power he derive[d]” from the CBA. We held that Coca-Cola Bottling was therefore distinguishable, and directed that the arbitrator’s award be enforced.

Where a CBA requires “just cause” to discipline or discharge an employee but fails to define the term, the arbitrator’s broad authority to interpret the contract, to which we must defer, includes defining and applying that term of the contract. See Misco, 484 U.S. at 41, 108 S.Ct. 364; Chauffeurs Local Union No. 878 v. Coca-Cola Bottling Co., 613 F.2d 716, 720-721 (8th Cir.), cert. denied, 446 U.S. 988, 100 S.Ct. 2975, 64 L.Ed.2d 847 (1980). Viewed from this perspective, the arbitrator’s decision to sustain the Union’s grievance must be enforced. The arbitrator found that, because Johnson’s random drug test proved to be negative, he had not violated any work rule and therefore should not have been kept on an LCA. This reasoning finds support in the testimony of AECI’s Senior Human Resources Coordinator: it is AECI’s policy to require a “second chance agreement,” rather than an LCA, if an employee voluntarily admits to violating the drug policy other than on the day of a random drug test. Here, Johnson was presented an LCA because he came forward on the day of his random test. But insisting on an LCA, rather than a less absolute commitment, was premised on a mutual mistake— that Johnson had violated AECI’s drug policy when he reported to work that day. It was within the arbitrator’s just cause discretion to conclude that Johnson’s conduct did not fall within the unyielding remedial terms of the LCA. “It is customary and appropriate for arbitrators to pass upon claims for reformation for mutual mistake, often applying principles more liberal than judicial equity, and upon claims for rescission if the mistake was unilateral and the other party knew and took advantage of it.” IUOE, Local No. 139 v. Carl A. Morse, Inc., 529 F.2d 574, 580 (7th Cir. 1976).

The arbitrator also found that Johnson’s termination was unfair because he was summarily terminated before he returned to work, without an inquiry to explore whether inadvertently taking the wrong prescription benzodiazepine drug was a drug policy violation, and if it was, whether the appropriate discipline was immediate discharge, or an extension of the suspension period until he could pass the return-to-work drug screen. The Union argued to the arbitrator that the plain language of the LCA was not violated because Johnson had not yet returned to work. Had the arbitrator made that explicit finding — well within his authority under Article XII of the CBA — a reviewing court would be required to accept the finding and enforce an award finding no just cause for the discharge. “A mere ambiguity in the opinion accompanying an award, which permits the inference that the arbitrator may have exceeded his authority, is not a reason for refusing to enforce the award.” Enter. Wheel, 363 U.S. at 598, 80 S.Ct. 1358. Because the arbitrator specifically invoked and applied the just cause provision of the CBA, the contract between AECI and the Union that defined his authority, his decision “draws its essence” from the CBA.

For these reasons, the arbitrator’s decision sustaining the Union’s griev*904anee must be enforced. However, the Union and Johnson grieved the discharge, not the suspension. Indeed, grieving the suspension would have been untimely, because Article XII of the CBA provides that a grievance must be filed “within eleven (11) working days from the time that the incident resulting in the grievance occurred.” An arbitrator must stay “within the areas marked out for his consideration,” that is, the issues submitted to him for decision by the parties. Lackawanna Leather Co. v. United Food & Commercial Workers Int’l Union, 706 F.2d 228, 231 (8th Cir. 1983) (en banc) (quotation omitted). Here, the issue submitted to the arbitrator for decision was whether “the employer was justified in discharging the grievant for violating the terms of the last chance agreement” (emphasis added). “A court may vacate a labor arbitration award if the arbitrator exceeds the scope of the submission by ruling on issues not presented to him by the parties.” Id. at 234 (John R. Gibson, J., dissenting), and authorities cited. Accordingly, we decline to enforce the portion of the award granting Johnson back pay from the day he was suspended until the day he was discharged.

The judgment of the district court is reversed, and the case is remanded to the district court with directions to enter final judgment enforcing the arbitrator’s award, as modified in accordance with this opinion.

concurring in the judgment in part and dissenting in part.

The collective bargaining agreement between the parties to this case provides that “[a]ny dispute over the interpretation or application of this Agreement, or other agreements made between Management and employees which can be verified, shall be settled through the grievance procedure” set forth in the CBA. One such “other agreement” is the Last Chance Agreement (“LCA”) between Leo Johnson and Associated Electric Cooperative, Inc. Therefore, when a dispute arose over the interpretation and application of the LCA, the matter was submitted to an arbitrator in accordance with the grievance procedure.

The arbitrator concluded that the LCA was “clearly unconscionable,” defining unconscionability as “an absence of meaningful choice on the part of one of the parties together with contract terms which are unreasonably favorable to the other party.” The arbitrator observed that “the manner in which a contract was entered into may well nullify the contract,” and found that because Johnson had not violated any work rule, “the company had no justification” for presenting Johnson with “an entire page full of command[ments] in the plant manager’s office.” For these reasons, the arbitrator ruled that the LCA was “void,” and that Johnson’s suspension and discharge should be evaluated under the “just cause” limitation that applies to discipline and discharge of employees under the CBA.

Under the limited scope of judicial review, the arbitrator’s decision should be upheld. The issue of the LCA’s unconscionability, and thus its validity, should be decided by an arbitrator and not by this court. It is not for this court to substitute its view that the LCA was “not ‘unconscionable.’ ” Ante, at 901-02. Once the arbitrator declared invalid the LCA and its mandatory termination provision, the arbitrator permissibly determined that there was no “just cause” for Johnson’s discharge. The arbitrator’s award should thus be confirmed.

The first step of the arbitrator’s analysis was a conclusion that the LCA was unconscionable and thus invalid. In the frequently analogous context of commercial arbitration governed by the Federal Arbi*905tration Act, it is well established that a challenge to the validity of an agreement (other than the agreement to arbitrate) is a matter for the arbitrator, not for a court, unless there is clear evidence that the parties intended to withhold the issue of validity from arbitration. The Court established this rule of separability between challenges to the validity of the agreement to arbitrate itself and challenges to the validity of the underlying agreement or other agreements in Prima Paint Corp. v. Flood & Conklin Manufacturing Co., 388 U.S. 395, 406, 87 S.Ct. 1801, 18 L.Ed.2d 1270 (1967), and reiterated it in Southland Corp. v. Keating, 465 U.S. 1, 11, 104 S.Ct. 852, 79 L.Ed.2d 1 (1984), Buckeye Check Cashing, Inc. v. Cardegna, 546 U.S. 440, 444-45, 126 S.Ct. 1204, 163 L.Ed.2d 1038 (2006), and Rent-A-Center, West, Inc. v. Jackson, 561 U.S. 63, 130 S.Ct. 2772, 2779-81, 177 L.Ed.2d 403 (2010). This court recognized the rule in Houlihan v. Offer-man & Co., 31 F.3d 692, 695 (8th Cir. 1994): “[A] claim of fraud in the inducement of the contract generally, because it does not go to the ‘making and performance of the agreement to arbitrate,’ is properly left to arbitration.” See also JLM Indus., Inc. v. Stolt-Nielsen SA, 387 F.3d 163, 170 (2d Cir. 2004) (“Claims of unconscionability and adhesion contracts are similarly included within the Prima Paint rule.”) (internal quotation omitted).

The FAA does not apply directly to this labor arbitration, but “federal courts have often looked to the Act for guidance in labor arbitration cases, especially in the wake of the holding that § 301 of the Labor Management Relations Act [of] 1947 empowers the federal courts to fashion rules of federal common law to govern ‘[s]uits for violations of contracts between an employer and a labor organization’ under the federal labor laws.” United Paperworkers Int’l Union, AFL-CIO v. Misco, Inc., 484 U.S. 29, 40 n. 9, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987) (internal citation omitted). Precedents applying the FAA “employ the same rules of arbitrability that govern labor cases.” Granite Rock Co. v. Int’l Bhd. of Teamsters, 561 U.S. 287, 130 S.Ct. 2847, 2857 n. 6, 177 L.Ed.2d 567 (2010). Not surprisingly, therefore, the Eleventh Circuit in the labor arbitration case of Mulhall v. UNITE HERE Local 355, 618 F.3d 1279 (11th Cir. 2010), deemed it highly likely that disputes over the validity of an agreement between union and employer were to be decided by the arbitrator charged with determining disputes over “the interpretation or application of’ that agreement. Id. at 1292-93. The Third Circuit similarly held that a laborer’s claim that a collective bargaining agreement was unenforceable due to expiration was analogous to a claim challenging a contract’s validity, and was thus a matter for the arbitrator rather than a court. N.J. Bldg. Laborers Statewide Benefits Fund v. Am. Coring & Supply, 341 Fed.Appx. 816, 820 (3d Cir. 2009); see also Int’l Union of Operating Eng’rs, Local Union No. 139 v. Carl A. Morse, Inc., 529 F.2d 574, 578 (7th Cir. 1976) (recounting authority of federal courts to fashion federal common law under the LMRA, and concluding that “[u]nder this judge-made law as well as under the terms of the Arbitration Act, the principle of separability carries equal force”). Indeed, in Shop ’N Save Warehouse Foods, Inc. v. United Food and Commercial Workers International Union, Local No. 88, 61 F.3d 632 (8th Cir. 1995), which the court deems “analogous” to this case, ante, at 902-03, it was the arbitrator, not a court, who decided that a last chance agreement had not been consummated and thus did not govern the relationship between employer and employee. Id. at 635.

The dispute over the unconscionability of Johnson’s LCA is subject to arbitration “unless it may be said with positive assurance that the arbitration clause is not sus*906ceptible of an interpretation that covers the asserted dispute,” with any doubts about arbitrability resolved “in favor of coverage.” AT & T Techs., Inc. v. Commc’ns Workers of Am., 475 U.S. 643, 650, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986). The issue submitted to the arbitrator here — “Was the employer justified in discharging the grievant for violating the terms of a last chance agreement?” — was broad enough to encompass the antecedent question whether the LCA was valid in the first place. See Mulhall, 618 F.3d at 1292-93; ACE Capital Re Overseas Ltd. v. Cent. United Life Ins. Co., 307 F.3d 24, 33-34 (2d Cir. 2002) (agreement to arbitrate disputes “with reference to the interpretation” of the agreement or “with respect to any transaction involved” encompassed claim of fraudulent inducement of the contract generally). The arbitrator thus had authority to determine the validity of the LCA between Johnson and Associated Electric, and a federal court must defer to the arbitrator’s determination as long as the award is not merely the arbitrator’s “own brand of industrial justice.” Misco, 484 U.S. at 36, 108 S.Ct. 364. Even serious error by an arbitrator acting within his authority does not suffice to overturn his decision. Id. at 38, 108 S.Ct. 364.

This arbitrator’s determination of unconscionability is debatable, but the parties bargained for the arbitrator’s judgment. The court’s eonclusory assertion that the LCA was not unconscionable when Johnson and the company entered into it, ante, at 901-02, is not sufficient to justify disregarding the arbitrator’s decision on that point — especially when the court later relies on the arbitrator’s unconscionability rationale that Johnson violated no work rule to conclude that the LCA is unenforceable based on a “mutual mistake.” Ante, at 903.

For these reasons, the arbitrator permissibly looked beyond the mandatory termination clause of the LCA to consider whether there was “just cause” for Johnson’s discharge. Like the court, ante, at 902-04, I conclude that the arbitrator’s determination that there was no “just cause” for termination must be upheld. The arbitrator’s award should thus be confirmed. Associated Electric raised no separate challenge in the district court or in this court to the arbitrator’s award of back pay for the dates between Johnson’s suspension and discharge, so that issue is waived. In any event, the first issue submitted to the arbitrator raised the validity of the Last Chance Agreement and the second issue asked broadly “what should be the remedy” if the employer was not justified in discharging Johnson for violating the LCA. The suspension was premised on the same alleged misconduct that the company cited to justify the LCA. The arbitrator, having found that the LCA was unconscionable and thus invalid, at least arguably acted within the scope of the submission by including a remedy for a suspension that was tied to the LCA. See generally Lackawanna Leather Co. v. United Food & Commercial Workers Int’l Union, 706 F.2d 228, 232 (8th Cir. 1983); cf. John Morrell & Co. v. Local Union 304A of United Food and Commercial Workers, 913 F.2d 544, 561 (8th Cir. 1990) (vacating award where arbitrator was not “even arguably” acting within the scope of the issue submitted).

The company’s purported victory in gaining rejection of the arbitrator’s unconscionability determination may well be Pyrrhic, because the court ultimately rules against the company in part on a broader ground. Concluding that “the Union did not agree to the LCA between Johnson and AECI,” ante, at 902, the court suggests that a last chance agreement is not enforceable by the employer when an em*907ployee waives union representation at the time of the agreement — a broad and unsettled proposition that this arbitrator declined to adopt. See R. Doc. 1-1, Arb. Dec. at 8; cf. Foss Steel Emps. Union v. Foss Steel Corp., No. 92-2068, 16 F.3d 1223, 1994 WL 28610, at *5 (6th Cir. Jan. 31, 1994) (rejecting union’s claim that a last chance agreement was invalid because the union representative did not sign it). Although the court says that an arbitrator cannot “ignore” a last chance agreement signed only by an employer and employee, as a practical matter the court requires the arbitrator to ignore the LCA’s termination provision and apply the “just cause” standard of the CBA as though there were no LCA. It is unnecessary here to reach difficult questions about waiver of union representation. The arbitrator’s award should be sustained as permissible on the narrower grounds set forth in the arbitral decision.