OPINION

ALICE M. BATCHELDER, Circuit Judge.

Truck Drivers Local No. 164 (“Union”) appeals from the district court’s grant of summary judgment in favor of Allied Waste Systems, Inc. (“Allied”), which vacated an arbitrator’s award ordering reinstatement of Grievant Keith Miller (“Miller”). On appeal, the Union argues that the district court erred in vacating the arbitrator’s award. At oral argument, both parties agreed that this case is directly impacted by our recent en banc decision in Michigan Family Resources, Inc. v. Service Employees International Union, 475 F.3d 746, 752-53 (6th Cir.2007), which held that courts are without authority to overturn an arbitrator’s award so long as *213 the arbitrator was “arguably construing or applying the contract and acting within the scope of his authority.” Id. After carefully reviewing the arbitrator’s decision and the parties’ arguments, we find that the arbitrator was faithfully attempting to construe and apply the terms of the collective bargaining agreement, that the arbitrator was acting within the scope of his authority, and that the district court lacked legal authority upon which to vacate the arbitrator’s award. We accordingly REVERSE the district court’s decision and REMAND with instructions to reinstate the arbitrator’s award and for further proceedings consistent with this opinion in regard to the Union’s demand for additional back pay.

Allied is engaged in the business of collecting and disposing of nonhazardous solid waste, and the Union represents Allied’s employees at its Adrian, Michigan, location. Allied acquired its Adrian, Michigan, facilities from Laidlaw Waste Services in 1999, and for a few years after this acquisition, Allied and the Union operated under the predecessor collective bargaining agreement negotiated between Laidlaw and the Union. In May 2003, the Union and Allied entered into a new agreement, which borrowed in large part from the language of the predecessor agreement.

Several provisions of the May 2003 agreement are relevant to our review of the arbitrator’s award. Article 18 of that agreement reserves management rights to Allied, stating:

“Except as expressly and specifically limited or restricted by a provision of this Agreement, the Company has and shall retain the full right of management and direction of the Company and its operations. Such rights and responsibilities of management include, but are not limited to, the right ... to discharge and otherwise discipline employees for just cause.”

Article 8 governs the employer’s right to discharge or suspend employees. Section 8.1 states that “[t]he right to discharge and the maintenance of discipline shall be the exclusive right and responsibility of the Company except that the Company shall not discharge or otherwise discipline an employee without just cause.” Section 8.2 prescribes the allowable discipline for a violation of the “Company’s Mandatory Safety and Work Rules” — distinguishing between a violation of Section 1 of those rules, which permits Allied to discharge the employee immediately, and a violation of Section 2 of those rules, which requires Allied to give the employee at least one warning notice prior to discharge.

Article 9 governs the arbitration and grievance procedures. Section 9.4 outlines the process and procedures by which arbitration is to be conducted, and Sections 9.4(D), 9.4(F), and 9.4(G) define the scope of the arbitrator’s power. Section 9.4(D) states:

[T]he arbitrator shall have no power or authority to amend, alter[,] or modify this Agreement, but shall be limited to deciding whether or not a violation of its expressed terms has been committed. ... The arbitrator shall have no power to substitute his discretion for that of the Company in cases where the Company has retained discretion or the right to act under this Agreement.

Section 9.4(F) provides:

The decision of the arbitrator ... shall be final and binding upon the parties when rendered upon a matter within the authority of the arbitrator and within the scope of the matters subject to arbitration provided in this Agreement, and shall be void insofar as the decision ex *214 ceeds the authority of the arbitrator or passes upon matters not expressly made subject to arbitration under the terms of this Agreement.

And most relevant to this dispute, Section 9.4(G), states: “It is understood and agreed that the degree of discipline up to and including discharge imposed for just cause shall be in the sole discretion of management and shall not be subject to modification by an arbitrator.” The agreement also contains a “zipper clause,” which states that the terms of the enacted agreement “shall supersede and render ineffective any past practices, addendum, letters of understanding, oral or written agreement as may now exist or as may have existed.”

On April 4, 2005, Allied employee and Union bargaining-unit member, Keith Miller, drove a garbage collection route normally assigned to another driver. While backing his truck down the left lane of a dead-end residential street, Miller “hooked” a low-hanging overhead wire, pulling it from a nearby house. Miller immediately informed dispatch of this incident; Allied supervisors arrived on the scene and completed a “Notice Form” summarizing the accident. The supervisors observed that Miller was backing down the wrong side of the street, that Miller violated Allied’s “Zero Tolerance Safety Guidelines,” and that Miller violated Allied’s “Employee Safe Driving and Safe Practices.”

On the same day as the accident, Allied suspended Miller without pay pending further investigation. On the following day, Allied terminated Miller because, according to Allied, he violated a rule in Section 1 of the Company’s Mandatory Safety and Work Rules, which permitted immediate discharge under Section 8.2 of the collective bargaining agreement. Two days later, Miller filed a grievance, contending that he did not violate a Section 1 rule and, consequently, that Allied should reinstate him with back pay. Within a week, the company denied Miller’s grievance, and the parties proceeded to arbitration.

At arbitration, the parties vehemently disputed which set of rules comprised the “Company’s Mandatory Safety and Work Rules” referenced in Section 8.2 of the agreement. The parties conceded that during negotiation of the current agreement, neither side brought up Section 8.2, which was the primary cause of this contractual ambiguity. Allied argued that it had been using two sets of rules — the “Employee Safe Driving and Safe Practices” handbook and the “Zero Tolerance Safety Guidelines” — and that these rules were the ones referenced in Section 8.2 of the agreement. The Union contended that the applicable rules were those that were actually entitled “Mandatory Safety and Work Rules” and were attached to the predecessor agreement. The arbitrator sided with the Union, reasoning that Allied’s proposed rules had “a different nomenclature than in [Section 8.2 of the agreement] and they ha[d] a different structure — i.e., no Section 1 or Section 2.” After determining that the Union’s proposed rules applied, the arbitrator concluded that Miller’s conduct violated Section 2 of those rules — not Section 1 as alleged by Allied — and that the collective bargaining agreement required Allied to give Miller at least one warning notice prior to discharge.

The arbitrator then analyzed Miller’s termination assuming that Allied’s proposed rules applied. The arbitrator reasoned that even those rules contemplate degrees of discipline and do not automatically mandate discharge. For example, the Employee Safe Driving and Safe Practices handbook permits “disciplinary action up to and including immediate discharge,” *215 and the Zero Tolerance Safety Guidelines state that Allied generally will conduct “progressive discipline” but that an employee will be immediately discharged if his improper conduct causes an “accident.” After acknowledging these degrees of discipline, the arbitrator determined that even though Miller violated some of Allied’s proposed rules, his termination was inappropriate because this “incident involved an accident only in an obviously hypertechnical sense: the telephone lines had drooped far below standards, and [Allied] incurred no loss as a result of the incident.” The arbitrator, in short, determined that Miller’s discharge was unwarranted under either the Union’s or Allied’s proposed rules.

Allied cautioned the arbitrator that the collective bargaining agreement severely circumscribed his authority to review or modify the reasonableness of Miller’s discipline, emphasizing Section 9.4(G)’s admonition that “the degree of discipline ... imposed for just cause shall be in the sole discretion of management and shall not be subject to modification by an arbitrator.” The arbitrator, however, perceived an internal tension between Section 9.4(G), which, according to Allied, limited the arbitrator’s authority to review or modify the degree of discipline imposed by management, and Section 8.1, which prohibited Allied from disciplining an employee without just cause. The arbitrator attempted to reconcile this tension, reasoning:

The term “just cause” entails a two-prong inquiry. First, did the Grievant violate an Employer rule or policy which warrants discipline? If the answer to the first is in the affirmative, it is then necessary to consider whether the discipline imposed is reasonable under the circumstances of the matter before the Arbitrator. The severity of the discipline is an integral part of the inquiry.

The arbitrator concluded that because the just-cause inquiry required him to consider the reasonableness of a grievant’s discipline, the agreement implicitly authorized him to evaluate the severity of Miller’s discipline.

The arbitrator then proceeded to his resolution of the grievance, reiterating that Miller had violated Section 2 of the Union’s proffered rules as well as various provisions of Allied’s proffered Employee Safe Driving and Safe Work Practices handbook. The arbitrator made two distinct findings regarding just cause. First, he held that Allied lacked just cause to terminate Miller because termination was not “reasonable” and it “exceeded the penalty allowed” in Section 8.2 of the agreement. Second, he found that Allied had just cause to issue a written warning to Miller because Section 8.2 of the agreement permitted a warning notice for a violation of Section 2 of the Mandatory Safety and Work Rules. The arbitrator’s award stated: “The Grievant’s termination is set aside and, in lieu thereof, a Written Warning may be issued. The Grievant is to be reinstated to his former position with back pay and benefits.... ”

Approximately two weeks later, the Union filed suit in district court, seeking to compel Allied to comply with the arbitrator’s decision, and asking for additional back pay for the period following the arbitrator’s award. Allied filed its answer and counterclaim, asking the court to vacate the arbitrator’s award. The parties filed cross-motions for summary judgment. The district court denied the Union’s motion, granted Allied’s motion, and vacated the arbitrator’s decision. The court rejected the arbitrator’s conclusion that the rules referenced in Section 8.2 were the “Mandatory Safety and Work Rules” proposed by the Union, rather than the two sets of rules presented by Allied. The *216 court reasoned that because the Union’s proffered rules were part of the prior collective bargaining agreement, the zipper clause, which stated that the new agreement would supersede any past practices or agreements, voided the application of those rules. The court then, apparently relying on Section 9.4(G) of the agreement, held: “[I]n altering the discipline that was given to Miller, the arbitrator exceeded the scope of his authority, and, in doing so, he violated the express terms of the Collective Bargaining Agreement.” The Union filed a motion for reconsideration pursuant to Fed.R.Civ.P. 59(e), which was denied by the district court, and the Union filed a timely notice of appeal to this court.

II.

Although we review the district court’s grant of summary judgment de novo, Gage Prods. Co. v. Henkel Corp., 393 F.3d 629, 637 (6th Cir.2004), our review of the underlying “labor-arbitration decision[ ] is ... very limited,” Mich. Family Res., 475 F.3d at 752 (quotations and citations omitted); see Tenn. Valley Auth. v. Tenn. Valley Trades and Labor Council, 184 F.3d 510, 514-15 (6th Cir.1999) (“[0]ur review of an arbitration award is one of the narrowest standards of judicial review in all of American jurisprudence.”) (quotations omitted). This circuit recently refined the scope of judicial review over labor-arbitration awards, holding that we will consider only the questions of “procedural aberration” outlined by the Supreme Court in United Paperworkers International Union v. Misco, Inc., 484 U.S. 29, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987), and Major League Baseball Players Association v. Garvey, 532 U.S. 504, 121 S.Ct. 1724, 149 L.Ed.2d 740 (2001). See Mich. Family Res., 475 F.3d at 753. The three questions of procedural aberration ask: (1) “Did the arbitrator act ‘outside his authority’ by resolving a dispute not committed to arbitration?”; (2) “Did the arbitrator commit fraud, have a conflict of interest[,] or otherwise act dishonestly in issuing the award?”; and (3) “[I]n resolving any legal or factual disputes in the case, was the arbitrator ‘arguably construing or applying the contract’?” Id. “So long as the arbitrator does not offend any of these requirements, the request for judicial intervention should be resisted even though the arbitrator made serious, improvident[,] or silly errors in resolving the merits of the dispute.” Id. (quotations omitted).

At the outset, we note that the district court did not have the benefit of our recent decision in Michigan Family Resources. The parties, however, did, but their briefs do not discuss the case, although they both acknowledged at oral argument that it directly impacts the issues before this court. The parties have therefore failed to raise their arguments in terms of the three questions of procedural aberration. Moreover, the Union curiously framed most of its arguments as a challenge to the district court’s reasoning, rather than focusing on the analysis in the arbitrator’s decision. In a situation such as this, where we are reviewing de novo the district court’s decision to vacate an arbitrator’s award, the focus is on the arbitrator’s analysis, not that of the district court. We will recast the parties’ arguments, placing the proper focus on the arbitrator’s decision and the analytical approach outlined in Michigan Family Resources.

Under even the most generous reading of Allied’s brief, it does not allege that the arbitrator engaged in fraud, labored under a conflict of interest, or otherwise acted dishonestly; thus we need not consider this sort of procedural aberration. But Allied’s arguments impact the remaining two questions — whether the arbitrator ex *217 ceeded his authority and whether the arbitrator was arguably construing or applying the contract — and we will consider both of these issues.

We begin with the question of whether the arbitrator exceeded his authority in issuing his decision. Allied argues that the arbitrator exceeded his authority by modifying Miller’s discipline from a termination to a written warning because the collective bargaining agreement prohibited the arbitrator from modifying the severity of the discipline imposed. This argument certainly implies that the arbitrator exceeded the scope of his authority under the agreement, but in Michigan Family Resources we severely curtailed the “scope of authority” concept. In that case, we stated: “An arbitrator does not exceed his authority every time he makes an interpretive error; he exceeds that authority only when the collective bargaining agreement does not commit the dispute to arbitration.” Mich. Family Res., 475 F.3d at 756 (emphasis added). Therefore, even though Allied’s argument implies that the arbitrator exceeded the scope of his authority, this argument — because it does not challenge whether the agreement “commit[ted] the dispute to arbitration” — is better characterized as a challenge to the arbitrator’s interpretation. Allied does not argue that this dispute — i.e., a grievance challenging a bargaining-unit member’s termination— was not properly before the arbitrator; Allied could not in good faith assert such an argument because it is clear that the agreement commits this sort of dispute to arbitration. Section 8.1 prohibits Allied from “discharging] or otherwise disciplining] an employee without just cause,” and Section 9.4(D) authorizes the arbitrator to “deeid[e] whether or not a violation of [the] expressed terms [of the agreement] has been committed.” In light of this express, unambiguous contractual language, we find that the arbitrator was not operating outside the scope of his authority as prescribed in the agreement, and his decision cannot be overturned on that basis.

We next consider whether the arbitrator was arguably construing and applying the agreement, or whether he ignored the terms of the agreement and “dispense[d] his own brand of industrial justice.” See United Steelworkers of Am. v. Enter. Wheel & Car Corp., 363 U.S. 593, 597, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960). We must resist the temptation to overturn an arbitration decision merely because, in our opinion, the arbitrator made “serious, improvident, or silly” legal or factual errors. Mich. Family Res., 475 F.3d at 753. “[I]n most cases, it will suffice to enforce the award that the arbitrator appeared to be engaged in interpretation, and if there is doubt we will presume that the arbitrator was doing just that.” Id. It will only be in the “most egregious” cases where we find that the arbitrator was not arguably construing or applying the contract; his interpretation must be “so untethered to” the terms of the agreement that it casts doubt on whether he in fact was engaged in interpretation. Id.

At arbitration, the parties disputed which work rules were referenced in Section 8.2 of the collective bargaining agreement. The arbitrator reasoned that the Union’s rules must apply because Section 8.2 refers to a set of rules divided into two sections and only the Union’s rules were divided in that manner. The district court objected to the arbitrator’s adoption of the Union’s rules, concluding that the Union’s rules, which were originally attached to the predecessor collective bargaining agreement, were superseded under the zipper clause in the current agreement. Even if we were to agree with the district *218 court and conclude that the arbitrator incorrectly determined that the Union’s rules were those referenced in Section 8.2, 1 we find this to be a classic instance of labor-contract interpretation. “It is the arbitrator’s construction which was bargained for; and so far as the arbitrator’s decision concerns construction of the contract, the courts have no business overruling him because their interpretation of the contract is different from his.” Enter. Wheel & Car Corp., 363 U.S. at 599. The arbitrator was indisputably construing the contract; he acknowledged that Section 8.2 discussed a set of rules divided into two sections and reasonably concluded that the Union’s rules fit that description better than the two sets of rules proffered by Allied. Because it is clear that the arbitrator was construing the contract— whether correctly or incorrectly — the arbitrator’s adoption and application of the Union’s rules does not provide a legally sufficient basis for vacating his award. See Misco, 484 U.S. at 38, 108 S.Ct. 364.

The major issue in this case — indeed, the primary basis upon which the district court vacated the arbitrator’s award — is whether the arbitrator’s award violated Section 9.4(G) of the agreement. Section 9.4(G) states that “the degree of discipline ... imposed for just cause shall be in the sole discretion of management and shall not be subject to modification by an arbitrator.” Allied implored the arbitrator to recognized that Section 9.4(G) prohibited him from even considering — not to mention altering — the level of discipline imposed against Miller. The arbitrator, however, determined that Section 9.4(G) could not be read so broadly because such an expansive reading conflicted with other contractual provisions that expressly and unambiguously prohibited Allied from “discharging] or otherwise disciplining] an employee without just cause.” The arbitrator reasoned that the just-cause inquiry required him first to evaluate whether the grievant violated a work rule and then “to consider whether the discipline imposed [was] reasonable under the circumstances.” He thus concluded that, notwithstanding Allied’s expansive reading of Section 9.4(G), the collective bargaining agreement authorized him to consider the degree of discipline imposed by Allied.

Following arbitration, Allied thought that the arbitrator had violated Section 9.4(G) in another way, namely, by modifying the degree of discipline imposed after he expressly found just cause to discipline Miller (i.e., issue a written warning). The district court agreed, finding that “the arbitrator ... violated the express terms of the [collective [bargaining [a]greement” by “altering the discipline that was given to Miller.” Allied contends that Section 9.4(G) clearly prohibits the arbitrator from modifying the degree of discipline whenever he finds that any degree of discipline (e.g., written warning, suspension, termination) would be supported by just cause. Thus, according to Allied, the arbitrator violated Section 9.4(G) because once he found just cause to issue a written warning, he was without authority to modify the degree of discipline selected by Allied (i.e., termination).

*219 The Union argues that Allied’s broad interpretation of Section 9.4(G) conflicts with Section 8.2 of the agreement. Section 8.2 prescribes the allowable discipline for an employee’s violation of the Mandatory Safety and Work Rules — distinguishing between a violation of Section 1 of those rules, which permits Allied to discharge the employee immediately, and a violation of Section 2 of those rules, which requires Allied to give the employee at least one warning notice prior to discharge. The Union contends that Allied’s construction of Section 9.4(G) effectively negates Section 8.2’s distinction in the level of allowable discipline for different work-rule violations by stripping the arbitrator of authority to enforce that distinction. For example, an arbitrator who found, as the arbitrator here did, that the grievant violated a Section 2 rule, rather than a Section 1 rule, would be prohibited from reducing the grievant’s discipline to a written warning, even though Section 8.2 of the agreement expressly states that Allied is permitted to impose only a written warning against a first-time offender of those rules. The Union argues that Section 9.4(G) cannot be interpreted in a manner that effectively nullifies Section 8.2. In essence, then, the Union believes that 9.4(G), as properly understood, restricts the arbitrator’s authority to modify the degree of discipline only where he finds that the particular degree of discipline actually imposed by the employer was supported by just cause. Under this interpretation, the arbitrator here did not violate Section 9.4(G) because he found no just cause to support Miller’s termination (i.e., the particular degree of discipline actually imposed by the employer) and therefore was not limited by Section 9.4(G)’s purported restriction on his authority.

We find that Section 9.4(G) is no2 clear on its face and that it can reasonably be interpreted as urged by either Allied or the Union. 2 More importantly, the arbitrator, when construing the limitations on his authority in Section 9.4(G) (although he did so in response to a slightly different argument), was indisputably construing and applying the contract. “He referred] to, quote[d] from[,] and analyze[d] the pertinent provisions of the agreement, and at no point [did] he say anything indicating that he was doing anything other than trying to reach a good-faith interpretation of the contract.” See Mich. Family Res., 475 F.3d at 754. Based on his reasonable interpretation of the agreement, the arbitrator believed that he had authority to review the severity of Miller’s discipline, declare Miller’s termination to be without just cause, and reduce Miller’s discipline to a written warning. Regardless of whether we agree with the arbitrator’s precise interpretation, we lack authority to overturn his decision because it is clear that he was “arguably construing and applying” an unclear contractual provision. See Misco, 484 U.S. at 38, 108 S.Ct. 364. We therefore find no basis upon which to vacate the arbitrator’s award. 3

*220 We acknowledge that, by including Section 9.4(G) in the agreement, Allied attempted to “limit the arbitrator’s authority to fashion a remedy by careful drafting of the collective bargaining agreement.” See Kar Nut Prods. Co. v. Int’l Bhd. of Teamsters, No. 92-2084, 1993 WL 304467, at *3 (6th Cir. August 10, 1993). Cf. Eberhard Foods, Inc. v. Handy, 868 F.2d 890, 892 (6th Cir.1989) (“There is nothing ... in the [collective bargaining agreement] or work rules which expressly limits or removes from the arbitrator the authority to review the remedy in this case.”). Despite this attempt to restrict the arbitrator’s authority, Allied did not draft Section 9.4(G) with sufficient precision, leaving it unclear and in tension with other provisions in the agreement. Therefore, while it is true that parties to a collective bargaining agreement can limit an arbitrator’s authority, they will succeed in doing so only to the extent that they produce a clearly crafted, internally consistent agreement. Allied has failed to do so here.

III.

The Union requests that we award Miller back pay from the date of the arbitrator’s award until the date of Miller’s eventual reinstatement, which, at least as of the date of oral argument in this matter, had not yet to occurred. See Lynchburg Foundry Co. v. United Steelworkers of Am., Local 2556, 404 F.2d 259, 262 (4th Cir.1968) (stating that “the employee is entitled to reinstatement and compensation for the period following the [arbitrator’s award]”). Allied argues that the first sentence in Section 9.4(G) of the collective bargaining agreement — a portion of that section we have yet to address — prevents our making any such award. That sentence provides:

Should it be determined that an employee, other than probationary employee was disciplined or discharged without just cause, he shall be restored to his former status; provided, however, that the arbitrator shall not award back pay for a period exceeding ninety (90) days and provided further that the Company shall have the right to credit against any back pay awarded any earnings, compensation, or enumeration [sic] received by the employee from any source whatsoever including unemployment compensation and worker’s [sic] compensation payments during the period involved.

Miller was discharged on April 5, 2005, and the arbitrator ordered him reinstated on August 31, 2005. The arbitrator’s award stated that “[Miller] is to be reinstated to his former position with back pay and benefits subject to the limitations found in Article 9.4(G).” Pursuant to the limitations on back pay in Article 9.4(G), Miller would have received back pay for only 90 of the more than 145 days between his discharge and the arbitrator’s decision. Allied further argues, citing Yamaha Int’l Corp. v. United Furniture Workers of America, AFL-CIO, 892 F.2d 80, 1989 WL 153964 (6th Cir.1989) (unpublished), 4 that, even if the CBA permitted the award of *221 additional back pay, we lack the authority to award such relief.

In Yamaha I, the arbitrator awarded the union grievant reinstatement without back pay and Yamaha filed an action in the district court to vacate the award. The district court ordered the award enforced, and additionally ordered back pay from the date of the award' to the date of the district court’s entry of judgment. The Union’s brief on appeal included a request to enlarge the district court’s judgment to include back pay for a period subsequent to the district court’s order; we affirmed the district court but did not address the Union’s request. See Yamaha Int’l Corp. v. United Furniture Workers of America, 842 F.2d 334, 1988 WL 23685, at *1(6th Cir.l988)(unpublished). After the mandate had issued on our opinion, the Union filed a motion in the district court to include back pay for the period after the district court’s order; the district court denied the motion — which it denominated a Rule 60(b)(6) motion — because it believed that the issuance of the mandate precluded the court from addressing its merits. On appeal, we concluded that the district court had correctly viewed the motion as one brought under Rule 60(b)(6), but that the court was not barred from considering the motion on its merits, and we remanded for the court to do just that. See id. at * 1-2. On remand, the district court denied the motion, and the Union appealed. We affirmed, noting that Yamaha had neither posted a supersedeous bond nor sought to stay the district court’s order when it appealed, and that the Union “at all times had the right or opportunity to require Yamaha to reinstate [the griev-ant], but chose, for whatever reason, not to exercise that course of action.” Yamaha II, 1989 WL 1539649 at *2. Further, we observed, the Union had not attempted to obtain a rehearing in the court of appeals. Because a Rule 60(b)(6) motion “should only be granted in exceptional or extraordinary circumstances which are not addressed by the other clauses of Rule 60(b),” id., and the Union had failed to protect its rights through any of the procedures available to it, we found that the Union had not demonstrated any such circumstances, and the district court had not abused its discretion in denying the motion. Taken together, Yamaha I and Yamaha II — at least implicitly — indicate that back pay from the date of an arbitrator’s award until the date of reinstatement may be an appropriate remedy.

More recently, this issue was addressed in Mansfield Plumbing Prod. v. Teamsters, Chauffeurs & Helpers Local Union No. 10, 2005 WL 3544085 (N.D.Ohio, 2005), a case whose facts — although considerably more complicated than those before us here — similarly raise the issue of whether additional back pay is a permissible judicial remedy. In that case, Mansfield had terminated the employee, and, although the arbitrator ordered reinstatement, Mansfield instead terminated the employee again, on grounds different from those on which it had terminated him the first time. This second termination also went to arbitration, and resulted in a different arbitrator’s reversing the termination and ordering reinstatement in accordance with the first reinstatement order. The second arbitrator did not award any back pay beyond that ordered by the first arbitrator. During the pendency of the second arbitration, Mansfield filed suit to vacate the first arbitration award, and the Union counterclaimed, seeking, among other things, additional back pay. Prior to the district court’s ruling in that case, Mansfield filed suit to vacate the second award, and again, the Union counterclaimed. The district court ordered the first award enforced but did not mention additional back pay. Mansfield reinstated the grievant, *222 dismissed its action to vacate the second arbitrator’s award, paid the grievant 120 days’ back pay (the CBA limited back pay awardable by an arbitrator to 120 days), but did not pay any additional back pay. The Union then sought summary judgment on its counterclaim in the second action for additional back pay.

The district court separated into several discrete periods the time for which the Union sought additional back pay and held — for reasons not material to the instant case — that it was without jurisdiction to award additional back pay for all but one of them. The court held, however, that additional back pay was appropriate for the four-month period from the second arbitration award ordering reinstatement until the actual reinstatement of the griev-ant. The district court summed up the situation before it and sensibly held that

[e]ven though Mansfield was challenging both arbitration orders in this court, it was legally obligated to reinstate and pay Martin. It did not do so. To hold otherwise would [ ] provide a great incentive for employers to challenge every arbitration decision virtually cost-free, since even if they lost, they would be saved from paying wages for the pen-dency of the appeal.

Id. at *7. In reaching its conclusion, the district court also held that

[a]n award of back pay for the four months between the second arbitration decision and reinstatement does not go beyond the terms of the CBA, as Mansfield contends. To the contrary, back pay is consistent with and directly results from the CBA.... If an award is to be final and binding, the employer is required to reinstate the employee and pay him. If they fail to reinstate him, they remain obligated to pay him, unless the arbitration award is overturned by a court of law.

Id.

We think that Mansfield is correctly decided, 5 and for the reasons stated by the district court in that case, we conclude, first, that the language on which Allied relies in Article 9.4(G) of the CBA here limits only the arbitrator’s ability to award back pay, and does not limit the ability of the court to do so. We further conclude that additional back pay from the time of an arbitrator’s reinstatement award until the time that a grievant is reinstated is an appropriate judicial remedy. Finally, however, because we do not have before us the necessary facts to determine the amount of the back pay due to Miller, we must remand this matter to the district court for further proceedings consistent with this opinion.

IV.

For the foregoing reasons, we REVERSE the order of the district court granting summary judgment to Allied and REMAND to the district court with instructions to reinstate the arbitrator’s award, and for the limited purpose of calculating the appropriate award of back pay.

. Although it is not necessary to our resolution of this suit, we do not agree with the district court’s analysis on this issue. The zipper clause is inapplicable when determining which rules should apply under Section 8.2. The rules referenced in Section 8.2— whichever set of rules the arbitrator determines those to be — have been expressly incorporated into the new agreement and therefore are not superseded as provided in the zipper clause. The arbitrator recognized that the zipper clause did not impact this analysis, and we agree with his conclusion.

. Counsel for Allied, in what may have been a "Freudian slip," acknowledged at oral argument that Section 9.4(G) "maybe is a little bit ambiguous,” and later stated, in complete contradiction, that "there is no ambiguity” because this provision consists of “plain language.” As counsel for the Union aptly recognized, however, Allied cannot "have it both ways,” and, given these alternatives, we con-elude that there is some ambiguity in Section 9.4(G).

. Allied also contends that the arbitrator’s decision should be vacated because he improperly reduced Miller’s discipline based on "general considerations of fairness and equity instead of the precise terms of the agreement.” See Cement Divs., Nat'l Gypsum Co. v. United Steelworkers, Local 135, 793 F.2d 759, *220 766 (6th Cir.1986). This "fairness and equity’’ inquiry derives from the four-part Cement Divisions test, which we overruled in Michigan Family Resources, 475 F.3d at 753, and is no longer germane to the analysis the court must undertake in determining whether to enforce or vacate an arbitrator’s award. Thus this argument — grounded as it is in terms of fairness and equity — can no longer carry the day.

. This case came before us on several occasions. For ease of reference, we refer to Yamaha Int’l Corp. v. United Furniture Workers of America, 842 F.2d 334 (6th Cir.1988) as Yamaha I, and Yamaha Int’l Corp. v. United Furniture Workers of America, AFL-CIO, 892 F.2d 80 (6th Cir.1989) as Yamaha II.

. We note with some concern the district court's apparent misunderstanding of the result we reached in Yamaha II. but we note as well that this error did not affect the district court’s overall analysis.