LIPEZ, Circuit Judge.

This case requires us to decide whether a decision rendered by the National Labor Relations Board (NLRB or Board) after a *104 remand from a decision of this court is consistent with that decision. Goodless Electric Company (Goodless) was first accused of unfair labor practices in 1994 when it refused to recognize a union for collective bargaining purposes. An administrative law judge exonerated Goodless, but the Board reversed his decision. We reversed the Board, ruled that the Board’s precedents required a finding in favor of Goodless, and remanded the case to the Board for proceedings consistent with that decision. Misinterpreting that decision and its mandate, the NLRB once again decided on remand that Goodless had violated the law. We again reverse.

Before beginning the discussion, we must establish a shorthand notation for three of the four decisions that have previously addressed this ease. An administrative law judge decided in favor of Goodless Electric Company, concluding that it had not engaged in unfair labor practices. The NLRB reversed this decision in Goodless I. Goodless Elec. Co., Inc., 321 NLRB 64, 1996 WL 233230 (1996) (Goodless I). 1 We reversed the Board in Goodless II, and remanded the case for “proceedings in accordance with this opinion.” NLRB v. Goodless Elec. Co., 124 F.3d 322, 331 (1st Cir.1997) (Goodless II). Upon remand, the NLRB again decided against Goodless in Goodless III, the decision under review. Goodless Elec. Co., Inc. (Supplemental Decision and Order), 332 NLRB No. 96, 2000 WL 1675503 at *1 (2000) (Goodless III).

A. Legal Background

A union must usually demonstrate majority support among an employer’s employees in order to enter a collective bargaining agreement with an employer. However, in the construction industry, the short-term nature of the employment and the contractor’s need for predictable costs and a steady supply of skilled labor makes such arrangements impractical. Thus, “[cjollective bargaining agreements in the construction industry are commonly negotiated before the employees are hired because employers must be able to fix labor costs to make bids, and have a supply of skilled craftsmen ready for quick referral.” Timothy Volk, Prehire Agreements in the Construction Industry, 9 J.L. & Com. 243, 245 (1989). In response to this industry practice, Congress passed Section 8(f) of the National Labor Relations Act in 1959. 29 U.S.C. § 158(f). This portion of the Act provided that construction industry employers may recognize unions prospectively. Id. Specifically, Section 8(f) provides:

It shall not be an unfair labor practice ... for an employer engaged primarily in the building and construction industry to make an agreement covering employees engaged ... in the building and construction industry with a labor organization of which building and construction employees are members ... because (1) the majority status of such labor organization has not been established ... or (2) such agreement requires as a condition of employment, membership in such labor organization ....

Id.

As we explained in Goodless II, “[ujnder Section 8®, a construction industry employer may enter into a relationship with a union whereby the union bargains on behalf of the employer’s employees pri- or to a showing that the union has gar *105 nered the support of a majority of the employees.” Goodless II, 124 F.3d at 323. A Section 8(f) employer-union relationship is known as a “prerecognition agreement;” the employer does not formally recognize the union, but only agrees to bargain with it for a limited period of time. The union may obtain more permanent collective bargaining rights if it can convert the Section 8(f) relationship into a Section 9(a) relationship. Section 9(a) provides for a traditional collective bargaining agreement, whereby

Representatives designated or selected for the purposes of collective bargaining by the majority of the employees in a unit appropriate for such purposes, shall be the exclusive representatives of all the employees in such unit for the purposes of collective bargaining in respect to rates of pay, wages, hours of employment, or other conditions of employment. ...

29 U.S.C. § 159(a). “Under Section 9(a), once a union has become the representative of a majority of the employees in an appropriate bargaining unit, the employer is required to bargain with the union as the employees’ bargaining representative.” Goodless II, 124 F.3d at 324.

Unions are often eager to convert a Section 8(f) relationship into a more permanent Section 9(a) relationship. The precise requirements for converting a Section 8(f) into a Section 9(a) relationship have been delineated in many NLRB precedents:

The NLRB has held that Section 8(f) status may change to Section 9(a) status by virtue of either a Board-certified election or as the result of the employer’s voluntary recognition of the union as the majority collective bargaining agent. Voluntary recognition requires the union’s unequivocal demand for, and the employer’s unequivocal grant of, voluntary recognition as the employees’ collective bargaining representative based on the union’s contemporaneous showing of majority employee support.

Id. (citing James Julian, Inc., 310 NLRB 1247, 1252 (1993)). This case concerns a dispute over whether Goodless voluntarily recognized Local No. 7 of the International Brotherhood of Electrical Workers (the Union).

B. Factual Background

The background facts of the case are essentially undisputed. They have been summarized in Goodless II, 124 F.3d at 323-27, and are developed at length in the findings of fact appended to the NLRB administrative law judge’s original decision in the case. See Goodless I, 321 NLRB at 70-92. We review only their basic outline here.

Goodless and the Union established a Section 8(f) relationship in 1988, from which either Goodless or the Union could withdraw upon giving 150 days notice. By 1990, the economy in the region began to falter and Goodless sought relief from certain provisions of the agreement in order to keep its business competitive. In June, 1992, Goodless indicated to the Union that “any relationship between Goodless and the Union would expire as of June 30, 1993.”

The next month, the Union threatened to cut off “target money” to Goodless if it failed to sign a “letter of assent” affirming its Section 8(f) relationship. 2 The letter included the following language:

The Employer agrees that if a majority of its employees authorize the Local Union to represent them in collective bar *106 gaining, the Employer will recognize the Local Union as the NLRA [National Labor Relations Act] Section 9(a) collective bargaining agent for all employees performing electrical construction work within the jurisdiction of the Local Union on all present and future jobsites.

Leon Goodless signed the letter on behalf of Goodless on July 15,1992.

Almost a year later, Goodless and the Union discussed the possibility of extending Goodless’s Section 8(f) relationship with the union beyond the original June 30, 1993 termination date. When negotiations stalled, the Union’s business agent, Douglas Bodman, held a meeting of all Goodless employees. He encouraged them to “sign authorization cards as evidence of their desire for continued representation,” and all did so. The cards stated:

I authorize Local Union No. 7 of the International Brotherhood of Electrical Workers to represent me in collective bargaining with my present and future employers on all present and future job-sites within the jurisdiction of the Union. This authorization is non-expiring, binding and valid until such time as I submit a written revocation.

Goodless II, 124 F.3d at 325. Bodman presented the cards at Goodless’s next meeting with Union representatives on June 25, 1993. Although Leon Goodless reacted angrily to the presentation of the cards, he later consented to a six-month extension of bargaining with the Union, agreeing to continue the 8(f) relationship from July 1, 1993, to December 31, 1993.

At the end of 1993, Goodless again indicated its desire to terminate its relationship with the Union. The Union responded (via letter) on December 21, 1993, claiming that the letter of assent signed on July 15, 1992, bound Goodless to recognize the Union as the exclusive bargaining agent if a majority of its employees authorized the Union to represent them in collective bargaining. The Union claimed to have demonstrated majority support at the June 25, 1993, meeting, and therefore alleged that Goodless could neither repudiate its collective bargaining relationship with the Union nor negotiate directly with its employees.

Goodless ignored the letter and ceased recognizing the Union for collective bargaining purposes as of January 1, 1994. Contending that it had achieved Section 9(a) status, the Union complained to the NLRB that Goodless had engaged in unfair labor practices. 3

As noted, the Administrative Law Judge who first heard the case ruled in favor of Goodless. See Goodless I, 321 NLRB at 91-92. In Goodless I, the Board reversed that decision and decided that the Union became the Section 9(a) bargaining representative of Goodless’s employees when it presented the signed cards to Leon Good-less. In Goodless II, we reversed the Board and found that Goodless was not guilty of any unfair labor practices. We remanded the case to the Board for proceedings consistent with Goodless II. In the decision under review, Goodless III, the Board again found that Goodless had committed unfair labor practices.

*107 II.

In deciding whether our decision in Goodless II permitted the Board’s decision in Goodless III, we first explain briefly the law of the case doctrine. We next summarize the law of this case as set forth in Goodless II. We then explain the Board’s flawed understanding of that law in Good-less III.

A. The Law of the Case

The doctrine of the law of the case “posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case.” Arizona v. California, 460 U.S. 605, 618, 103 S.Ct. 1382, 75 L.Ed.2d 318 (1983). This rule of practice promotes finality and judicial efficiency by “protecting against the agitation of settled issues.” Christianson v. Colt Indus. Operating Corp., 486 U.S. 800, 816, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988) (quoting IB J. Moore, J. Lucas & T. Currier, Moore’s Federal Practice ¶ 0.404[1] at 118 (1984)). When an appellate opinion clearly addresses a disputed issue, it “instructs an inferior [tribunal] to comply, with [this decision] on remand.” Field v. Mans, 157 F.3d 35, 40 (1st Cir.1998). An appellate court’s mandate controls all issues that “ ‘were actually considered and decided by the appellate court, or as were necessarily inferred from the disposition on appeal.’ ” Cohen v. Brown Univ., 101 F.3d 155, 188 (1st Cir.1996) (quoting Commercial Union Ins. Co. v. Walbrook Ins. Co., 41 F.3d 764, 770 (1st Cir.1994)).

Although the Board adheres to a policy of nonacquiescence 4 in its application of decisions of the courts of appeals, it recognizes as it must that it cannot ignore the law of the case doctrine. Indeed, in Good-less III, the Board said that, “[h]aving accepted the court’s remand, we are bound by the law of the case established in the court’s opinion.” Goodless III, 332 NLRB No. 96, 2000 WL 1675503, at *4.

B. The Law of This Case

In reversing the Administrative Law Judge’s finding that Goodless had committed no unfair labor practices, the Board decided that the Union became the Section 9(a) bargaining representative of Good-less’s employees when it presented the signed cards to Leon Goodless on June 25, 1993. Finding that “the letter of assent [signed by Leon Goodless on July 15,1992] constituted, for the remainder of its term, both a continuing request by the Union for 9(a) recognition and a continuing, enforceable promise by [Goodless] to grant voluntary recognition on that basis if the Union demonstrated majority support,” Goodless I, 321 NLRB at 66, the Board concluded that the Union had demonstrated majority support contemporaneously with Good-less’s recognition because the letter signaled Goodless’s continuing willingness to recognize the Union whenever it had majority support among Goodless’s workers. *108 The Board ordered Goodless to recognize the Union and to take several remedial measures.

On appeal, we determined “that the NLRB misapplied its own precedent.” Goodless II, 124 F.3d at 327. We found that “Board case law ... has set forth only two means by which a union may obtain Section 9(a) status during the course of a Section 8(f) relationship: (1) through a Board-certified election, or (2) through the employer’s voluntary grant of recognition” in accordance with the standards enunciated in cases such as J & R Tile, Inc. v. Bricklayers and Allied Craftsmen, 291 NLRB 1034, 1036, 1988 WL 214248 (1988), and Golden West Electric, 307 NLRB 1494, 1495, 1992 WL 183678 (1992). Goodless II, 124 F.3d at 328-29. We explained that the Board’s decision to treat the July, 1992 letter of assent as an open offer to grant Section 9(a) recognition was an unwarranted attempt to rely on technical principles of contract law to supplant the requirement “that recognition be based on a contemporaneous showing of majority support.” Id. at 330.

Thus, in Goodless II we held that “Good-less did not violate Section 8(a)(5)” in refusing to recognize the union. Id. at 331. We announced that “a finding in favor of Goodless is required.” Id. at 330. We ended the opinion with the following order: “For the foregoing reasons, we reverse and remand to the National Labor Relations Board for proceedings in accordance with this opinion.” Id. at 331.

C. The Board’s Decision on Remand (Goodless III)

On remand, the Board again found that Goodless had engaged in unfair labor practices. The Board asserted that “a union’s performance of the valid majoritarian conditions specified in a prospective 9(a) recognition clause ... is, in effect, a third option, in addition to the ‘two option[s]’ that the court identified as the only available options for achieving 9(a) status.” Goodless III, 332 NLRB No. 96, 2000 WL 1675503 at *7 (quoting Goodless II, 124 F.3d at 330). Although the Board acknowledged that “the Board’s construction industry precedent at the time of the events at issue made no express provision for agreements like the one contained in the parties’ 1992 letter of assent,” Id. at *5, the Board supported its third option by discussing precedents from “outside the construction industry” which upheld the validity of prospective recognition agreements. Id. at *5-*6 (discussing Snow & Sons, 134 NLRB 709 (1961); Kroger Co. v. Retail Clerks Local No. 455, 219 NLRB 388, 389, 1975 WL 5788 (1975)).

Despite the Board’s reliance on these other precedents, the Board’s reasoning in Goodless I and Goodless III is structurally identical: in both decisions, the Board focused on the legal significance of the letter of assent that Goodless signed on July 15, 1992. Goodless I held that the letter constituted a standing offer to recognize the union because of basic contract law principles; Goodless III stated that the letter was equivalent to a “prospective recognition agreement” upheld by the Board in settings outside the construction industry, id. at *6. Both decisions are at odds with Goodless II’s central holding: “Voluntary recognition requires the union’s unequivocal demand for, and the employer’s unequivocal grant of, voluntary recognition as the employees’ collective bargaining representative based on the union’s contemporaneous showing of majority employee support.” See Goodless II, 124 F.3d at 324 (citing James Julian, Inc., 310 NLRB 1247, 1252, 1993 WL 148961 (1993)).

Having acknowledged that it must comply with the law of the case, the Board had to explain why its “freedom of action on *109 remand,” Goodless III, 332 NLRB No. 96, 2000 WL 1676503 at *4, permitted it to reach the same result for different reasons. That explanation began with the Board’s assertion that we misapprehended in Goodless II the true significance of the Board’s precedents:

Board precedent, if read literally, as the court did, appeared to require that a union’s demand for 9(a) recognition, the employer’s agreement to recognize the union, and the union’s showing of majority status must all be simultaneous.

Id. at *4 (citing Goodless II, 124 F.3d at 328-29). To disabuse us of this literal reading, the Board said that it could clarify on remand the true scope of its precedents because “the court stated [in Goodless 17] that it could not accept the Board’s departure from precedent ‘in the absence of some cogent explanation, an explanation that has not been forthcoming,’ ” id. at *7 (quoting Goodless II, 124 F.3d at 330-31). The Board took this language as an invitation to reinstate its earlier ruling on remand, provided that it developed a “cogent explanation” for its decision.

As further support for its freedom of action on remand, the Board noted that Goodless II cited Shaw’s Supermarkets, Inc. v. NLRB, 884 F.2d 34 (1st Cir.1989), “a case in which the court, as here, also remanded and in which the Board clearly was not foreclosed from reaffirming its prior decision provided it adequately explained why it was departing from precedent.” Goodless III, 332 NLRB No. 96, 2000 WL 1676503, at *8 (citing Shaw’s Supermarkets, Inc., 303 NLRB 382, 1991 WL 113270 (1991) (on remand)). 5 Finally, the Board parsed the language of our order at the end of Goodless II, where we wrote: “For the foregoing reasons, we reverse and remand to the National Labor Relations Board for proceedings in accordance with this opinion. Costs to respondent.” Goodless II, 124 F.3d at 331 (emphasis in original). In the Board’s view, “[i]f the court’s intent were merely to vacate the Board’s prior Order and to dismiss the complaint, there would have been no need to remand the case.” Goodless III, 332 NLRB at *7.

Other than a prohibition against saying that it was right in Goodless I for all of the reasons disapproved by us in Goodless II, the Board concluded that there was no law of the case that constrained its freedom of action on remand. It could simply reaffirm the result with a different rationale that met the “cogent explanation” standard. Addressing the three reasons cited by the Board for its authority to reaffirm its finding of unfair labor practices by Goodless, we explain why the Board’s reading of our decision in Goodless II is indefensible.

1. The Shaw’s Litigation

In Shaw’s I, the Board found that Shaw’s Supermarkets had committed unfair labor practices. We vacated that decision in Shaw’s II, finding that the Board’s precedents “dictate a result in Shaw’s favor” since Shaw’s conduct “lies tucked well within the boundary of the lawful.” Shaw’s II, 884 F.2d at 36, 41. On remand, we permitted the Board “to modify or change its rule; to depart from, or to keep *110 within, prior precedent, as long as it focuses upon the issue and explains why change is reasonable.” Shaw’s II, 884 F.2d at 41. The Board saw no need to change its law:

We respectfully decline the court’s invitation to change extant Board law. For, with due respect to the court, we continue to believe that, under that law, conduct like that involved herein is unlawful. However, given the law of this case, we shall dismiss the complaint.

Shaw’s III, 303 NLRB at 382; see also, e.g., Camvac Int’l, Inc., 302 NLRB 652, 653 (1991) (“Having accepted the Sixth Circuit’s remand as law of the case, we are bound by the Court’s rationale as it applies to this proceeding, and we cannot overlook the specifics of the court’s directive.”); Memorial Hosp. of Roxborough, 231 NLRB 419 (1977) (stating that “we recognize our acceptance of the court’s decision on remand as binding on us for the purpose of deciding this case”). In other words, the Board recognized in Shatv’s III that the one option it did not have on remand was declaring Shaw’s conduct unlawful under extant law after we had decided otherwise. That recognition eluded the Board in Goodless III. 6

2. The Remand

In our order at the end of Good-less II, we did not simply remand to the Board. We reversed and remanded. Although we are not suggesting that the word “reversed” has been used in court orders with unvarying meaning, we deem it significant here that the word “reverse” is defined to mean, inter alia, “to alter to the opposite in character or tendency; change completely.” Random House Webster’s Unabridged Dictionary 1647 (2d ed. 1997). The opposite result is a finding in favor of Goodless, not another finding against it on different grounds. By contrast, we did not use in our order the word “vacate,” which means “to render inoperative; deprive of validity; void; annul.” Id. at 2100. An order to vacate only wipes the slate clean, leaving the next outcome uncertain, absent other direction. We left no uncertainty about the proper outcome here.

Moreover, we reversed and remanded to the Board “for proceedings in accordance with this opinion.” Goodless II, 124 F.3d at 331. In that opinion, we concluded that “[u]nder the plain terms” of Board precedents, “a finding in favor of Goodless is required.” Id. at 330. We added that “Goodless did not violate Section 8(a)(5) by repudiating that relationship or by unilaterally changing the terms and conditions of employment under the circumstances of this appeal.” Id. Further proceedings before the Board that contravene these explicit holdings in favor of Goodless are hardly “in accordance with [our] opinion” in Goodless II.

If that is so, the Board says, why bother to remand to us if we could only dismiss the complaint against Goodless? Goodless III, 332 NLRB No. 96, 2000 WL 1675503, at *7. There are at least two answers, both of which reflect respect for Board procedures. If there were ancillary issues before the Board that needed to be addressed in conjunction with the dismissal of the complaint, the remand would have given the Board the opportunity to address them. Furthermore, our decision in Goodless II gave the Board the opportunity on remand to dismiss the claim against *111 Goodless while announcing that, henceforth, its new construction of the contemporaneity requirement would govern this area of labor law. See NLRB v. Majestic Weaving Co., 355 F.2d 854, 859 (2d Cir.1966) (permitting the Board, “after appropriate proceedings, [to] ... fashion for prospective application a principle along the general lines of that adopted here”). However, the Board could not reverse our holding in Goodless II by declaring that we had misapprehended Board precedent and then reasserting its unfair labor practices finding against Goodless.

3. “Some Cogent Explanation”

After concluding in Goodless II that “a finding in favor of Goodless is required,” we added that “[w]e cannot accept the Board’s departure from its own precedent in this case in the absence of some cogent explanation, an explanation that has not been forthcoming.” Goodless II, 124 F.3d at 330-31. Read literally in a spirit of nonacquiescence, and isolated from the rest of the text, this language might embolden the Board to find an invitation for a cogent explanation that would make the finding against Goodless acceptable to us. Read fairly with fidelity to the principles of the law of the case recognized by the Board in Shaw’s III, this language precluded an unfair labor practices finding against Goodless on the basis of extant law.

III. Conclusion

In its effort to find “freedom of action on remand,” Goodless III, 332 NLRB No. 96, 2000 WL 1675503, at *4, the Board focused on isolated language from Goodless II to justify its renewed unfair labor practice findings against Goodless. In fact, the Board has chosen to ignore our earlier ruling and disregard the law of the case. Goodless II stated unequivocally that “a finding in favor of Goodless is required.” Goodless II, 124 F.3d at 330. We reversed Goodless I, further confirming that conclusion. We now reverse Goodless III, with an explicit instruction that the Board dismiss the charges against Goodless.

So ordered. Costs to respondent.

. The decision of the administrative law judge is reported as an appendix to Goodless I, 321 NLRB at 70-92.

. "Target money was financial assistance provided by the Union to aid union employers in competition with non-union electrical contractors.” Goodless II, 124 F.3d at 325 n. 4.

. Specifically, the Union charged that Good-less violated two sections of the National Labor Relations Act. See 29 U.S.C. § 158(a)(5) (providing that "It shall be an unfair labor practice for an employer ... to refuse to bargain collectively with the representatives of his employees....”); 29 U.S.C. § 158(a)(3) (providing that "It shall be an unfair labor practice for an employer ... by discrimination in regard to hire or tenure of employment or any term or condition of employment to encourage or discourage membership in any labor organization....”).

. Nonacquiescence refers to the "selective refusal of administrative agencies to conduct their internal proceedings consistently with adverse rulings of the courts of appeals.” Samuel Estreicher & Richard L. Revesz, No-nacquiescence by Federal Administrative Agencies, 98 Yale L.J. 679, 681 (1989). The National Labor Relations Board, "more than most [agencies], has openly asserted the authority to decline to acquiesce.” Id. at 706. The Board is committed to pressing its own view of the law until the Board itself or the Supreme Court overrules it; it claims that piecemeal acceptance of particular circuits’ interpretations of the law would frustrate its development of a national labor policy. Id. at 706 (citing Insurance Agents' Int’l Union, 119 N.L.R.B. 768, 773 (1957)). However, the Board does "acquiesce[] to [an appellate court's] treatment of a particular case on remand.” Id. at 706 n. 148.

. For purposes of this opinion, the Shaw’s cases will be referred to as follows:

Shaw's I: Original NLRB decision.

Shaw’s II: Our decision vacating Shaw’s I and remanding it back to the NLRB for reconsideration (Shaw’s Supermarkets, Inc. v. NLRB, 884 F.2d 34, 35 (1st Cir.1989)).

Shaw’s III: Decision of the NLRB on remand (Shaw’s Supermarkets. Inc., 303 NLRB 382, 1991 WL 113270 (1991) (Supplemental Decision and Order)).

. The Board argues on appeal that Shaw’s II also gave it the option of conceding, with an adequate explanation, that it was departing from precedent in finding Shaw's conduct an unfair labor practice, and then reaffirming its prior decision. Whether that is an accurate reading of Shaw’s II is irrelevant here. In this case, the Board insists that it did not depart from precedent on remand. Instead, it insists that it only clarified extant law.