GARLAND, Circuit Judge:

Lee Lumber and Building Material Corporation petitions for review of a National Labor Relations Board (NLRB) decision, while the Board cross-applies for enforcement. The Board held that the company committed several unfair labor practices, including an unlawful refusal to bargain, and ordered it to cease and desist from such practices. We read the scope of the Board's decision as applied to Lee Lumber to be significantly more limited than does the company, and accordingly we do not reach some of the broader points upon which the company requests rulings. We deny Lee Lumber's petition and grant the Board's cross-application for enforcement.

I

Lee Lumber's petition brings this case to us for the second time, twelve years after the events from which it originally arose. In 1997, we reviewed an earlier Board decision that held that the company committed a number of violations of sections 8(a)(1) and (5) of the National Labor Relations Act (NLRA), 29 U.S.C. § 158(a)(1) (5), and that (inter alia) ordered the company to bargain with Carpenter Local No. 1027. Lee Lumber and Building Material Corp. v. NLRB ( Lee Lumber I), 117 F.3d 1454 (D.C. Cir. 1997). We affirmed the Board's decision in all respects but two, and remanded the case for further proceedings. Id. at 1456, 1458. Our earlier opinion sets forth in detail the facts and procedural history that we review here.

A

In October 1988, the NLRB certified Carpenter Local 1027 as the exclusive bargaining representative of petitioner's mill shop employees. The company and the union entered into a collective bargaining agreement that was effective from May 26, 1989, through May 25, 1990. In February 1990, the union informed the company that it wanted to begin negotiating for a renewal contract. Around that time, the employees conducted a straw poll that indicated that a majority still wished to be represented by the union.

Sometime after the poll, two employees prepared and began circulating a petition seeking decertification of the union. A majority of the employees signed the petition, and the company allowed the employees to take paid time off from work to bring the petition to the Board's regional office, notwithstanding the company's general rule against payment for time spent away from work on personal business. It also assisted the employees with transportation and parking expenses. On March 29, the union filed its first unfair labor practice charge against Lee Lumber, alleging illegal assistance to the employees' decertification efforts. On April 11, relying on the pending decertification petition, the company refused to bargain with the union. On May 8, however, after the union filed another unfair labor practice charge alleging an unlawful refusal to bargain, the company agreed to negotiate.

The parties held the first of five bargaining sessions on May 23 and the last on June 25. By the end of those sessions, they had almost reached agreement on a new contract, and had scheduled a sixth session for July 3. On July 2, however, the company received a second petition signed by a majority of employees, this one stating that the group "hereby decertified [the union]." Upon receiving the petition, the company refused to bargain further, and subsequently withdrew its recognition from the union and made unilateral changes in the unit employees' terms and conditions of employment. Thereafter, the union filed additional unfair labor practice charges against the company.

On February 27, 1992, the NLRB issued its initial decision in this matter. 306 NLRB 408, 1992 WL 41348 (1992). The Board found that Lee Lumber violated sections 8(a)(1) and (5) of the NLRA, 29 U.S.C. § 158(a)(1) (5), by providing unlawful assistance to the employees who filed the April decertification petition, by refusing to bargain with the union in April, and by failing to provide the union with requested information. The Board also found that the company violated section 8(a)(5) by again refusing to bargain in July, and by later withdrawing recognition and unilaterally changing the terms and conditions of employment. The Board held that the company could not rely on the employees' July petition as objective evidence of the union's loss of support, because it was tainted by the company's unlawful refusal to bargain in April and by its unlawful assistance to the employees' decertification efforts.

As a remedy, the Board issued an affirmative bargaining order, requiring the company to recognize and bargain with the union. It also ordered the company to resume payments to a union apprenticeship fund, to make the fund whole for past delinquencies, and to post copies of the usual notice acknowledging that the Board found that the company had violated the NLRA and averring that the company would not do so in the future.

Lee Lumber filed a petition for review in this court on March 26, 1992. The NLRB moved to dismiss the petition without prejudice so that it could reconsider, in light of two of our intervening decisions, its positions on the lawfulness of the July withdrawal of recognition and on the appropriateness of an affirmative bargaining order. We granted the Board's motion and, four years later, the Board issued a Supplemental Decision and Order reaffirming its original decision on both issues. 322 NLRB 175, 1996 WL 523011 (1996). The Board held that when an employer unlawfully refuses to recognize or bargain with an incumbent union, and the union subsequently loses majority support, there is a presumption that the employees' disaffection from the union is the result of the employer's unlawful conduct. Absent unusual circumstances, this presumption of taint may be "rebutted only by an employer's showing that employee disaffection arose after the employer resumed its recognition of the union and bargained for a reasonable period of time without committing any additional unfair labor practices that would detrimentally affect the bargaining." Id. at 178 (emphasis added). The Board held that Lee Lumber failed to overcome the presumption because it did not bargain for a reasonable period.

Following issuance of the Supplemental Decision in 1996, the company again petitioned for review in this court. In Lee Lumber I, issued in 1997, we held that the Board's rebuttable presumption of taint, including its "reasonable period of time" requirement, was both "rational" and "consistent with" the NLRA. 117 F.3d at 1459. Noting that "Lee Lumber has raised numerous [other] challenges to the Board's handling of its case," we affirmed the Board "in all respects" save two. Id. at 1462.

First, we held that the Board inadequately explained its application of the reasonable period of time test to Lee Lumber. Although the Board had announced that its determination of what constituted a "reasonable" period would "`not depend on either the passage of time or on the number of meetings between the parties, but instead on what transpired and what was accomplished during the meetings,'" it failed to apply this standard in deciding Lee Lumber's case. Id. (quoting Supplemental Decision, 322 NLRB at 179). Rather, the Board looked primarily at the number of sessions the parties had held and the length of time that had passed, and apparently ignored the considerable progress the parties had made by the time of the break-off in negotiations. We held that the "Board's failure to explain this inconsistency is arbitrary," and "remand[ed] the question to the Board for correction of this flaw." Id. We further suggested that "[o]n remand the Board may also wish to provide a fuller explanation of its `reasonable period of time' standard" because, "[a]s it stands now, it is not entirely clear how any of the . . . factors cut." Id.

Second, we criticized the Board's decision to issue an affirmative bargaining order. Such an order "requires a company to bargain with the union" and "also imposes a `decertification bar' on employees." 117 F.3d at 1460. As a consequence, the "union that is the subject of the bargaining order will continue as the employees' representative, regardless of the employees' wishes, until a `reasonable time' has passed." Id. at 1460-61. We reminded the Board that this circuit has "repeatedly held" that the Board may not impose an affirmative bargaining order unless it "explain[s] why that remedy is appropriate given the facts of that particular case." Id. (citing Caterair Int'l v. NLRB, 22 F.3d 1114, 1123 (D.C. Cir. 1994); Williams Enters., 956 F.2d at 1237; Peoples Gas Sys., Inc. v. NLRB, 629 F.2d 35, 46 (D.C. Cir. 1980)). Since the Board did not make "the particularized findings that our case law requires," we remanded "with instructions to either vacate the order or explain why an affirmative bargaining order is necessary given the facts of this case." Id. at 1462. Moreover, "[w]ithout deciding the issue," we expressed "serious doubt as to how the Board possibly could make a determination that a bargaining order was appropriate on the facts of this case." Id.

B

In June 2001, the Board issued its Second Supplemental Decision and Order, addressing the issues we had remanded. 334 NLRB No. 62, 2001 WL 746722 (2001). Pursuant to our remand, the Board announced that it had reconsidered its "reasonable period of time" standard and had concluded that a new rule was appropriate. Although the Board had not previously required that a "reasonable period of time" be of any minimum length, it now concluded that "an insulated period of a defined length" was necessary and would "provide a measure of certainty that [was] lacking under existing law." Id. at 4. Under the new rule, "when an employer has unlawfully refused to recognize or bargain with an incumbent union, a reasonable period of time for bargaining before the union's majority status can be challenged will be no less than 6 months, but no more than 1 year." Id. at 1. To determine whether the period will be longer than the mandatory six months, the Board said it would employ "a multifactor analysis," using factors "similar to those the Board has been examining for years." Id. at 4. These include:

(1) whether the parties are bargaining for an initial contract; (2) the complexity of the issues being negotiated and of the parties' bargaining processes; (3) the amount of time elapsed since bargaining commenced and the number of bargaining sessions; (4) the amount of progress made in negotiations and how near the parties are to concluding an agreement; and (5) whether the parties are at impasse.

Id.

In discussing these factors individually, the Board addressed the specific concerns raised in our opinion. First, while acknowledging that its prior statements may have been misleading, the Board explained that it had not meant to imply that the passage of time or the number of meetings is irrelevant to whether a reasonable period of time has passed, but simply that those factors are not alone dispositive. 334 NLRB No. 62, at 5. Second, while it reaffirmed its view that the degree of progress toward reaching a contract is a relevant factor, the Board explained that "which way the factor cuts depends on the context." Id. at 6. When "the parties have almost reached agreement and there is a strong probability that they will do so in the near future," the Board said it will view this fact as evidence that a reasonable period of time for bargaining has not yet elapsed. Id. In light of the new six-month mandatory period, however, "if the parties are still not close to reaching a contract after bargaining for 6 months or more (whether or not they have made progress)," this factor will weigh in favor of a conclusion that a reasonable period of time has passed. Id. at 7.

The Board then turned to the facts of this case. It first noted that, because Lee Lumber did not bargain for six months before refusing to bargain with the union in July 1990, the company would have breached the six-month rule had it been applicable. Recognizing that application of the new rule would be retroactive, however, the Board held that even without the six-month rule, a reasonable period of time had not elapsed under the multifactor analysis. Id. The Board noted that the parties had met in only five negotiating sessions over the course of little more than a month, and concluded that this "brief time spent in bargaining, with few bargaining sessions, weigh[ed] heavily against finding that a reasonable time had elapsed." Id. at 8. It also found that the "parties' apparent nearness to concluding a contract, plus the fact that the parties were not at impasse — indeed, they had scheduled another negotiating session for the day after the July petition was presented — strongly demonstrate[d] that additional progress in the near future was a real possibility." Id. Those factors, the Board held, outweighed the countervailing factors: that the parties were not bargaining for an initial agreement, and that the issues and processes were not complex. Accordingly, the Board reaffirmed its earlier conclusions that a reasonable period of time had not elapsed, and that Lee Lumber therefore violated section 8(a)(5) by refusing to bargain, by withdrawing recognition, and by unilaterally implementing changes in the terms and conditions of employment of unit employees.

Finally, the Board reconsidered the question of remedy. It declared that "[a]lthough normally we would issue a bargaining order in a case such as this, given the court's observations [in Lee Lumber I] and the unfortunate delays of the case here at the Board, we recognize that such an order would likely be unenforceable." 334 NLRB No. 62, at 8. Accordingly, the Board limited the remedy "to ordering the Respondent to cease and desist from further unlawful refusals to bargain." Id. While it kept in place the provision of the original order enjoining Lee Lumber from withdrawing recognition from the union, the Board said that provision would remain in effect only until, after complying with the other provisions of the original order, the company "is presented with objective evidence sufficient to warrant its challenging the Union's majority status again." Id.

II

As it did in Lee Lumber I, the company raises numerous challenges to the Board's decision. In Lee Lumber I, however, this court affirmed the Board "in all respects save for (1) its application of its `reasonable period of time' test to the facts of this case, and (2) its issuance of an affirmative bargaining order." 117 F.3d at 1462. Accordingly, many of the company's current challenges, which simply reassert its previous claims, must be dismissed under the law-of-the-case doctrine. These include Lee Lumber's attacks on the Board's presumption that an unlawful refusal to bargain with an incumbent union taints the union's subsequent loss of majority support, and on its determination that employers must bargain for "a reasonable period of time" to remove that taint. Lee Lumber I expressly affirmed these Board holdings. Id. at 1458-60. Also readily dismissed are Lee Lumber's challenges to the Board's determination that the company committed unfair labor practices by refusing to bargain in April 1990 and by refusing to provide the union with requested information, as well as its challenge to the Board's order requiring the company to resume payments to the union apprenticeship fund and to make the fund whole for past delinquencies. All of those arguments were raised in the company's briefs in Lee Lumber I, and were rejected by this court.

The "`[l]aw-of-the-case doctrine holds that decisions rendered on the first appeal should not be revisited on later trips to the appellate court.'" McKesson HBOC, Inc. v. Islamic Republic of Iran, 271 F.3d 1101, 1106 (D.C. Cir. 2001) (quoting Crocker v. Piedmont Aviation, Inc., 49 F.3d 735, 739 (D.C. Cir. 1995)). Accordingly, the only issues left for our decision are the two that we remanded for further consideration in 1997. We consider each of those below.

A

The first issue that remains for review is the lawfulness of the Board's determination that Lee Lumber did not bargain for a reasonable period of time before cutting off negotiations in July 1990. Our role in reviewing the Board's decision is limited. The Supreme Court "has emphasized often that the NLRB has the primary responsibility for developing and applying national labor policy," and that courts therefore must accord its legal rules "considerable deference." NLRB v. Curtin Matheson Scientific Inc., 494 U.S. 775, 787, 110 S.Ct. 1542, 1549, 108 L.Ed.2d 801 (1990). We must "uphold a Board rule as long as it is rational and consistent" with the NLRA, "even if we would have formulated a different rule had we sat on the Board," and "even if it represents a departure from the Board's prior policy." Id. We "review the Board's factual conclusions" only for "substantial evidence," and must "uphold the Board's application of law to facts unless arbitrary or otherwise erroneous." Harter Tomato Prods. Co. v. NLRB, 133 F.3d 934, 937 (D.C. Cir. 1998).

As noted in Part I above, in response to our remand on the reasonable time issue, the Board announced a new rule: "[W]hen an employer has unlawfully refused to recognize or bargain with an incumbent union, a reasonable period of time for bargaining before the union's majority status can be challenged will be no less than 6 months, but no more than 1 year." Second Supplemental Decision, 334 NLRB No. 62 at 1. Lee Lumber asks us to overturn the six-month rule, contending that it operates as a de facto six-month bargaining order and impermissibly interferes with employee free choice. We need not, and indeed cannot, reach the merits of this argument. We need not reach them because, at the same time the Board announced the new six-month rule, it acknowledged that it would be problematic to apply the rule retroactively to Lee Lumber, and held that "even in the absence of" the rule "we would find, under the multifactor analysis, . . . that a reasonable time had not elapsed." Id. at 7-8. Because, as we discuss below, that finding is reasonable on the facts of this case, it is unnecessary for us to consider the merits of the six-month rule.

Moreover, even if the Board had not relied on an independent ground in finding Lee Lumber's refusal to bargain unlawful, we could not reach the merits of the six-month rule because we are without jurisdiction to do so. Under section 10(e) of the NLRA, "[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); see Woelke Romero Framing, Inc. v. NLRB, 456 U.S. 645, 665-66, 102 S.Ct. 2071, 2082-83, 72 L.Ed.2d 398 (1982). Lee Lumber failed to object to the six-month rule below, and there are no extraordinary circumstances that excuse that failure. It is true, of course, that the company could not have challenged the rule prior to the Second Supplemental Decision, since the rule was announced for the first time in that decision. But after the decision was issued, Lee Lumber could have filed a motion for reconsideration, thereby giving the Board an opportunity to consider its arguments. The company's failure to seek Board reconsideration bars our review under section 10(e). See Woelke, 456 U.S. at 666, 102 S.Ct. at 2083 ("Woelke could have objected to the Board's decision in a petition for reconsideration or rehearing. The failure to do so prevents consideration of the question by the courts."); Cobb Mechanical Contractors, Inc. v. NLRB, 295 F.3d 1370, 1378 (D.C. Cir. 2002) ("Even if Cobb could not have made [the] argument before issuance of the Board decision, its failure to move to reconsider (or reopen the record) bars it from raising the issue on appeal.").

Lee Lumber's attack on the Board's finding under its multifactor analysis, by contrast, is not barred by section 10(e). The relevance and applicability of the various factors that compose that analysis were issues raised below and directly addressed by the Board. But while we have jurisdiction to consider the company's arguments, we reject them on their merits. We conclude that the Board adequately answered the concerns we raised in remanding the case, and hold that its finding that a reasonable period of time had not passed was neither arbitrary nor unsupported by substantial evidence.

In making that finding, the Board first noted that the company had cut off bargaining after little more than a month, and that during that month the parties had held only five bargaining sessions. This "brief time spent in bargaining, with few bargaining sessions, weigh[ed] heavily against finding that a reasonable time had elapsed." Second Supplemental Decision, 334 NLRB No. 62, at 8. Acknowledging that its comments on this subject in its first Supplemental Decision may have been misleading, the Board explained that the weight it placed on the passage of time and number of meetings accurately reflected its precedents. Id. at 5 n. 37. We cannot say that the Board's reading of those decisions is unreasonable. Nor can we say that it is arbitrary for the Board — in applying a test aimed at determining whether "a reasonable period of time has elapsed" — to consider the actual period of time that did elapse and the number of meetings that took place during that time.

Also relevant to the Board's finding was the "parties' apparent nearness to concluding a contract, plus the fact that the parties were not at impasse — indeed, they had scheduled another negotiating session for the day after the July petition was presented." Id. at 8. These factors, the Board said, "strongly demonstrate[d] that additional progress in the near future was a real possibility" and that a reasonable period of time had not yet passed. Id. Again, the Board cited numerous precedents that were consistent with its explanation of the role of the proximity-to-agreement factor, while recognizing that two others could be viewed as inconsistent; to the extent that the two were inconsistent, the Board overruled them. And again, the Board's reading of its own cases is not unreasonable. Moreover, without commenting on the merits of the Board's approach in general, at least in this case, where so little time had passed and so few bargaining sessions had taken place, we conclude that it was not arbitrary for the Board to take into consideration the fact that the employer withdrew recognition from the union just as an agreement appeared to be in hand.

In announcing its decision, the NLRB explained that the factors in its multifactor analysis "must be considered together," and that "none is dispositive individually or necessarily entitled to special weight." 334 NLRB No. 62, at 7. The central question, the Board said, "is whether the union has had enough time to prove its mettle in negotiations, so that when its representative status is questioned, the employees can make an informed choice, without the taint of the employer's prior unlawful conduct." Id. This analytic approach is neither facially unreasonable nor inconsistent with the NLRA. As we said in Lee Lumber I, the Board's presumption of taint "supports employee free choice because it prevents an employer from `pointing to an intervening loss of employee support for the union when such loss of support is a foreseeable consequence of the employer's unfair labor practice.'" 117 F.3d at 1459 (quoting Fall River Dyeing Finishing Corp. v. NLRB, 482 U.S. 27, 51 n. 18, 107 S.Ct. 2225, 2240 n. 18, 96 L.Ed.2d 22 (1987)). Moreover, since the Board's approach is fact-specific, we need not consider hypotheticals about the logic of its application to other situations. Because we have no warrant for disputing the Board's expert judgment that, on the facts of this case, the union did not have "enough time to prove its mettle," we are bound to uphold the Board's determination.

B

The second issue we must consider is the lawfulness of the NLRB's order that Lee Lumber cease and desist from refusing to bargain with the union. The company contends that the cease and desist order, combined with the new rule that an employer must bargain for at least six months to dissipate the taint of an unlawful refusal to bargain, "is effectively a per se bargaining order for six months in every case, irrespective of the facts." Pet'r Br. at 21. As Lee Lumber understands the Board's order in this case, it must bargain with the union for at least six months, during which time the union is insulated from any challenge to its majority status. Such a remedy, the company contends, contravenes Lee Lumber I's instruction "to either vacate the order or explain why an affirmative bargaining order is necessary given the facts of this case." 117 F.3d at 1462.

We need not decide whether an order like that described by Lee Lumber would be permissible, as the company plainly misunderstands the nature of the order that the NLRB has issued. The Board did state that "normally we would issue a bargaining order in a case such as this." Second Supplemental Decision, 334 NLRB No. 62, at 8. But it also noted this court's critical observations in Lee Lumber I, as well as "the unfortunate delays of the case here at the Board," and concluded that "rather than engender more litigation and further delay over the propriety of a bargaining order, we will limit our remedy to ordering the Respondent to cease and desist from further unlawful refusals to bargain." Id. Although the Board "retain[ed] the provision of the [original] Order enjoining the Respondent from withdrawing recognition from the Union," it made clear that the provision would remain effective only until, after complying with "the other provisions of the Order," the company is "presented with objective evidence sufficient to warrant its challenging the Union's majority status again." Id. (citing Levitz, 333 NLRB No. 105 (2001)). Contrary to Lee Lumber's assumption that it must continue to bargain for six months regardless of whether the union loses the support of a majority of the employees, the Board expressly recognized that its "cease and desist remedy will not ensure that the Respondent will recognize and bargain with the Union for a reasonable period of time." Id. (emphasis added).

In its briefs and at oral argument, the Board confirmed this reading of the remedial order. According to Board counsel, the order bars Lee Lumber from challenging the union's majority status only until the company posts the required notice to employees and makes the required payments to the apprenticeship fund — the "other provisions of the Order" referred to in the portion of the Second Supplemental Decision quoted above. Thereafter, Lee Lumber may challenge the union under the Board's generally applicable standards. In short, because the employer can challenge the union's majority status when presented with sufficient objective evidence, and "the employees can petition for decertification at any time," Williams Enters. v. NLRB, 956 F.2d 1226, 1237-38 (D.C. Cir. 1992), the Board is correct that "this is the kind of remedial order that has been endorsed, and distinguished from affirmative bargaining orders, by the court of appeals," Second Supplemental Decision, 334 NLRB No. 62, at 8-9 (citing Williams Enters., 956 F.2d at 1237). We do so again today.

III

For the foregoing reasons, we deny Lee Lumber's petition for review and grant the Board's cross-application for enforcement.