The Office of Personnel Management (“OPM”) and the Nuclear Regulatory Commission (“NRC”) (collectively “petitioners”) challenge decisions of the Federal Labor Relations Authority (“FLRA” or the “Authority”) declaring that proposals of the American Federation of Government Employees, Local 32 and the National Treasury Employees Union are negotiable. The Authority has submitted cross-applications for enforcement of its orders. Petitioners assert that the Authority applied the wrong legal standard in these decisions and that even if the Authority used the proper test that it misapplied that test. Because the FLRA applied the law of this case and reconciled its treatment of these proposals with FLRA precedent and because petitioners waited until this case had been decided *327three times by the FLRA and twice by this Court and was before this Court for the third time before pressing these arguments, we deny the petitions for review and grant the cross-applications for enforcement.
I. Background
Intervenors, the American Federation of Government Employees, Local 32 (“AFGE”) and the National Treasury Employees Union (“NTEU”), submitted for collective bargaining with the petitioning agencies proposals defining “competitive area.” As we explained in our previous opinions in these cases,
a competitive area is simply a grouping of employees within an agency, according to their geographical or organizational location, who compete for job retention when a particular position is abolished or some other adverse action constituting a RIF [reduction in force] is imposed. In such circumstances, an employee holding the affected position may be able to prevail over less senior or less qualified employees who hold different positions but are within the same competitive area.
AFGE, Local 32 v. FLRA, 853 F.2d 986, 988 (D.C.Cir.1988) (“Local 32 II”) (footnote omitted). The AFGE proposed the following definition: “The Competitive Area shall be the Washington Metropolitan Area.” AFGE, Local 32, and OPM, 14 FLRA 754 (1984) (“AFGE-FLRA I”), remanded, 774 F.2d 498 (D.C.Cir.1985) (“Local 32 I”), on remand, 22 FLRA 478 (1986) (“AFGE-FLRA II”), remanded, Local 32 II, 853 F.2d 986, on remand, 33 FLRA 335 (1988) (“AFGE-FLRA III”). The NTEU proposed that “commuting area” be used “as the area of competition____” NTEU and NRC, 20 FLRA 172 (1985) (“NTEU-FLRA I”), remanded, No. 85-1749 (D.C.Cir. Jan. 22, 1986) (unpublished order), on remand, 22 FLRA 707 (1986) (“NTEU-FLRA II”), remanded, Local 32 II, 853 F.2d 986, on remand, 33 FLRA 400 (1988) (“NTEU-FLRA ///”). In both AFGE-FLRA I and NTEU-FLRA I the FLRA held that because the proposals would affect nonbargaining unit employees the petitioning agencies were not required to bargain over competitive areas.
In AFGE-FLRA I, the Authority considered its earlier decision in Association of Civilian Technicians, Pennsylvania State Council and Pennsylvania Army and Air National Guard, 14 FLRA 38 (1984) (“ACT”). In ACT the Authority had required bargaining over a competitive area proposal. The proposal in ACT had stated that “[n]on-bargaining unit technicians will not compete with bargaining unit technicians for bargaining unit positions.” ACT, 14 FLRA at 38. The FLRA had held the proposal in ACT negotiable, stating that a proposal directly affecting conditions of unit employment and otherwise lawful was within the duty to bargain notwithstanding that it would affect nonunit employees. Id. at 39. In AFGE-FLRA I the Authority distinguished ACT as involving a proposal that did not affect nonunit employees because it limited the competitive area to the bargaining unit. NTEU-FLRA I reached the same result without discussing ACT.
The unions petitioned this Court for review of both AFGE-FLRA I and NTEU-FLRA I. In Local 32 I, reviewing AFGE-FLRA I, we found unconvincing the Authority’s attempt to distinguish ACT. Noting the inconsistency with the ACT decision, we remanded the case to the Authority. We directed the Authority to “provide a reasoned explanation for any failure to adhere to its own precedents,” Local 32 I, 774 F.2d at 502, and suggested that it consider the standard applied in private sector cases involving the negotiability of proposals affecting nonbargaining unit members. Id. at 503-04 (citing the “vitally affects” test of Allied Chemical & Alkali Workers of America, Local Union No. 1 v. Pittsburgh Plate Glass Co., Chemical Division, 404 U.S. 157, 92 S.Ct. 383, 30 L.Ed.2d 341 (1971)). We remanded NTEU-FLRA I without decision shortly thereafter.
On remand the Authority again held in both AFGE-FLRA II and NTEU-FLRA II that the proposals were not negotiable. This time the FLRA announced a balancing *328test to determine whether proposals affecting the conditions of employment of nonunit employees are negotiable. The Authority stated that it would determine
whether the nature and degree of the impact of the proposal is so intrinsically related to the working conditions of non-unit employees so as to invade the purview of other unit representatives or require the agency to act in a way that will have a significant effect on the rights of employees not represented by the union offering the disputed proposal.
AFGE-FLRA II, 22 FLRA at 482. The Authority stated that in determining whether a proposal that affects conditions of employment of nonunit employees is negotiable, the Authority would “balance the right of the union to negotiate over the conditions of employment of bargaining unit employees and the right of the agency to set the conditions of employment of non-bargaining unit employees.” Id. The Authority concluded that ACT was consistent with this balancing test because ACT “would have directly determined the competitive area only for bargaining unit positions and employees.” Id. at 485. In NTEU-FLRA II the FLRA followed its AFGE-FLRA II decision and rationale.
AFGE-FLRA II and NTEU-FLRA II, and two other cases were consolidated and petitions for review were brought in this Court. In our second consideration we found the Authority again unsuccessful in explaining how its rulings comported with ACT. The Authority had again distinguished ACT, holding that the ACT proposal (defining competitive area as the bargaining unit) had not implicated interests of nonunit employees. We found this explanation unconvincing. The proposal in ACT surely had a significant effect on non-unit employees. The definition of a competitive area affects the interests both of employees included within the competitive area and those excluded from it by expanding or limiting both the positions for which employees may compete in a RIF and the class of persons with whom an employee will compete for job retention. The proposal may have benefited the nonunit employees by insulating them from challenge by unit employees or it may have harmed them by limiting the number of positions for which they could compete if their jobs were being eliminated, but the definition would affect the interests of nonunit employees. We found that the Authority had again failed to “articulate an intelligible rationale for determining when an impact on nonunit employees precludes mandatory bargaining over a competitive area proposal” and directed the Authority to consider the private sector’s “vitally affects” standard as discussed in Pittsburgh Plate Glass Co., Chemical Division, 404 U.S. at 179, 92 S.Ct. at 397, and other cases. “Under that standard, the expert adjudicator inquires only whether vital interests of unit employees would be affected by a given proposal, and permits bargaining over such proposals without regard to the potential effect on nonunit employees.” Local 32 II, 853 F.2d at 993.
On the second remand in both cases the Authority adopted the private sector “vitally affects” test to determine whether there is a duty to bargain over proposlls that affect employees outside the bargaining unit. In both cases the Authority limited its examination to the interests of the unit employees and concluded that the proposals vitally affected the interests of unit employees and that thus the proposals were within the duty to bargain.
II. Analysis
Petitioners now challenge the Authority’s decisions. Although parties before the Authority, petitioners did not intervene in either of the prior petitions for review of these cases. Petitioners’ primary challenges to the Authority’s decisions are that the Authority was in error to apply the “vitally affects” test and that if that test was appropriate the FLRA misapplied it in these cases. The history and posture of these cases demonstrate that we need not again consider the applicability of the “vitally affects” test.
A. Law of the Case
By holding that the proposals were within the duty to bargain, the FLRA has *329answered this Court’s primary concern: that the decisions not requiring negotiation were inconsistent with the FLRA’s decision in ACT. Holding that the proposals in these cases “vitally affect[ed] the working conditions of employees in the bargaining unit,” the Authority ordered negotiation and achieved a result consistent with its decision in ACT. AFGE-FLRA III, 33 FLRA at 338, NTEU-FLRA III, 33 FLRA at 402. Consequently the concern that motivated our remands in the first two decisions has been fulfilled. The FLRA has satisfied the instructions we gave.
Petitioners' challenge is to the Authority’s use of the “vitally affects” test. Petitioners concede, as they must, that our-prior decisions in this case strongly counseled the FLRA to apply the “vitally affects” test. Having held that the Authority previously acted improperly by deciding these cases in a manner inconsistent both with its own earlier cases and with the private sector negotiability standard, we cannot now entertain an objection that the Authority should be reversed for following our instructions.1
The doctrine of the law of the case counsels against our issuing new instructions to the FLRA at this point in the development of this controversy. “If there is an appeal from the judgment entered after remand, the decision on the first appeal establishes the law of the case to be followed on the second.” 1 B J.W. Moore, Moore’s Federal Practice 110.404[1], at 119 (1988 & Supp. 1989).
This laudable and self-imposed restriction is grounded upon the sound public policy that litigation must come to an end. An appellate court cannot efficiently perform its duty to provide expeditious justice to all “if a question, once considered and decided by it were to be litigated anew in the same case upon any and every subsequent appeal.” Not only does the doctrine promote judicial efficiency but it also discourages “panel shopping” at the circuit level, for in today’s climate it is most likely that a different panel will hear subsequent appeals.
Lehrman v. Gulf Oil Corp., 500 F.2d 659, 662 (5th Cir.1974), cert. denied, 420 U.S. 929, 95 S.Ct. 1128, 43 L.Ed.2d 400 (1976). See also Laffey v. Northwest Airlines, Inc., 740 F.2d 1071, 1091-92 (D.C.Cir.1984).
B. Participation of Petitioners
Petitioners raise their challenge to the use of the “vitally affects” test for the first time in the present petitions. Although petitioners participated in these cases at the Authority, initially and following both remands, petitioners filed briefs with the Authority only in the initial negotiability decisions. Petitioners’ Brief at 14 n. 3. Petitioners did not intervene in either of the two earlier petitions for review of these cases. More importantly, petitioners never sought leave to file additional materials or to amend their briefs before the Authority. Petitioners at no time objected to the Authority that the Authority should not apply or that it incorrectly applied the “vitally affects” test.
This failure does not merely counsel against our reconsidering the “vitally affects” test, as the law of the case doctrine does; it deprives us of jurisdiction. This Court’s jurisdiction to hear petitions for review of the FLRA is conferred by 5 U.S.C. § 7123, which states that “[n]o objection that has not been urged before the Authority or its designee, shall be considered by the court, unless the failure or neglect to urge the objection is excused because of extraordinary circumstances.” The Supreme Court has held that a court of appeals is without jurisdiction to consider an issue not raised before the Authority. EEOC v. FLRA, 476 U.S. 19, 23, 106 S.Ct. 1678, 1680, 90 L.Ed.2d 19 (1986) (per curiam) (dismissing cert.) (citing and adopting *330Department of the Treasury v. FLRA, 707 F.2d 574, 579 (D.C.Cir.1983) and FLRA v. Social Security Administration, 753 F.2d 156, 160-61 (D.C.Cir.1985) (holding review of issues never placed before the Authority is barred)).
Petitioners defend their failure to raise before the Authority the objections they raise here as mere inability to presciently object to the rationale of the Authority’s decisions before the Authority rendered those decisions. First, it should hardly have surprised petitioners that after twice being instructed by this Court to consider the use of the “vitally affects” test the Authority would actually do so. Moreover, even if petitioners did not anticipate that the Authority would follow this Court’s subtle goading toward the “vitally affects” test, petitioners could have sought leave to supplement their briefs or sought reconsideration under the Authority’s procedures. 5 C.F.R. §§ 2429.26 & .17 (1989). We made clear in AFGE, Local 2031 v. FLRA, 878 F.2d 460 (D.C.Cir.1989), that the failure of a party to raise an objection before the FLRA is fatal to its ability to argue the objection before this Court even if the party’s adversary has alluded to the issue before the Authority. Id. at 466; see also AFGE, Local 2782 v. FLRA, 803 F.2d 737, 742 (D.C.Cir.1986).
III. Conclusion
Petitioners have failed at the administrative level to object to the use of the private sector “vitally affects” standard applied by the FLRA as suggested in our prior opinions. Because they cannot raise this objection for the first time before this Court, the petitions for review are denied and the orders of the FLRA are enforced.
. Judge Silberman, in a concurring statement, explains with vigor his reservations to the governance of this case by the "vitally affects” test. That is a substantive matter rationally aired. We resist, however, Judge Silberman’s attributions of impropriety to prior panels. Those panels, we have no reason to doubt, labored conscientiously to assure that the Authority would consistently hew to principled "legal theory" and avoid indulgence in "ad hocery." See Pacific Northwest Newspaper Guild v. NLRB, 877 F.2d 998, 1003 (D.C.Cir.1989).