Opinion for the Court filed by Chief Judge GINSBURG.
GINSBURG, Chief Judge.The United States Department of Health and Human Services (HHS) appeals from a judgment of the district court vacating three policy announcements for lack of notice and comment rulemaking and ordering approval of a cost allocation plan (CAP) submitted by the State of Nebraska Department of Health and Human Services (Nebraska). Because Nebraska challenged only HHS’s rejection of its proposed CAP, the district court erred in vacating the announcements. The court also abused its discretion when it determined the CAP should be approved rather than remanding the matter for the Department to reconsider its decision without reference to the policy announcements.
I. Background
The Congress has enacted several statutes aimed at improving child welfare services provided by the several States. Title IV-E of the Social Security Act, 42 U.S.C. § 670 et seq., makes funds available to state programs that offer “foster care and transitional independent living programs for children” and “adoption assistance for children with special needs.” Id. § 670. Title IV-B of the Act, id. § 620 et seq., offers federal funds to “State public welfare agencies in [order to] establish[ ], extend[], and strengthen[] child welfare services.” Id. § 620(a). The amount of money a State may receive under Title IV-B is capped, see id., whereas under Title IV-E a State may obtain reimbursement without limit for 75% of the costs it incurs to train employees, see id. § 674(a)(3)(A).
In order to obtain reimbursement under Title IV-E, a State must submit to the HHS Division of Cost Allocation (DCA) a CAP detailing the State’s expenditures. See 45 C.F.R. § 95.517(a) (limiting financial assistance to that provided “in accor*216dance with [a State’s] approved [CAP]”). A question that arises when a State prepares its CAP is how it should allocate expenditures that benefit more than one federal program. See id. § 95.507(a)(4) (DCA evaluates “correctness and fairness” of State procedures for “allocating all costs to each of the programs operated by the State agency”). For example, each child protection and safety worker (PSW) in Nebraska handles cases under Title IV-B and, we are told, is “expected to handle” cases under Title IV-E. Nebraska therefore must determine how to allocate the costs of training PSWs between the two programs. Title IV-E cases constitute only 21.5% of all child welfare cases the PSWs manage but, left to its own devices, Nebraska could allocate all PSW training costs to Title IV-E and thus avoid the cap on reimbursement under Title IV-B.
Not surprisingly, therefore, allocation decisions have been constrained by those who pay the piper. The federal Office of Management and Budget has instructed the States to allocate their costs so as to produce “an equitable result in consideration of relative benefits derived” by each federal program. Cost Principles for State, Local and Indian Tribal Governments, 60 Fed.Reg. 26,484, 26,492 (May 17, 1995). The Administration for Children and Families (ACF, formerly ACYF) within HHS, which oversees Title IV-E programs, adopted a similar requirement of proportional allocation in three policy announcements, Allowable Administrative Costs of the Foster Care Program Under Title IV-E of the Social Security Act, ACYF-PA-87-05 (Oct. 22, 1987); Federal Financial Participation in the Costs of Training for Employees of the State Title IV-E Agency, Foster Parents, Adoptive Parents and Employees of Private Child Placing and Child Care Agencies, ACYFPA-90-01 (June 14, 1990); and Allocation of Costs for All Training Under the Title IV-E Program, ACF-IM-91-15 (July 24, 1991), each requiring that States allocate the costs of training child welfare workers “to Title IV-E, State foster care and other State/Federal programs in such a manner as to assure that each participating program is charged its proportionate share of the costs.”
Despite the ACF’s repeated instruction to allocate costs proportionately, Nebraska submitted a CAP that allocated all the costs of training its PSWs to Title IV-E and the DCA approved it in 1993. In 1996, the DCA realized its mistake and directed Nebraska henceforth to allocate training costs among all benefitting programs. Nebraska submitted a new CAP but continued to charge all training costs for 1996 through 1999 to Title IV-E. The DCA responded in 1999, invoking the three ACF announcements and directing the State to allocate its expenditures proportionately among all benefitting programs. Instead, Nebraska challenged the DCA’s disapproval before the Departmental Appeals Board (DAB), where it argued the three ACF announcements were invalid because they had been issued without the notice and comment required for rule-making by the Administrative Procedure Act, 5 U.S.C. § 553. The Board rejected this argument and upheld the DCA’s decision, after which Nebraska sought review in the district court.
The State sought declaratory and injunctive relief from the court, to wit: (1) “a declaration that DCA’s disapproval actiop and the Board’s decision upholding DCA’s action are contrary to law,” and (2) “an injunction restraining HHS from disapproving the State’s CAP and from refusing to pay 75% of the total costs that Nebraska incurs to train its foster care workers.” Compl. ¶ 10. The court granted summary judgment in favor of Nebraska on the ground that HHS had treated the ACF announcements as “binding rule[s]” with*217out having followed the requisite notice and comment procedure. Although Nebraska had not challenged the future applicability of the ACF announcements, the court said in a memorandum opinion that it would vacate the three announcements and “reinstate the agency’s previous practice of approving primary program cost allocation plans” until HHS lawfully promulgated a new regulation. In its separate order, however, the court did not vacate the announcements, which caused some confusion.
The district court also determined it could itself “fully resolvef ] the issue of the approvability of Nebraska’s disputed CAP provision.” In order to determine what HHS’s “previous practice” of approval had been, the court consulted a 1985 policy memorandum written by the Commissioner of the ACYF and a 1984 letter to New York State written by another HHS official.* Based upon those documents the court concluded Nebraska’s CAP should have been approved.
II. Analysis
On appeal HHS does not challenge the district court’s ruling that the announcements were invalidly promulgated. Rather it makes three arguments concerning the relief ordered by the court. First, HHS maintains the district court did not actually vacate the three policy announcements because vacatur is not specified in the order accompanying its memorandum opinion. Alternatively, if the district court did vacate the announcements, then it erred. Finally, the district court should have remanded to HHS, rather than deciding itself, the ultimate question whether to' approve Nebraska’s CAP in view of the invalidity of the announcements.
A. Were the Announcements Vacated?
Despite the discussion of vacatur in the district court’s memorandum opinion, HHS maintains that, because Federal Rule of Civil Procedure 58(a)(1) requires “[e]very judgment ... [to] be set forth on a separate document,” the court’s failure to vacate the announcements in a separate order “raises the question whether [vacatur] was actually granted.” The question is, as Nebraska points out, not a hard one. The Supreme Court has made clear that the “separate document” requirement “is not designed as a trap for the inexperienced .... [It] should be interpreted to prevent loss of the right of appeal, not to facilitate [it].” Bankers Trust Co. v. Mallis, 435 U.S. 381, 386, 98 S.Ct. 1117, 55 L.Ed.2d 357 (1978) (internal quotation marks omitted). In this case the district court in its memorandum opinion “clearly evidenced its intent” to vacate the announcements, id. at 387, 98 S.Ct. 1117; therefore, they were vacated notwithstanding the court’s failure so to state in the judgment.
B. Should the Announcements Have Been Vacated?
HHS next argues the district court erred in vacating the policy announcements because Nebraska did not seek an order striking down the announcements “on their face[s].” According to HHS, because Nebraska sought only to overturn the DAB’s adjudicatory decision concerning its CAP, the proper remedy was to set aside the Board’s decision and remand the *218CAP to HHS for further proceedings. Nebraska, on the other hand, argues vacatur “is the normal remedy for an unlawful agency rule” and was proper in this case, for which point it cites CropLife America v. EPA, 329 F.3d 876 (D.C.Cir.2003). We review the district court’s decision to vacate, as we do any decision to grant or withhold equitable relief, for abuse of discretion. See Massachusetts v. Microsoft Corp., 373 F.3d 1199, 1207 (D.C.Cir.2004).
As is evident from Nebraska’s complaint, the final agency action challenged in this case was the decision of the Board upholding, on the basis of the three announcements, the DCA’s rejection of Nebraska’s CAP. See Compl. ¶¶37, 44, 48 (failure to approve CAP is “inconsistent with congressional intent” and DAB’s decision “should be reversed”). Hence the State asked the court to enjoin HHS from rejecting the proposed CAP and from refusing to pay 75% of the costs Nebraska incurred training PSWs. Id. ¶ 10. Nowhere in its complaint did Nebraska request vacatur of the announcements, presumably for good and sufficient reasons. See, e.g., Fair Employment Council of Greater Wash., Inc. v. BMC Mktg. Corp., 28 F.3d 1268, 1273 (D.C.Cir.1994) (no standing to pursue injunction where plaintiffs failed to allege likelihood defendant would violate their rights in the future).
We have long held that “[a]n injunction must be narrowly tailored to remedy the specific harm shown.” Aviation Consumer Action Project v. Washburn, 535 F.2d 101, 108 (D.C.Cir.1976); see also Va. Soc’y for Human Life, Inc. v. FEC, 263 F.3d 379, 393 (4th Cir.2001) (district court should not have enjoined agency from applying challenged regulation to any party when “[a]n injunction covering [plaintiff] alone adequately protects it from the feared prosecution”); Meinhold v. U.S. Dep't of Def., 34 F.3d 1469, 1480 (9th Cir.1994) (error to enjoin DOD from applying regulation to all military personnel where plaintiff “sought only to have his discharge voided and to be reinstated”); Gulf Oil Corp. v. Brock, 778 F.2d 834, 842-43 (D.C.Cir.1985) (injunction overbroad where it prohibited disclosure not only of plan in question but also of all “substantially similar” documents). Because Nebraska did not challenge the validity of the ACF announcements apart from their application as binding rules in the ease before the Board, and accordingly did not make out a case for continuing relief, the district court abused its discretion in vacating them.
Nebraska’s reliance upon CropLife America is misplaced. In that case, the petitioners challenged directly, and we vacated, a “directive” the EPA had issued without notice and comment rulemaking. 329 F.3d at 878-79. Although vacatur may or may not be appropriate when a rule has been held invalid on a procedural ground, see Allied-Signal, Inc. v. U.S. Nuclear Regulatory Comm’n, 988 F.2d 146, 150-51 (D.C.Cir.1993), no analysis of “the seriousness of the [rule’s] deficiencies” and the “disruptive consequences of an interim change,” id. (internal quotation marks omitted), is either necessary or relevant here, because only the decision, not the rule on which it depends, was challenged.
C. Should the CAP Have Been Remanded?
Finally, HHS argues the district court •should have remanded to it the question whether Nebraska’s proposed CAP would have been approved under its “previous practice,” as set forth in the 1984 Letter and the 1985 Memorandum upon which the district court relied. Nebraska insists the court did not need to remand the issue because “[t]he record establishes beyond legitimate dispute ... [that the CAP] was approvable.”
*219When a final agency action is challenged in the district court, that court “sits as an appellate tribunal .... [If it] determines that [the] agency made an error of law, the court’s inquiry is at an end: the case must be remanded to the agency for further action consistent with the corrected legal standards.” PPG Indus., Inc. v. United States, 52 F.3d 363, 365 (D.C.Cir.1995) (internal quotation marks omitted); see also Esch v. Yeutter, 876 F.2d 976, 993 (D.C.Cir.1989) (court should not “mak[e] the substantive decision” itself). Therefore, it is clear the district court erred when it ordered approval of Nebraska’s CAP. The agency must be given the first opportunity to determine whether Nebraska’s program meets the standard that was in place before the announcements were issued. As the Supreme Court has explained, because “agency decisions are frequently of a discretionary nature or frequently require expertise, the agency should be given the first chance to exercise that discretion or to apply that expertise.” McKart v. United States, 395 U.S. 185, 194, 89 S.Ct. 1657, 23 L.Ed.2d 194 (1969).
The wisdom of this course is brought home by examination of Nebraska’s claim that the proposed CAP certainly would have been approved under the HHS guidelines previously in use. Although the 1985 Memorandum allows training to be charged entirely to Title IV-E when at least 85% of that training is “directed toward” a Title IV-E program, that crucial phrase may be susceptible to more than one interpretation. And it is for HHS to interpret its own policies in the first instance, see Aulenback, Inc. v. FHA, 103 F.3d 156, 162-63 (D.C.Cir.1997), subject only to quite deferential review by the courts, Carus Chem. Co. v. EPA, 395 F.3d 434, 439 (D.C.Cir.2005). The district court’s decision to approve the CAP was inconsistent with this allocation of authority between the agency and the court.
III. Conclusion
The district court erred when it ordered relief beyond prohibiting the DCA and the DAB from relying upon the three ACF announcements in determining whether to approve Nebraska’s CAP. Therefore, we remand this case to the district court for further proceedings consistent with this opinion.
So ordered.
See Memorandum from Dodie Livingston, Commissioner, Administration for Children, Youth and Families, to William Acosta, Regional Administrator, OHDS, and Tommy Sullivan, Regional Program Director, ACYF (Oct. 7, 1985); Letter from Nicholas Cordasco, Director, Office of Fiscal Operations, to Robert J. Donahue, Director, Office of Human Resource Development, New York State Department of Social Services (June 14, 1984).