Opinion for the Court filed by Circuit Judge RANDOLPH.
RANDOLPH, Circuit Judge:
The complicated procedural history of these consolidated appeals from the district court masks the simplicity of the three issues presented. In light of the complexities, a summary of these issues would serve no useful purpose at this point. We will begin instead with an abbreviated account of how the cases reached this court.
. I.
More than a decade ago, the Environmental Protection Agency designated St. Louis, Missouri a "nonattainment" area of "moderate" classification for ozone. See 56 Fed. Reg. 56,694, 56,751, 56,788 (Nov. 6, 1991) (codified at 40 C.F.R. § 81.314, 81.326). As a consequence of EPA's designation, Missouri and Illinois had to revise their state implementation plans to attain the primary standard for ozone, 42 U.S.C. § 7511a(a); the time for attainment became November 15, 1996, see 42 U.S.C. § 7511(a)(1) tbl.l; and EPA had to determine, within six months of the attainment date (by about May 15, 1997), whether St. Louis had reached the primary standard. See 42 U.S.C. § 7511(b)(2)(A). If St. Louis were not in attainment, the Clean Air Act directed EPA to reclassify the area — to the "serious" level, or a higher level applicable to the area's "design value" (as calculated by EPA using readings from the area) — and to publish a notice of nonattainment in the Federal Register within the same six month window. See id. § 7511 (b)(2)(A)(i)-(ii) & (B).
The higher an area's nonattainment classification, the more stringent and numerous are the requirements placed upon the States to take action to improve the region's air quality. See generally 42 U.S.C. § 7511a. If, for instance, St. Louis's classification were at the "serious" level, Illinois and Missouri would have to implement an "enhanced" vehicle inspection and maintenance program to reduce hydrocarbon and nitrogen oxide emissions from motor vehicles. See 42 U.S.C. § 7511a(c)(3).
In November 1998, after giving EPA notice, the Sierra Club filed a complaint, invoking the Act's citizen-suit provision. 42 U.S.C. § 7604(a)(2). The complaint alleged that EPA had not performed its nondiscretionary duty to publish a timely notice of nonattainment in the Federal Register and a notice of the reclassification of St. Louis's ozone status. The argument was in the alternative: either EPA had made a determination of nonattainment and failed to publish it, or EPA had not made a determination although the Act required it to do so. EPA admitted that it had not made the required determination. After permitting the States of Missouri and Illinois and several associations to intervene as defendants, the court ordered EPA to make a determination of St. Louis's ozone air quality attainment status by March 12, 2001, and to publish any required notices in the Federal Register by March 20, 2001. Sierra Club v. Browner, 130 F.Supp.2d 78, 95 (D.D.C.2001) (amended by order on Feb. 14, 2001). The court refused to order EPA to make its determination retroactive, as the Sierra Club had urged, and it rejected the argument that the EPA had already made the attainment determination, as the Sierra Club also argued. See id. at 90-94.
On March 19, 2001, EPA published a notice of its determination that the St. Louis area had failed to attain the primary ozone standard by November 15,1996, and that reclassification by operation of law to the "serious" category would occur on the effective date of the rule, May 18, 2001. See 66 Fed. Reg. 15,578. On the same day, EPA proposed another rule that would delay the effective date of the March 19 determination until June 29, 2001. See 66 Fed. Reg. 15,591. Shortly thereafter, EPA issued a notice of proposed rulemaking to extend the attainment date until November 15, 2004, and to withdraw the March 19, 2001, reclassification and nonattainment determinations. See 66 Fed. Reg. 17,647 (Apr. 3, 2001). The Sierra Club petitioned this court for a writ of prohibition on the proposed rules, which we denied. See In re Sierra Club, No. 01-1141, 2001 WL 799956, at *1 (D.C.Cir. June 8, 2001). After EPA finalized these proposed rules, see 66 Fed. Reg. 27,036 (May 16, 2001) & 66 Fed. Reg. 33,996 (June 26, 2001), the Sierra Club petitioned for judicial review in the Seventh Circuit of the two rulemakings; its petitions are still pending. The Sierra Club also filed a motion in the district court to enforce the court's judgment, claiming that EPA's rulemakings regarding St. Louis's attainment status and its time limits violated the order. The district coui't denied the motion. We consolidated the Sierra Club's appeal from the denial of its motion with its appeal from the district court's original order.
II.
The Sierra Club's first argument is that before this lawsuit began EPA had already taken final agency action by determining that St. Louis had failed to attain the required ozone standard. As evidence, it cites several documents, including most prominently a March 1998 letter from the EPA Administrator to the Governor of Missouri discussing St. Louis's air quality. The relevant portion of the letter is as follows:
In recent years, Missouri has employed a variety of stationary source and fuel regulations which have resulted in improved air quality for the St. Louis area. While this progress is positive, it has not been sufficient to solve the air quality problem in the area. As you know, we have been considering whether to reclassify the St. Louis area's nonattainment status from moderate to serious. Recent air quality improvements and Missouri's commitments to implement an enhanced vehicle emissions inspection program, and opt into the Federal reformulated gasoline (RFG) program, are among the factors being considered.
While the Sierra Club thinks this excerpt reflects EPA's final determination that St. Louis was not in attainment for ozone, the last two sentences indicate otherwise. Besides, EPA has maintained throughout this litigation that it makes nonattainment determinations and reclassifications simultaneously and only through rulemaking. The Sierra Club counters that under the Clean Air Act and the Administrative Procedure Act the agency must proceed by adjudication rather than rulemaking, despite the fact that the Clean Air Act requires EPA determinations to be published in the Federal Register. 42 U.S.C. § 7511(b)(2)(B). This misses the point. No matter what the Sierra Club thinks the Clean Air Act or the APA required of EPA, the fact remains that "EPA's established practice for making a final decision concerning nonattainment and reclassification is to conduct a rulemaking under the APA, not to issue a letter, a list, or some other informal document." Brief of Appellee at 28; see, e.g., 63 Fed. Reg. 8128 (Feb. 18, 1998) (Dallas-Fort Worth nonattaim ment determination); 62 Fed. Reg. 65,025 (Dec. 10, 1997) (Santa Barbara); 62 Fed. Reg. 60,001 (Nov. 6, 1997) (Phoenix). In other words, if there has not been a ralemaking there has not been an attainment determination. More than that, if the Sierra Club were right that in this case EPA took the alternative route of adjudication, see NLRB v. Bell Aerospace Co., 416 U.S. 267, 294, 94 S.Ct. 1757, 1771-72, 40 L.Ed.2d 134 (1974); Public Util. Dist. No. 1 V. FERC, 272 F.3d 607, 620 (D.C.Cir. 2001) (per curiam), there is no explaining the absence of anything to indicate that such an adjudication occurred, or when. Still further, to credit the Sierra Club's ai'gument would require us to assume that the adjudication took place in secret, without notice to the States of Missouri and Illinois, and without their participation, perhaps in violation of the Due Process Clause of the Constitution, see generally Henry J. Friendly, Some Kind of Hearing, 123 U. Pa. L. Rev. 1267 (1975), and that EPA then kept the determination in its pocket and deprived it of legal effect by failing to publish- it in thé Federal Register. The scenario may not be impossible, but it is surely incredible. We constantly remind agencies to draw only rational inferences. Courts must do the same.
The Sierra Club also argues that EPA .made a determination in a rulemaking. It points to a 1998 EPA rule listing areas that had attained ozone standards; the rale did not include St. Louis on the list. See 63 Fed. Reg. 31,014, 31,059 (June 5,1998). The focus of the rule was not the St. Louis area's attainment status. The rale instead provided a foundation for EPA's plan to switch from one-hour to eight-hour attainment standards. EPA specifically noted that the purpose of the rale was not to reclassify any areas. See 63 Fed. Reg. 31,017. Furthermore, the status quo for St. Louis's air quality after 1991 was "nonattainment," so the fact that it was not included on a list of regions that had attained compliance does not, in itself, indicate that EPA had made the statutory determination.
The next issue is whether the district court erred in refusing the Sierra Club's request for what it calls "nunc pro time" relief—that is, to order EPA to date its attainment determination May 15, 1997, although it actually made the decision pursuant to the court's direction in a rule published on March 19, 2001.
"Nunc pro tunc" is a fancy phrase for backdating. Translated as "now for then," Black's Law Dictionary 1097 (7th ed. 1999), it is an ancient tool of equity designed to give retroactive effect to the order of a court. See, e.g., Mitchell v. Overman, 103. U.S. 62, 65, 26 L.Ed. 369 (1880); Eppes ex rel. Wayles v. Randolph, 6 Va. (2 Call) 125, 180, 186-87 (1799); Broom's Legal Maxims 94 & n.5 (6th, Am. ed. 1868). Courts have not been consistent in their use of this power. See In re Auto-Train Corp., 810 F.2d 270, 275 (D.C.Cir.1987). One line of authority holds that the "power to amend . must not be confounded with the power to create" and limits nunc pro tunc relief to situations in which a clerical error creates a defect in the record that a nunc pro tunc order can relieve. See Gagnon v. United States, 193 U.S. 451, 457-59, 24 S.Ct. 510, 511-12, 48 L.Ed. 745 (1904); see also Gray v. Brignardello, 68 U.S. (1 Wall.) 627, 636, 17 L.Ed. 693 (1863); Cent. Laborers' Pension, Welfare & Annuity Funds v. Griffee, 198 F.3d 642, 644 (7th Cir.1999) ("[T]he only proper office of a nunc pro tunc order is to correct a mistake in the records; it cannot be used to rewrite history."). While this formulation appears to predominate, there are other cases that speak of nunc pro tunc orders and judgments which supply "action[s] that did not occur on the earlier date." In re Auto-Train Corp., 810 F.2d at 275 (citing In re Triangle Chems., Inc., 697 F.2d 1280, 1288-89 (5th Cir.1983)). On several occasions, this court has directed agencies to readjudicate matters retroactive to the date of the initial determination, often—but not always—invoking the Latin phrase in our opinion. See Ethyl Corp. v. Browner, 67 F.3d 941, 945 (D.C.Cir.1995), and cases there cited.
In any event, what Sierra Club sought— to have the effective date of EPA's court-ordered determination converted to the date the statute envisioned, rather than the actual date of EPA's action — was a form of relief the district court quite properly rejected. Court-ordered or not, EPA engaged in rulemaking. We have held that the APA prohibits retroactive rule-making. See Georgetown Univ. Hosp. v. Bowen, 821 F.2d 750, 756-58 & n. 11 (D.C.Cir.1987), aff'd, 488 U.S. 204, 109 S.Ct. 468, 102 L.Ed.2d 493 (1988). The relevant provisions of the Clean Air Act contain no language suggesting that Congress intended to give EPA the unusual ability to implement rules retroactively. See 821 F.2d at 758. There may be an exception for situations in which the "statute prescribes a deadline by which particular rules must be in effect" and the "agency misses that deadline." See Bowen v. Georgetown Univ. Hosp., 488 U.S. 204, 224-25, 109 S.Ct. 468, 480, 102 L.Ed.2d 493 (1988) (Scalia, J., concurring). Even then, retroactivity must be "reasonable," id. (Scalia, J., concurring), and it is far from that here. Although EPA failed to make the nonattainment determination within the statutory time frame, Sierra Club's proposed solution only makes the situation worse. Retroactive relief would likely impose large costs on the States, which would face fines and suits for not implementing air pollution prevention plans in 1997, even though they were not on notice at the time. The district court adhered to. the limits of its jurisdiction by ordering EPA to perform the nondiscretionary function of making an attainment determination. See 42 U.S.C. § 7604(a)(2). Even if it could have gone further and ordered the relief the Sierra Club requested, we see no basis for concluding that the court should have been compelled to take that step.
The final issue deals with the Sierra Club's motion to enforce the district court's judgment through an injunction preventing EPA from taking further action on its proposéd rules to postpone St. Louis's nonattainment date, and to withdraw its nonattainment determination and resulting classification change.
The district court was well aware of EPA's plans. The agency asked the court to clarify whether its order would prevent EPA from engaging in another rulemaking to postpone the effective date of its court-ordered determination of attainment. The court ruled that its order did not restrict EPA from engaging in such later rulemakings. By the time of the motion to enforce the judgment, there was no doubt that EPA had complied with the court's original directive and performed its non-discretionary duties. The objection is that once having complied, EPA undid what the order required and thereby violated it. To accept this contention would require us to read the court's order as restricting more than the court itself intended. Given the level of respect we owe to a district court's decision regarding what its orders forbid or require, see United States v. Western Elec. Co., 46 F.3d 1198, 1205 (D.C.Cir. 1995), and the district court's limited jurisdiction in a citizen suit to order only EPA's performance of non-discretionary duties, see 42 U.S.C. § 7604(a)(2), we cannot say the court's rejection of the Sierra Club's motion was in error.
The Sierra Club takes note of our denial of its motion for a writ of prohibition, and our statement that it had "adequate means to obtain the relief requested" and could "move before the district court for enforcement of the district court's January 29, 2001 order." In re Sierra Club, 2001 WL 799956, at *1. We do not think much can be read into this. A writ of prohibition will not issue unless the applicant has no other adequate forum in which to seek relief — adequate in the respect of having a forum in which to bring the action, not a forum that will rule in the applicant's favor. See In re Sealed Case No. 98-8077, 151 F.3d 1059, 1063 (D.C.Cir.1998). Our order also said that the Sierra Club could seek judicial review of EPA's final actions regarding the extension of the St. Louis attainment area's effective date and withdrawal of its nonattainment classification in the Seventh and Eighth Circuits. In re Sierra Club, 2001 WL 799956, at *1. The Sierra Club is now pursuing that avenue of relief. If it succeeds in having the mies vacated, the non-attainment classification rule promulgated pursuant to the district court's order will presumably stand.

Accordingly, the order of the district court granting summary judgment to the Sierra Club but denying nunc pro tunc relief, and the court's order denying the Sierra Club's motion to enforce the judgment are affirmed.