Reversed and remanded by published opinion. Judge KING wrote the majority opinion, in which Judge HAMILTON joined. Judge LUTTIG wrote a dissenting opinion.
OPINION
KING, Circuit Judge:
We are presented with the question of whether the district court had jurisdiction to entertain a taxpayer’s mandamus action against the District Director of the Internal Revenue Service (IRS) and, if it did, whether it should have granted the writ compelling the District Director to allow a federal death tax credit that the IRS had previously agreed was accurate and allowable. On the narrow facts before us in this appeal, we conclude that the district court had jurisdiction and that the writ should be granted. Accordingly, we reverse the district court’s dismissal for lack of jurisdiction, and remand for further proceedings.
I.
Mansy Y. Michael died on May 30, 1988, and his estate (the Estate) filed a federal estate tax return on August 30, 1989, reporting taxes in the amount of $175,487.1 The IRS audited the return and assessed the estate an additional amount. The Estate originally objected to the additional assessment, but after negotiating extensively with the IRS, it consented to increase its estate taxes by $85,775.99.
On July 31, 1992, the IRS sent the Estate an Estate Tax Closing Letter (the Closing Letter) which confirmed, pursuant to the parties’ negotiations, that the total estate tax had been assessed at $261,-262.99. On its face, the letter purported not to be a “formal closing agreement un[505]*505der section 7121 of the Internal Revenue Code,” but represented that the IRS would not “reopen this case, however, unless Revenue Procedure 85-13, reproduced on the back of this letter, applies.”
A substantial portion of the Estate was located in the United Kingdom and was administered there. Following the receipt of the closing letter, the Estate submitted to the IRS a timely “proof of credit” verifying that the Estate had paid taxes in the United Kingdom in the amount of $228,-939.50 with respect to property situated there. The IRS credited this amount as a foreign death tax credit against the estate tax that had been assessed.2 The IRS then sent the Estate an Estate Tax Computation Form indicating a balance due of $67,976. The Estate paid the balance on September 17, 1993, thus fully satisfying the estate tax burden as negotiated by the parties and assessed by the IRS.
On June 21, 1994 — over nine months later — the IRS reopened the case. The District Director’s office sent a letter to the Estate notifying it of a newly discovered error in the estate tax return. Namely, the IRS claimed that it had miscalculated the amount of the gross estate by simply failing to include the assets listed on Schedules B, D, and F of the return. As the IRS asserted, “This error resulted in the estate’s not being assessed the tax on these assets in [the] first audit.” As a result, the IRS concluded that its initial assessment had been $139,134 too low.
The District Director was aware that it could not assess additional taxes against the estate because, as he acknowledged and explained in his June 21, 1994 letter, “the normal statute of limitations has expired.” The District Director then took the extraordinary action that spawned this lawsuit, which the IRS now explains in its. brief with surprising candor:
The IRS ... could not assess this additional amount against the taxpayer because the statute - of limitations for assessing additional estate tax already had expired. Instead, the IRS reduced the amount of the claimed foreign death tax credit by the amount of the addition.al tax it determined to be due. The reduction of the claimed foreign death tax credit caused taxpayer to have an unpaid balance in its assessed tax liability-
The Estate responded with an administrative appeal, asking the District Director to reinstate the full amount initially allowed as a foreign death tax credit. When the administrative appeal was denied, the Estate filed this mandamus action in the district court, again seeking to compel the District Director to acknowledge the full amount of the foreign death tax credit. The IRS moved to dismiss, arguing that the district court was deprived of jurisdiction by the Anti-Injunction Act, I.R.C. § 7421, and that the Estate’s mandamus petition should be denied on the merits. The district court granted the IRS’s motion, finding that the plaintiff was not entitled to mandamus relief.3
[506]*506II.
Initially, we must determine whether the district court properly dismissed this action for lack of jurisdiction. We review that decision de novo. Flood v. New Hanover County, 125 F.3d 249, 251 (4th Cir.1997).
A.
Two competing statutes mark the jurisdictional boundary at issue here. The positive grant of jurisdiction is found in the Mandamus and Venue Act (the Mandamus Act): “The district court shall have original jurisdiction of any action in the nature of mandamus to compel an officer or employee of the United States or any agency thereof to perform a duty owed to the plaintiff.” 28 U.S.C. § 1361. Though the Mandamus Act grants district courts jurisdiction over any suit seeking mandamus, it does not override the Anti-Injunction Act, I.R.C. § 7421. The Anti-Injunction Act withdraws all courts’ jurisdiction over suits filed “for the purposes of restraining the assessment or collection of any tax.”
To prevail, therefore, the Estate must show either that its claim does not implicate the Anti-Injunction Act or that it fits within the narrow exception to that act. For purposes of this opinion, and although we harbor serious doubts on this point, we will nevertheless assume that the Estate’s mandamus action—which seeks to require the IRS to allow the full amount of its foreign death tax credit—would have the effect of “restraining the assessment or collection” of its taxes.
B.
Thus the district court lacked jurisdiction unless this action fits within the narrow but well-established exception to the Anti-Injunction Act. Because we hold that this case does come within the exception, the Anti-Injunction Act did not destroy the jurisdiction conferred on the district court by the Mandamus Act.
As explained above, the plain text of the Anti-Injunction Act deprives all courts of jurisdiction over any suit “for the purpose of restraining the assessment or collection of any tax.” I.R.C. § 7421(a). But the Supreme Court has recognized an exception to this otherwise absolute language: “Only upon proof of the presence of two factors could the literal terms of § 7421(a) be avoided: first, irreparable injury, the essential prerequisite for injunctive relief in any case; and second, certainty of success on the merits.” Bob Jones Univ. v. Simon, 416 U.S. 725, 737, 94 S.Ct. 2038, 40 L.Ed.2d 496 (1974) (citing Enochs v. Williams Packing & Nav. Co., 370 U.S. 1, 6-7, 82 S.Ct. 1125, 8 L.Ed.2d 292 (1962)).4 The Estate’s action is precisely the rare type of suit for which this exception was crafted.
1.
In analyzing the “certainty of success” factor, we must determine whether “under the most liberal view of the law and the facts, the United States cannot establish its claim,” Williams Packing, 370 U.S.at 7, 82 S.Ct. 1125; see also International Lotto Fund v. Virginia State Lottery Dep’t, 20 F.3d 589, 592 n. 3 (4th Cir.1994) (recognizing that Anti-Injunction Act destroys jurisdiction unless it is “clear that the government ‘could in no circumstances ultimately prevail on the merits’ ” (quoting American Friends, 419 U.S. at 10, 95 S.Ct. 13)). In this case, the IRS [507]*507claims that there is a deficiency in the Estate’s return. In order to view the circumstances supporting this claim in the light most favorable to the IRS, we will adopt its own characterization of the operative facts.
First, the IRS asserts that its collection efforts are based on the tax assessed in its Closing Letter of July 31, 1992. In this letter—which was issued after extensive negotiations between the IRS and the Estate—the IRS assessed a net estate tax of $261,262.99. Second, the IRS acknowledges that the Estate discharged a portion of that tax liability by providing the IRS with “proof of credit,” which demonstrated its payment of U.K. estate taxes in the amount of $228,939.50. Before the district court, and again at oral argument of this appeal, the IRS admitted that it does not contest the validity or amount of the foreign death tax credit that resulted from this payment. E.g., IRS Motion to Dismiss (“The [IRS] agrees that this amount [$228,939.50] represents the correct amount of foreign death tax credit to which the estate is entitled for U.S. federal estate tax purposes.”).
Third, the Estate paid the balance of net taxes due, plus interest, all as calculated by the IRS on the Estate Tax Computation sheet that it issued. This cash amount, which the IRS admits receiving, totaled $67,976. The IRS further concedes in its brief that payment of this balance, taken, together with the full amount of the foreign death tax credit would satisfy the Estate’s tax liability as assessed in the IRS’s Closing Letter. If, as the IRS contends, it did not thereafter assess any additional taxes; and if, as the IRS concedes, the claimed foreign death tax credit is valid and accurate; and if, as the IRS further concedes, the taxpayer has paid the assessed balance of $67,976, then there is no outstanding, assessed tax that the IRS may collect from the Estate.
Nor does the IRS claim that it validly assessed additional taxes after July 31, 1992. Instead, the IRS has conceded throughout these proceedings that, at the time it discovered its claimed mistake in the original assessment, the statute of limitations barred it from assessing additional taxes. The IRS is undoubtedly correct on this point; § 6501(a) of the I.R.C. requires the IRS to make all assessments on an estate tax return no later than three years after its filing. Here, the Estate’s return was filed on August 30, 1989. As a result, the IRS could not assess additional taxes after August 30, 1992. Indeed, the IRS notes in its letter of June 21, 1994, that “the normal statute of limitations has expired.” Because the IRS’s own version of the facts indicates that the Estate has paid' all taxes that have been and could ever be assessed on its return, the IRS’s claim for further tax payments would appear to be doomed.5
Nevertheless, the IRS argues that its reduction of the foreign death tax credit and the resulting deficiency determination were authorized by Lewis v. Reynolds, 284 U.S. 281, 52 S.Ct. 145, 76 L.Ed. 293 (1932). In Lewis, the IRS audited an income tax return and, within the applicable statute of limitations, assessed additional taxes. Id. at 283, 52 S.Ct. 145. The taxpayer paid the additional amount and sued the IRS for a refund. In the meantime, the statute [508]*508of limitations ran, which prevented the IRS from assessing any further taxes on the return. But in response to the refund suit, the IRS again recalculated the taxes for the year in question, and it concluded that the taxpayer still had underpaid its taxes. As a result, the IRS refused the taxpayer’s refund request.
The Supreme Court agreed with the IRS, holding that, although the IRS had been powerless to assess or collect additional taxes at the time of the refund suit, it was nevertheless permitted to recalculate those taxes in order to determine whether the taxpayer had overpaid its tax burden for the year in question:
An overpayment must appear before refund is authorized. Although the statute of limitations may have barred the assessment and collection of any additional sum, it does not obliterate the right of the United States to retain payments already received when they do not exceed the amount which might have been properly assessed and demanded.
Id.
Thus Lewis simply provided the IRS with a “shield” it could use to ward-off refund suits; it did not forge a “sword” with which the IRS could assess or collect additional taxes in violation of § 6501(a). Indeed, cases that follow Lewis have emphasized the difference between refund suits and those in which the IRS seeks to collect a deficiency: “A deficiency determination, by which the IRS seeks to establish a taxpayer’s additional tax liability, is patently different from a refund determination, by which the taxpayer seeks repayment or credit from the IRS.” Bachner v. Commissioner, 81 F.3d 1274, 1277 (3d Cir.1996). Lewis simply authorizes the IRS to “retain” tax payments in the face of a refund suit if, based on its calculations at the time of that suit, the IRS determines that the taxpayer did not actually overpay its properly calculated tax burden.
But Lewis cannot support the IRS’s actions in this case. While Lewis does allow the IRS to refuse certain refunds, it does not allow the IRS’s “collection of any additional sum” after the limitations period has expired, as it has sought to do here. Id.6 Such a reading of Lewis would nullify the statute of limitations.
Lewis cannot be read as trumping § 6501(a), even taking the “most liberal view of the law and facts.” Williams Packing, 370 U.S. at 7, 82 S.Ct. at 1129.7 Given the IRS’s admission that Lewis is the only case which even arguably authorizes its actions here, we conclude that the IRS’s claim for further payment on the Estate’s return is baseless and certain to fail on the merits.8
[509]*509Nor could the IRS possibly fare any better if the Estate now paid the alleged deficiency and sought a refund. Any such payments would be “overpayments” under I.R.C. § 6401, thus would be subject to mandatory refund. See I.R.C. § 6402. This is true regardless of which of its actions—the July 31, 1992 Closing Letter or the June 21, 1994 reopening letter—the IRS relies on as the “assessment” being litigated.
Presuming that the 1992 Closing-Letter represents the operative assessment, the IRS itself has admitted that this letter did not assess the taxes on which its claimed deficiency is based. The IRS conceded in its 1994 reopening letter that the calculation error had caused it not to assess the taxes in question: “This error resulted in the estate’s not being assessed the tax on these assets in [the] first audit.” Because the Estate has, as shown above, undeniably discharged all taxes actually assessed in the closing letter, any current payment by the Estate would be payment of unassessed taxes.
The Estate would plainly be entitled to refund of any such amounts. Ewing v. United States, 914 F.2d 499, 504 (4th Cir.1990). In Ewing,-we were required to interpret I.R.C. § 6401, which specifies the consequences of an assessment or collection made in violation of the statute of limitations:
The term “overpayment” includes that part of the amount of the payment of any internal revenue tax which is assessed or collected after the expiration of the period of limitations properly applicable thereto.
I.R.C. § 6401. If a tax payment is an “overpayment,” the IRS must refund it. I.R.C. § 6402(a) (“In the case of any overpayment, the [IRS] ... shall ... refund any balance.”); Alexander v. United [510]*510States, 44 F.3d 328, 331 (5th Cir.1995) (“[P]ayments made after the limitations period are defined as ‘overpayments’ and, as such, must be refunded.”).
The taxpayers in Ewing had made certain payments to the IRS, even though the IRS had never formally assessed those taxes. Some payments were made within the limitations period, and others were made after that period. Applying § 6401 to these facts, we concluded that while the IRS could retain unassessed tax payments it received within the limitation period, it must refund the other payments: “Since the amounts paid in 1985 were ‘collected’ by the IRS outside of the period for assessment, with no assessment having been made, they come within [§ 6401’s] definition of ‘overpayment’.” Ewing, 914 F.2d at 504.
Thus Ewing makes clear that, where a tax liability has not been formally assessed, any payments of that liability submitted after the limitations period are overpayments under § 6401 and must be refunded. Here, the allegedly outstanding taxes were not assessed in the Closing Letter; in fact, they have never been assessed. If the Estate nonetheless pays the deficiency now and seeks a refund of its payment, Ewing would require the IRS to return those amounts. Ewing, 914 F.2d at 504.
The result of a refund suit is equally clear if the IRS relies on its 1994 reopening letter as the operative assessment. That letter was sent more than three years after the Estate’s return was filed in 1989. As a result, any payment submitted in response to an assessment in that letter would constitute collection of a tax assessed after the statute of limitations, thus would be an overpayment under the plain language of § 6401. See Alexander, 44 F.3d at 331. As a result, the Estate would be entitled to a mandatory refund of any such payment.
It is undeniable, then, that the IRS cannot prevail against the Estate under any reading of the law, whether applied to the status quo or in the context of any future refund suit.
2.
But the Anti-Injunction Act still requires us to examine whether the Estate will suffer irreparable injury if not granted the relief it seeks. “Americans United”, 416 U.S. at 758, 94 S.Ct. 2053. The IRS contends that the Estate cannot be irreparably injured because it has another, adequate legal remedy. Cf. American Friends, 419 U.S. at 11, 95 S.Ct. 13 (inadequacy of available remedies goes to prove irreparable harm). Specifically, the IRS argues that the Estate may simply pay the disputed tax and seek a refund, first from the IRS, then in district court if necessary.
Under ordinary circumstances, the availability of a refund suit does negate any claim of irreparable injury. Id.; “Americans United”, 416 U.S. at 762, 94 S.Ct. 2053; Bob Jones Univ., 416 U.S. at 746, 94 S.Ct. 2038; International Lotto Fund, 20 F.3d at 591. These are not ordinary circumstances. In this case the actions of the IRS are transparently baseless, in that it is pursuing this matter after the statute of limitations clearly has barred collection or assessment of further taxes. A refund suit under such circumstances is an inadequate remedy.
We must remember that this case began with the IRS’s broken promise to the Estate. The IRS and the Estate had agreed on the Estate’s tax liability after extensive negotiations. According to the terms of the Closing Letter that followed those negotiations, the IRS represented that it would not reopen the case “unless Revenue Procedure 85-13 ... applies.”
Under Section 4 of Rev. Proc. 85-13, reopening by the IRS is permissible in only three circumstances.9 At oral argu[511]*511ment, the IRS expressly disavowed the applicability of the first two prongs of Section 4, relying solely on the third prong as the basis of its reopening. By disavowing reopening premised on subsections 1 and 2 of Section 4, the IRS acknowledges that the taxpayer did not engage in fraud, malfeasance, collusion, or concealment or misrepresentation of a material fact. The IRS further acknowledges that the prior closing did not involve a clearly defined substantial error based on an established IRS position.
As noted, however, the IRS claimed at oral argument that it is entitled to renege on its express representation to the taxpayer, embodied in the Closing Letter, under the catch-all, third prong of Section 4 of Rev. Proc. 85-13. Subsection 3 of Section 4 permits reopening when “[o]ther circumstances exist that indicate failure to reopen would be a serious administrative omission.” This “other circumstances” proviso of Rev. Proc. 85-13 is inappropriate and inadequate support for the IRS’s breach of its promise not to reopen the Estate’s case. Under these circumstances, we are skeptical of the bona fides of the IRS’s position that, when the applicable statute of limitations has expired, failure to reopen the Estate’s case for the purpose of increasing its tax liability results in a “serious administrative omission.”
Having reopened the case, the IRS then launched a thinly veiled attempt, however described, to assess taxes in violation of the statute of limitations. In its 1994 reopening letter, the IRS conceded that the statute of limitations barred its assessment of additional taxes. Nevertheless, and “even though the normal statute of limitations has run,” the IRS manufactured a deficiency by setting-off an admittedly valid foreign death tax credit against time-barred taxes it never assessed. At the end of the day, then, the IRS demanded additional taxes ' from a taxpayer who— upon the facts admitted by the IRS — had discharged all taxes that had ever been assessed against it. However the IRS labels its actions, they amount to an illegal assessment of taxes. See I.R.C. § 6501(a).
While this initial “mistake” is bad enough on its own, the IRS has maintained its baseless position for five more years. In the taxpayer’s administrative appeal, before the district court, and again before this court, the IRS has insisted — despite its utter lack of legal support — that the Estate should pay it more money. Such actions can have one of two possible causes; the IRS’s shocking ignorance of the laws it administers, or its utter disregard for the limits of those laws. Whatever the cause, the effect on the Estate is to force it either to pay the amount demanded or to continue fighting the IRS.
We simply will not, as the IRS requests, require the Estate to continue this fight in yet another forum. The IRS would have the taxpayer assemble the substantial sum needed to pay its manufactured deficiency- — -ten years after the Estate’s return was originally filed — and again pay its attorney to file a suit for refund of that payment. As we have demonstrated above, the IRS is certain to lose any such suit; it mil have to refund all payments. We will not require this waste of private, agency, and judicial resources.
Nor would forcing such a suit advance the purposes of the Anti-Injunction Act. The Act is designed to promote efficient and timely tax collection. It protects “the Government’s need to assess and collect taxes as expeditiously as possible with a minimum of preenforcement judicial inter[512]*512ference.... ” Bob Jones Univ., 416 U.S. at 736, 94 S.Ct. 2038(emphasis added). Requiring taxpayers to file pointless refund suits to retrieve taxes that are unquestionably time-barred when collected cannot promote speedy tax collection. In fact, it would legitimize just the opposite. See Williams Packing, 370 U.S. at 7, 82 S.Ct. 1125 (where IRS cannot prevail, “the central purpose of the [Anti-Injunction] Act is inapplicable”).
The Anti-Injunction Act also is meant to protect the IRS from litigation pending a suit for refund. Id. at 8, 82 S.Ct. 1125. Where, as here, the IRS acts in complete disregard for the tax code, it should not be surprised to find itself stripped of the code’s protections.
Furthermore, it is the IRS’s avoidance of the tax code’s ordinary assessment mechanism that has deprived the Estate of the opportunity to contest the claimed deficiency without a refund suit. In the usual case, when the IRS determines that additional taxes are due from an estate, it mails the estate a Notice of Deficiency. I.R.C. § 6212. The estate may then, without first paying the asserted deficiency, file a petition in the Tax Court seeking redetermination of the deficiency. I.R.C. § 6213.
Here, of course, the Estate could not avail itself of the usual pre-payment remedy in the Tax Court because the IRS never issued a Notice of Deficiency for the new amount. See Jensen v. IRS, 835 F.2d 196, 198 (9th Cir.1987) (IRS failure to send notice of deficiency deprived taxpayer of right to challenge deficiency in Tax Court). The reason for the IRS’s failure to mail a Notice of Deficiency is plain: The limitations period of § 6501(a) barred its formal assessment of additional taxes. By seeking additional payments despite § 6501(a), then, the IRS not only ignored the limitations period, but it also deprived the Estate of its usual, pre-payment remedy in the Tax Court. The IRS cannot be permitted to force a more costly remedy on the taxpayer by its own avoidance of the tax code.
Given the IRS’s foreclosure of a prepayment remedy, we are especially sensitive to the equities in this case. Both we and the Seventh Circuit have discounted the IRS’s argument that the taxpayer should seek other remedies where the equities of the case heavily favor the taxpayer:
We note that [the IRS’s] adequate remedy argument comes with particularly poor grace in the circumstances of this case. “Even tax administration does not as a matter of principle preclude considerations of fairness.” Angelus Milling Co. v. Commissioner of Internal Revenue, [325 U.S. 293, 297, 65 S.Ct. 1162, 89 L.Ed. 1619 (1945) ]. A suit for mandamus may be governed by equitable considerations ... and the equities here are all on the side of the taxpayers.
Vishnevsky v. United States, 581 F.2d 1249, 1255 (7th Cir.1978)(quoted in In re First Federal Sav. & Loan Ass’n, 860 F.2d 135, 139 (4th Cir.1988)).
The current action is the only reasonable and efficient method by which the Estate may defend its rights, and the Estate will be irreparably harmed without it. See American Friends, 419 U.S. at 11, 95 S.Ct. 13 (inadequacy of available remedies proves “irreparable injury, an essential prerequisite for traditional equity jurisdiction”). Because the IRS also is certain to fail on the merits of its position, the Estate’s action falls within the narrow exception to the Anti-Injunction Act. Bob Jones Univ., 416 U.S. at 737, 94 S.Ct. 2038. The district court therefore had jurisdiction to decide the merits of the Estate’s mandamus action. We now turn to this mandamus issue.
III.
A plaintiff may invoke the federal courts’ extraordinary power to issue a writ of mandamus only by proving the coexistence of three elements: “(1) the peti[513]*513tioner has shown a clear right to the relief sought; (2) the respondent has a clear duty to do the particular act requested by the petitioner; and (3) no other adequate remedy is available.” Baker, 860 F.2d at 138. Where mandamus relief is sought against a public official, “the alleged duty to act [must] involve a mandatory or ministerial obligation which is so plainly prescribed as to be free from doubt.” Id. In assessing the Estate’s claim, though, were main mindful that “the right to a writ of mandamus may turn on equitable considerations.” United States ex rel. Girard Trust Co. v. Helvering, 301 U.S. 540, 543, 57 S.Ct. 855, 81 L.Ed. 1272 (1937).
As our above discussion makes clear, the Estate showed that it has a clear right to have the full amount of the foreign death tax credit recognized, thus to be free from additional collection efforts. Further, the IRS has a clear duty to provide such relief. The District Director has no discretion in allowing the foreign death tax credit; in-, stead the tax code mandates this credit: “The tax imposed by section 2001 shall be credited with the amount of any estate, inheritance, legacy, or succession taxes actually paid to any foreign country.” I.R.C. § 2014(a). Given the Director’s lack of discretion, along with the baselessness of the I.R.S.’s actions, the Director had a clear duty to act as the Estate has requested.
As further stated above, no other avenue the Estate could pursue would “afford! ] a remedy equally adequate and complete.” Girard Trust Co., 301 U.S. at 544, 57 S.Ct. 855. Consequently, the Estate has no other reasonable way to vindicate its clear right to the requested relief, and the District Director has a clear duty to provide that relief. Finally, as in Baker, “the equities here are all on the side of the taxpayer[ ].” 860 F.2d at 139 (quoting Vishnevsky, 581 F.2d at 1255). We therefore conclude that the district court erred in ■ dismissing the taxpayer’s mandamus suit.
In so ruling, we do not intend to broaden the narrow class of cases for which mandamus relief is available. We have not declared “open season” on mandamus suits against the IRS. However, the mandamus remedy exists for extraordinary cases. We are satisfied that the law-less actions attempted by the IRS here—while unsettling—truly are extraordinary.10
IV.
We therefore reverse the judgment of the district court and remand for further [514]*514proceedings not inconsistent with this opinion.
REVERSED AND REMANDED.