GARWOOD, Circuit Judge:

On August 1, 2003, defendant-appellant, Frederick Charles Miller (Miller), pleaded guilty to one count of conducting a monetary transaction with criminally-derived funds and one count of evading income tax. He was sentenced to concurrent terms of ninety-six and sixty months' imprisonment and to a three-year period of supervised release. He was also ordered to pay restitution in the amount of $1,485,074.24. After his direct appeal and several collateral attacks failed, Miller filed a petition for a writ of audita querela with the district court on September 26, 2008, seeking to have the amount of his restitution order reduced. The district court dismissed the petition. For the reasons discussed below, we affirm.

FACTS AND PROCEEDINGS BELOW

Miller was the chief financial officer of Medical Select Management (MSM), which was formerly known as Harris Methodist Select. Between 1998 and 2001, he embezzled almost $1.2 million from MSM and neglected to pay taxes on it to the Internal Revenue Service (IRS). On June 18, 2003, he was indicted on one count of wire fraud, in violation of 18 U.S.C. § 1343, five counts of theft from a health care benefit program, in violation of 18 U.S.C. § 669, and five counts of conducting a monetary transaction with criminally-derived funds, in violation of 18 U.S.C. § 1957. A superseding indictment was filed on July 29, 2003, alleging that he had evaded income taxes for the calendar year 2000. On August 1, 2003, he pleaded guilty to one count of conducting a monetary transaction with criminally-derived funds and one count of evading income tax. The remaining ten counts were dismissed.

On November 12, 2003, the district court sentenced Miller to ninety-six months of imprisonment for conducting a monetary transaction with criminally-derived funds and sixty months for income tax evasion, to be served concurrently. It then sentenced him to a three-year term of supervised release and ordered him to make full restitution in the amount of $1,150,000.00 to MSM and $335,074.24 to the IRS. The court then ordered Miller to forfeit the sum of $924,105.84 immediately.

Miller filed a notice of appeal to this court on November 20, 2003. In May 2004, while that appeal was still pending, MSM revealed that it had recently recovered $170,405.00 in proceeds from money that Miller had embezzled in 1999. Miller asserts that the Government failed to credit this sum against his outstanding restitution obligation. The Government does not contest this assertion. However, Miller did not attempt to raise the issue of the Government's failure to credit this sum in his pending appeal, even though some of his assignments of error concerned the district court's restitution order. See United States v. Miller, 406 F.3d 323 (5th Cir.), cert. denied, 546 U.S. 929, 126 S.Ct. 207, 163 L.Ed.2d 278 (2005). Ultimately, we affirmed his sentence and the restitution order. Id. at 337.

On May 1, 2006, Miller filed a motion to vacate, set aside, or correct his sentence under 28 U.S.C. § 2255. However, he did not raise the Government's alleged failure to credit the sum recovered in May 2004 against his restitution obligation in that proceeding. The district court denied his motion on June 9, 2006. It entered a final judgment on July 10, 2006, and denied Miller's subsequent motion for reconsideration on August 1, 2006. It then denied his motion to clarify its order on August 11, 2006. On August 28, 2006, Miller filed a notice of appeal from the denial of his § 2255 motion. The district court denied his request for a Certificate of Appealability (COA) on August 29, 2006. On April 10, 2007, we also denied his motion for a COA. Miller then filed a motion for reconsideration, which we denied on June 22, 2007.

Meanwhile, on December 4, 2006, Miller had filed a 28 U.S.C. § 2241 petition for habeas corpus in the Dallas division of the Northern District of Texas. In this motion, he argued that the sum recovered by MSM in May 2004 entitled him to have the amount of his restitution order reduced. The case was referred to a Magistrate Judge, who recommended on December 8, 2006, that Miller's application be dismissed, because the Government's alleged failure to credit his restitution obligation did not place him "in custody" within the meaning of the habeas corpus statutes. On January 5, 2007, the district court accepted this recommendation and dismissed his § 2241 motion. Miller appealed this dismissal. We affirmed on December 11, 2007. Miller v. Berkebile, No. 07-10099 (5th Cir. Dec. 11, 2007), cert. denied, ___ U.S. ___, 128 S.Ct. 2933, 171 L.Ed.2d 868 (2008), available at http://coa.circ5.dcn/ShowDoc.aspx?dlsId=406078.

On September 26, 2008, Miller filed a petition for a writ of audita querela under 28 U.S.C. § 1651(a) in the Fort Worth division of the district court, arguing that his restitution order was unjust due to the ineffective assistance of counsel. On October 21, 2008, the district court entered an order dismissing the petition, and Miller did not appeal. The district court dismissed the petition, because it found that a writ of audita querela could not issue on the basis of ineffective assistance of counsel. Miller did not appeal the dismissal of that petition.

However, on December 3, 2008, Miller filed a second petition for a writ of audita querela based purely on the assertion that the district court's restitution order had been rendered infirm by the subsequent discovery of the money recovered in May 2004 and the Government's failure to credit that sum against his outstanding obligation. The district court dismissed this petition on December 5, 2008, on the ground that the amount of its November 2003 restitution order had not been rendered infirm by MSM's recovery of $170,405.00 in May 2004. The amount of money Miller had stolen, and therefore the amount he was ordered in November 2003 to repay, was unaffected by the May 2004 recovery. According to the district court, what Miller needed was for the Government to credit his obligation, not a reduction in the amount of the November 2003 restitution order that all parties agreed accurately reflected the amount he had stolen.

Miller filed a notice of appeal from the dismissal of this second petition on December 11, 2008.

DISCUSSION

Miller argues that the writ of audita querela is a post-conviction remedy that is available to a federal prisoner seeking a credit to his restitution obligation for the value of stolen property recovered after the entry of a criminal judgment including the restitution order. He then argues that the district court erred by declining to issue him such a writ. The Government asserts that no post-conviction remedy, including a writ of audita querela, can compel a federal court to alter retroactively the amount of a restitution order. It then argues that, even if there were such a remedy, it would not be appropriate in Miller's case. We decline to decide whether or not any post-conviction remedy could compel a federal court to alter a restitution order, because we agree with the Government that a writ of audita querela could not do so on the specific facts of Miller's case.

I. The Writ of Audita Querela

The writ of audita querela is a common law writ dating from the reign of Edward III that constitutes the initial process in an action brought by a judgment defendant to obtain relief against the consequences of the judgment on the ground that some defense or discharge has arisen since its rendition that could not be taken advantage of otherwise. United States v. Reyes, 945 F.2d 862, 863 n. 1 (5th Cir. 1991); Black's Law Dictionary 150 (9th ed. 2009). Audita querela is distinguished from coram nobis in that coram nobis attacks the judgment itself, whereas audita querela is directed against the enforcement, or further enforcement, of a judgment which, when rendered, was just and unimpeachable. 7A C.J.S. Audita Querela § 4 (2004). In other words, a writ of coram nobis attacks a judgment that was infirm at the time it was rendered for reasons that later came to light, while a writ of audita querela is used to challenge a judgment that was correct at the time it was rendered but which is made infirm by matters that arose after its rendition. Id.

Rule 60(b) of the Federal Rules of Civil Procedure expressly abolished the application of the writ of audita querela to civil judgments in 1948. Reyes, 945 F.2d at 865. However, the reasoning of the Supreme Court's opinion in United States v. Morgan, 346 U.S. 502, 74 S.Ct. 247, 98 L.Ed. 248 (1954), may allow the writ to be used to attack a criminal judgment. In Morgan, the Court held that the writ of coram nobis, which Rule 60(b) also had abolished in civil cases, was still available in criminal proceedings under the All Writs Act, 28 U.S.C. § 1651(a), where it was needed to fill a gap in the federal post-conviction remedial scheme. Morgan, 74 S.Ct. at 249-53 n. 4; United States v. Ayala, 894 F.2d 425, 428 (D.C. Cir. 1990). Accordingly, we have, as have several other circuits, acknowledged, with some reservation, that the writ of audita querela might also survive in criminal adjudications, if there is a gap for it to fill. United States v. Banda, 1 F.3d 354, 356 (5th Cir. 1993); Reyes, 945 F.2d at 865 n. 5. See also United States v. Holder, 936 F.2d 1 (1st Cir. 1991); Ayala, 894 F.2d at 429; United States v. Kimberlin, 675 F.2d 866 (7th Cir.), cert. denied, 456 U.S. 964, 102 S.Ct. 2044, 72 L.Ed.2d 489 (1982). We have yet to encounter a case that has required us to decide squarely whether or not the writ of audita querela survives in criminal cases.

Nevertheless, we have held that, if the writ survives, it can only be available where there is a legal objection to a judgment which has arisen subsequent to that judgment. Reyes, 945 F.2d at 866. Purely equitable grounds for relief do not justify the issuance of a writ of audita querela. Id. But see Ejelonu v. I.N.S., Dept. of Homeland Sec., 355 F.3d 539, 548 (6th Cir. Jan.8, 2004), rehearing en banc granted, opinion vacated (July 28, 2004), appeal dismissed (Oct. 18, 2004) (rejecting the position that a writ of audita querela cannot be based upon an equitable defense). Furthermore, the writ is only available where the legal objection raised cannot be brought pursuant to any other post-conviction remedy. Reyes, 945 F.2d at 866. See Banda, 1 F.3d at 356. This limitation follows from the reasoning of Morgan, which allows relief pursuant to a writ of audita querela only where a gap exists in the system of federal post-conviction remedies. Ayala, 894 F.2d at 428.

II. The Writ in Miller's Case

Miller sought a writ of audita querela to force the district court to reduce his restitution obligation by $170,405.00. He argues that this petition presents a legal defense that arose after final judgment in his case, because 18 U.S.C. § 3663A(b)(1)(B) requires that the amount of restitution ordered in a criminal case be offset by "the value . . . of any part of the property that is returned." 18 U.S.C.A. § 3663A(b)(1)(B) (West 2000). He also contends, and the Government agrees, that the relief he seeks cannot be obtained under any other post-conviction remedy, like habeas corpus or coram nobis. Therefore, he argues, the use of audita querela is appropriate in his case to fill a gap in the federal post-conviction remedial scheme.

A. Estoppel Based on Prior Arguments

Initially, we note that it is perhaps possible that Miller should be estopped from making his current argument. See generally Hopkins v. Cornerstone Am., 545 F.3d 338, 347 (5th Cir. 2008), cert. denied, ___ U.S. ___, 129 S.Ct. 1635, 173 L.Ed.2d 998 (2009) ("Judicial estoppel is an equitable doctrine that `prevents a party from asserting a position in a legal proceeding that is contrary to a position previously taken in the same or some earlier proceeding.'" (quoting Hall v. GE Plastic Pac. PTE Ltd., 327 F.3d 391, 396 (5th Cir. 2003))). In Miller's "Petition for a Reduction in Court-Ordered Mandatory Victim Restitution," which he filed on June 17, 2004, and in his first petition for a writ of audita querela, he argued that he had known the district court's restitution order was incorrect when it was issued, but that he had failed to object due to the ineffective assistance of counsel. Specifically, he asserted that, before his sentencing, he had returned $100,000.00 of the money he had embezzled from MSM in the form of a subordinated investment note that later matured into the $170,405.00 at issue in this appeal. The Government contested this assertion in its Pre-Sentence Report (PSR), arguing that, instead of returning this $100,000.00, he had spent it on a swimming pool in his backyard. Accordingly, the Government listed this amount as stolen in the PSR's restitution calculations. Although Miller's attorney objected to this listing in Miller's written objections to the PSR, he failed to raise the issue before the district court at sentencing.

The chief problem with this argument was identified by the district court in its order dismissing Miller's first petition for a writ of audita querela. Audita querela is only available where the judgment of the district court was correct at the time it was rendered, but is undermined by facts that later come to light. If Miller knew that the restitution order was incorrect at the time it was issued and failed to object to it due to the ineffective assistance of counsel, then the judgment was infirm from the beginning. Even though the absolute proof of this infirmity did not arise until May 2004, audita querela would be inappropriate to remedy the error, because the judgment was infirm at the time it was rendered due to the ineffective assistance of Miller's counsel.

However, we will ignore the issue of estoppel, because we find that Miller cannot mount a viable case for the issuance now of a writ of audita querela under the facts he has alleged in his second petition and his briefs.

B. Modifying Miller's Restitution Obligation

In his second petition for a writ of audita querela and in his appellate briefs before this court, Miller's argument omits any discussion of a possible ineffective assistance of counsel issue, as well as any hint that he might have returned the $170,405.00 at issue in this appeal before his sentence. Instead, he states that he was the "registered owner" of the subordinated investment note and had "dominion" over it until its maturity in April 2004. Accordingly, he contends that the district court's restitution order was correct at the time it was issued. The error he seeks to have corrected is the Government's failure to credit this obligation by the amount MSM announced it had recovered in May 2004. In other words, under Miller's current characterization of the facts, the issue presented is the same as would have occurred if in May 2004 he had tendered payment of $170,405.00 towards his restitution obligation and the Government had accepted it but refused to acknowledge its receipt.

We do not think that such a situation renders the district court's restitution order infirm. Under Miller's current characterization of the facts, all parties agree that the district court's restitution order correctly reflects the amount that Miller embezzled. The only disagreement is over whether or not Miller is entitled to a credit for the money recovered in May 2004. We do not think that a subsequent disputed payment renders the amount of the original restitution order infirm. Although 18 U.S.C. § 3663A provides that, when a criminal restitution order is issued, it must be offset by "the value . . . of any part of the property that is returned," we do not think that this language should be read to require district courts to formally modify restitution orders every time a defendant subsequent to the order makes a payment on his 18 U.S.C.A. § 3663A(b)(1)(B) (West 2000). Indeed, such a burden would be intolerable, given the number of impoverished defendants who are ordered to make modest restitution payments on a periodic basis. Similarly, where property that was accounted for in fixing the amount of a restitution order is returned after that order has already been issued, we do not think that modification of the order itself is required. This type of recovery is no different from a payment, and it should be accounted for in the same way.

If it still exists, the writ of audita querela can only be applied to rectify a judgment which, though correct when rendered, has since become infirm. Because all parties to this case agree that the district court's restitution order was initially correct, and because the statute does not require the order to be modified every time a subsequent payment is made on a restitution obligation, there is no infirmity in Miller's judgment for a writ of audita querela to rectify. Therefore, the district court did not err by dismissing his petition.

CONCLUSION

For the foregoing reasons, the judgment of the district court is

AFFIRMED.