CARL E. STEWART, Circuit Judge:
Texas Clinical Laboratories, Inc. and Texas Clinical Laboratories-Gulf Division, Inc. (collectively, the “TCLs”) appeal the district court’s judgment denying them additional interest on the principal of a Medicare reimbursement ruling rendered in their favor against the Department of Health and Human Services (the “DHHS”). For the reasons below, we affirm.
I.
The dispute between the TCLs and the DHHS began around 1986, when the DHHS implemented a new formula for calculating reimbursement for certain health care providers for travel expenses. The TCLs objected to this change and sought administrative review challenging two elements of the agency’s travel allowance formula: (1) the thirty-five miles per hour (“35 m.p.h.”) average speed used as the standard speed for delivery of services and (2) the median cost per specimen.
On January 31, 1992, an ALJ found that the median specimen figure was not supported by the record, that the 35 m.p.h. figure was not supported by the record, and that payment should be made by the DHHS for future claims that had not been addressed in an earlier hearing decision. The Office of Health Affairs Appeals Council (the “Appeals Council”) vacated *774the ALJ’s ruling, however, and remanded the action so that the DHHS could present evidence in support of the 35 m.p.h. figure and median cost per specimen. The Appeals Council also limited the scope of the ALJ’s decision to consider only claims presently before him. Upon remand, the same ALJ issued another ruling in favor of the TCLs, again finding that the DHHS had failed to produce evidence to support its use of the 35 m.p.h. figure and median cost per specimen. The Appeals Council, though, was persuaded by the DHHS’ representation that evidence existed to support the 35 m.p.h. and median cost per specimen figures and again reversed. This time, the Appeals Council remanded the matter to a different ALJ. In June 1995, the successor ALJ rendered the third ruling in favor of the TCLs; however, the Appeals Council reversed yet again, concluding that the DHHS presented sufficient evidence to support its use of the 35 m.p.h. and median cost per specimen figures.
The TCLs then filed an action in the Northern District of Texas seeking judicial review of the Appeals Council ruling. The district court granted summary judgment to the DHHS and dismissed the TCLs’ action. On appeal, we affirmed the district court dismissal of the TCLs’ median cost per specimen claim, but remanded the 35 m.p.h. claim because the record did not include any objective evidence to support the DHHS’ use of the 35 m.p.h. figure. See Texas Clinical Labs, Inc. v. Apfel, No. 00-10099, 2000 WL 34507667, at *1 (5th Cir. Dec. 22, 2000). The district court in turn remanded the case back to the administrative level directing that the record be supplemented with documentation on which the DHHS relied to determine the 35 m.p.h. figure.
After the administrative proceedings were re-opened, the DHHS introduced into evidence an e-mail in which it admitted for the first time that the 35 m.p.h. figure was not based on any objective evidence. In March 2003, the ALJ ruled in favor of the TCLs for the fourth time, awarding them $581,157 plus accrued interest. This time, the DHHS did not appeal. In December 2003, the DHHS issued two checks which included interest of $41,104.75, which the DHHS had calculated only from the March 2003 date of the ALJ’s fourth ruling.
The TCLs objected to the DHHS’ calculation of interest and, in May 2004, requested that the ALJ rule supplementally that interest began to accrue as of January 1992, the date of the first of the four ALJ rulings rendered in their favor. The ALJ held that he did not have the authority to rule on the issue, and the TCLs appealed. The Appeals Council ruled that the ALJ did have the authority to rule on the matter, and no additional interest was owed to the TCLs.
The TCLs appealed the Appeals Council’s ruling to the district court. After a dispute over standing was resolved in favor of the TCLs, Texas Clinical Labs, Inc. v. Leavitt, 535 F.3d 397 (5th Cir.2008), both parties filed summary judgment motions. The district court granted DHHS’ summary judgment motion, finding in its favor on alternative grounds: (1) that because waivers of sovereign immunity are to be construed narrowly, the Medicare statute cannot be read to waive immunity for interest on judgments subsequently reversed by the Appeals Council, and (2) that the Appeals Council interpretation of the regulation was entitled to Chevron deference.
II.
We review a grant of summary judgment de novo, applying the same standard as the district court. Wilson v. Sec’y, Dept. of Veterans Affairs, 65 F.3d 402, 403 *775(5th Cir.1995). Under the Administrative Procedures Act (“APA”), “[t]he district court, and this court ... may overturn the Secretary’s ruling only if it is arbitrary, capricious, an abuse of discretion, not in accordance with law, or unsupported by substantial evidence on the record taken as a whole.” Sun Towers, Inc. v. Schweiker (Sun Towers I), 694 F.2d 1036, 1038 (5th Cir.1983). In reviewing an agency’s decision under the arbitrary and capricious standard, there is a presumption that the agency’s decision is valid, and the plaintiff has the burden to overcome that presumption by showing that the decision was erroneous. Delta Foundation Inc. v. United States, 303 F.3d 551, 564 (5th Cir.2002). As Justice Scalia recently reminded us, the standard of review is thus highly deferential to the administrative agency whose final decision is being reviewed and a court “should not substitute [its] own judgment for the agency’s.” F.C.C. v. Fox Television Stations, Inc., — U.S. -, 129 S.Ct. 1800, 1810, 173 L.Ed.2d 738 (2009). An agency’s decision “need not be ideal or even, perhaps, correct so long as not ‘arbitrary’ or ‘capricious’ and so long as the agency gave at least minimal consideration to the relevant facts as contained in the record.” Am. Petroleum Inst. v. E.P.A., 661 F.2d 340, 349 (5th Cir.1999); see also, id. “The [agency’s] purely legal questions are reviewed de novo,” giving deference to the agency’s interpretation of the statute and regulations as appropriate. Alwan v. Ashcroft, 388 F.3d 507, 510 (5th Cir.2004).
Payment of interest on Medicare debts is required pursuant to 42 U.S.C. § 1395l a):
(j) Accrual of interest on balance of excess or deficit not paid Whenever a final determination is made that the amount of payment made under this part either to a provider of services or to another person pursuant to an assignment under section 1395u(b) (3) (B) (ii) of this title was in excess of or less than the amount of payment that is due, and payment of such excess or deficit is not made (or effected by offset) within 30 days of the date of the determination, interest shall accrue on the balance of such excess or deficit not paid or offset (to the extent that the balance is owed by or owing to the provider) at a rate determined in accordance with the regulations of the Secretary of the Treasury applicable to charges for late payments.
The crux of the problem in this case, however, is which of the four ALJ rulings rendered in the TCLs’ favor constituted a “final determination” for the purposes of triggering the accrual of interest.
Our review is governed by the classic two-step framework from Chevron USA v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984): If Congress “has directly spoken to the precise question at issue,” we “must give effect to [its] unambiguously expressed intent”; on the other hand, “if the statute is silent or ambiguous,” we must defer to the agency’s interpretation so long as it is “based on a permissible construction of the statute.” Id. at 842-43, 104 S.Ct. 2778. “We accord deference to agencies under Chevron because of a presumption that Congress, when it- left ambiguity in a statute meant for implementation by an agency, understood that the ambiguity would be resolved, first and foremost, by the agency, and desired the agency (rather than the courts) to possess whatever degree of discretion the ambiguity allows.” United States v. Mead, 533 U.S. 218, 240, 121 S.Ct. 2164, 150 L.Ed.2d 292 (2001) (Scalia, J. dissenting). In this case, while the Medicare statute requires interest to be paid on the unpaid balance of underpayments and overpayments, the statute does not define what type of rulings constitute *776“final determinations” upon which interest should accrue. Nor is its language so clear as to only permit a single interpretation. Since the statute does not unambiguously speak to the precise question at issue we look to the regulation for guidance.
A similar two-step test applies when interpreting an agency regulation. First, the court must ask whether the regulation is “ambigu[ous] with respect to the specific question considered.” Moore v. Hannon Food Sen., 317 F.3d 489, 495 (5th Cir.2003); Christensen v. Harris County, 529 U.S. 576, 588, 120 S.Ct. 1655, 146 L.Ed.2d 621 (2000). Second, if the regulation is ambiguous, the agency’s interpretation (as contained in, e.g., opinion letters) is “controlling unless plainly erroneous or inconsistent with the regulation.” Auer v. Robbins, 519 U.S. 452, 461, 117 S.Ct. 905, 137 L.Ed.2d 79 (1997). If the regulation is unambiguous, the court may still consider the agency’s interpretation, but only according to its persuasive power. See Skidmore v. Swift & Co., 323 U.S. 134, 140, 65 S.Ct. 161, 89 L.Ed. 124 (1944).
In relevant part, 42 C.F.R. § 405.378(c) reads:
(c) Definition of final determination.
(1) For purposes of this section, any of the following constitutes a final determination:
(ii) In cases in which an NPR [Notice of Public Rulemaking] is not used as a notice of determination (that is, primarily under part B), one of the following determinations is issued—
(A) A written determination that an overpayment exists and a written demand for payment;
(B) A written determination of an underpayment; or
(C) An Administrative Law Judge (ALJ) ruling that reduces the amount of an overpayment below the amount that CMS has already collected.
(2) Except as required by any subsequent administrative or judicial reversal, interest accrues from the date of final determination as specified in this subsection.
(emphasis added).
While the language of subsection 405.378(c)(1)(ii)(B) — “[a] written determination of an underpayment” — unambiguously identifies an ALJ’s written judgment as a “final determination” from which interest accrues, subsection 405.378(c)(2) creates ambiguity as to the effect of an order by the Appeals Council vacating and remanding an ALJ’s final determination on the accrual of interest. As a result, the regulation is not detailed enough to resolve the particular question before the court. On one hand, it would be completely consistent with the regulatory language for the court to decide that the litigation in this case constituted a single string of appeals of the 1992 judgment, and that interest began to accrue in 1992 on the portion of the judgment that was ultimately upheld. However, it would also be consistent with the regulation to conclude that a ruling by the Appeals Council vacating an ALJ judgment and remanding for additional proceedings nullifies the ALJ judgment and restarts the clock on the interest determination. This second interpretation is even more reasonable under the circumstances before the court, where there is a mixed judgment, i.e., an initial award amount containing claims that were ultimately resolved against the party asking for interest. Because the regulation comfortably bears more than one interpretation, we find it ambiguous and turn to the agency’s interpretation for guidance.
*777Generally, an agency’s interpretation of its own ambiguous regulation is “controlling” unless “plainly erroneous or inconsistent with the regulation.” Auer, 519 U.S. at 461, 117 S.Ct. 905 (quotation marks and citation omitted); Belt v. Em-Care, Inc., 444 F.3d 403, 408 (5th Cir.2006). This deference is inappropriate, however, where the interpretation is a novel litigating position “wholly unsupported by regulations, rulings, or administrative practice.” Brown v. Georgetown Univ. Hosp., 488 U.S. 204, 212, 109 S.Ct. 468, 102 L.Ed.2d 493 (1988) (explaining that “[d]eference to what appears to be nothing more than an agency’s convenient litigating position would be entirely inappropriate”); see also Auer, 519 U.S. at 462, 117 S.Ct. 905 (stating that a “post hoc rationalization” that does not represent the “agency’s fair and considered judgment on the matter in question” is not entitled to deference); Belt, 444 F.3d at 415.
The Appeals Council concluded that under section 405.378(c)(2) interest does not accrue on a final determination that is subsequently reversed by an administrative or judicial ruling.1 It also means, according to the Appeals Council that interest cannot accrue on a mixed judgment where part of that judgment is reversed. Accordingly, because the 1992 judgment was vacated by the Appeals Council, and because the original judgment resolved a mix of claims, only some of which were ultimately upheld, interest did not begin to accrue in 1992.
The TCLs respond that section 405.378(c)(2) has never been applied in the manner proposed by DHHS and instead means that erroneously collected interest will be refunded if, on appeal, the amount of overpayment or underpayment is adjusted. The TCLs urge the court to treat the twenty years of litigation in this case as a lengthy adjustment of the initial determination. Because they were eventually successful on their challenge to the 35 m.p.h. component, they argue that interest accrued from the initial judgment for the portion of the claim on which they were successful.
In support of their interpretation, the TCLs point to one prior agency statement and one unpublished case which suggest that interest accrues during the pendency of an appeal. In its comment on the final rule implementing the interest accrual statute, the Secretary stated, “[w]e believe that [starting interest accrual after exhaustion of all avenues of appeal] is inconsistent with congressional intent ... since it would encourage appeals simply to avoid or delay the payment of interest.” 47 Fed.Reg. 54811-01, 54812 (Dec. 6, 1982). According to the TCLs, in Bertschland Family Practice Clinic, P.C. v. Thompson, No. IP01-562-CH/F, 2002 WL 1364155 (S.D. Ind. June 4, 2002) the DHHS argued that interest accrued from an ALJ determination of an underpayment despite subsequent appeals and even though the determination did not finally calculate the amount owed.
Even assuming arguendo that the TCLs’ interpretation of the Secretary’s statement and Bertschland are correct, the TCLs fail to meaningfully challenge the agency’s interpretation of the effect of an Appeals Council reversal and remand on a mixed judgment. The TCLs do not point to a single comment or case suggesting that the agency has ever paid interest on a judgment that was reversed in whole or in part by the Appeals Council. In fact, the TCLs do not point to a single comment or *778case that addresses the application of the interest accrual regulation in the case of multiple ALJ judgments stemming from an Appeals Council reversal and remand.
Without stronger evidence that the agency has applied the regulation at issue inconsistently, there is little reason to believe that the DHHS’ interpretation— which was initially articulated in adjudication by the Appeals Council — is merely a litigating position rather than the agency’s “fair and considered judgment on the matter in question.” Auer, 519 U.S. at 462, 117 S.Ct. 905. Because the interpretation represents the DHHS’ considered judgment, it is entitled to substantial deference under Auer.
While the dissent argues that there is no other reason, besides “an automatic nod” to agency deference to support the conclusion that interest should not run on the favorable portion of the award we disagree. As the Secretary has stated “[t]he amount of [a] debt must be established before it becomes due and payable and thus subject to interest.” 56 Fed.Reg. 54811-01, 54812 (July 10, 1991). In this case, the 2003 ALJ decision specifically identified the exact amount of the principal due to the TCLs. In contrast, the 1992 decision did not establish the amount of the debt or identify an underpayment of $581,157 specifically related to the carrier’s decision to use the 35 m.p.h. component. Instead, the 1992 decision established underpayments of $692,865 to Texas Clinical Labs and $800,852 to Texas Clinical Labs — Gulf Division and included amounts based on three findings: (1) the median specimen figure was not supported; (2) the 35 m.p.h. figure was not supported; and (3) that payment should be made for future claims that had not been addressed in an earlier hearing. As noted above, the Appeals Council ultimately reversed the 1992 judgment’s conclusion that the median specimen figure was not supported and revised the scope of the claims addressed in the judgment. These conclusions were later affirmed by the district court and this court. The 1992 judgment cannot be considered a final determination because in addition to being a mixed judgment, the debt included inappropriate claims that were inseparably intertwined with the amount awarded for the m.p.h. component.2
*779III.
For the foregoing reasons, we affirm the district court’s judgment.
. At various points in their brief, the TCLs allege that the DHHS is arguing that the regulation means that interest does not accrue until all administrative and judicial appeals are exhausted. This is a mischaracterization; DHHS does not seem to dispute that if an ALJ judgment is not reversed then interest accrues from the date of judgment.
. There is also a more subtle explanation to support the conclusion that the agency's interpretation of the regulation is due considerable deference. “Apart from constitutional requirements, in the absence of a specific provision by contract or statute, or 'express consent ... by Congress’ interest does not run on a claim against the United States.” United States v. Louisiana, 446 U.S. 253, 264-65, 100 S.Ct. 1618, 64 L.Ed.2d 196 (1980): see also, 28 U.S.C. § 2516(a) (“Interest on a claim against the United States shall be allowed in a judgment of the United States Court of Federal Claims only under a contract or Act of Congress expressly providing for payment thereof.”) In cases where Congress has provided a limited waiver of sovereign immunity not only must that waiver be strictly construed but it must, in fact, be construed in favor of the sovereign. See, e.g., Gomez-Perez v. Potter, 553 U.S. 474, 128 S.Ct. 1931 1942, 170 L.Ed.2d 887 (2008); Library of Congress v. Shaw, 478 U.S. 310, 319, 106 S.Ct. 2957, 92 L.Ed.2d 250 (1986); McMahon v. United States, 342 U.S. 25, 27, 72 S.Ct. 17, 96 L.Ed. 26 (1951).
In this case, Congress has provided a limited waiver of sovereign immunity on claims of interest brought under 42 U.S.C. § 13951(j). Thus, because 42 U.S.C. § 1395Z(j) only offers a limited waiver of sovereign immunity it must be strictly construed, in term of its scope, in favor of the sovereign. The TCLs seek to impermissibly broaden the statute by including provisions that (1) require interest on any written determination of an underpayment; (2) require interest to be paid even if the underpayment determination itself is modified; and (3) require interest to begin before a debt is determined and a balance is calculated.
The doctrine of limited waiver of sovereign immunity also explains why we choose not to read 42 C.F.R. § 405.378(c)(ii)(B) in pari *779materia with 405.378(e)(1) which provides that interest on an overpayment runs against a provider “during periods of administrative and judicial appeal and until final disposition of the claim." Unlike the government, who is generally protected from the payment of interest by sovereign immunity, providers who are overpaid and ultimately must pay interest on the overpayment under 405.378(e)(1) are provided no such protection. If we were to read 405.378(c)(ii)(B) in pari materia with 405.378(e)(1) we would violate the principles of limited sovereign immunity by broadening the interpretation of when 405.378(c)(ii)(B) requires the government to pay interest on an underpayment.