
603 F.3d 57 (2010)
BAPTIST MEMORIAL HOSPITAL, Appellant
v.
Kathleen SEBELIUS, Secretary, Department of Health and Human Services, Appellee.
St. Agnes Medical Center, Appellant
v.
Kathleen Sebelius, Secretary, U.S. Department of Health and Human Services, Appellee.
Nos. 09-5248, 09-5258.
United States Court of Appeals, District of Columbia Circuit.
Argued March 22, 2010.
Decided April 30, 2010.
*59 Leslie D. Alderman III argued the cause for appellant Baptist Memorial Hospital. With him on the briefs was Kenneth R. Marcus.
Thomas J. Weiss, pro hac vice, argued the cause for appellant St. Agnes Medical Center.
Christine N. Kohl, Attorney, U.S. Department of Justice, argued the cause for appellee. With her on the brief was Anthony J. Steinmeyer, Assistant Director. Gerard Keating, Attorney, U.S. Department of Health & Human Services, and R. Craig Lawrence, Assistant U.S. Attorney, entered appearances.
Before: GINSBURG, TATEL, and GRIFFITH, Circuit Judges.
Opinion for the Court filed by Circuit Judge TATEL.
TATEL, Circuit Judge:
In these consolidated cases, two hospitals seek mandamus to compel the Secretary of Health and Human Services to reopen final Medicare reimbursement determinations regarding inpatient services provided by the hospitals. Concluding that the Secretary had no clear duty to reopen the payment decisions, the district court dismissed both cases for lack of mandamus jurisdiction. We agree with the district court on all counts and therefore affirm.

I.
The central issue presented in these cases has been the focus of extensive litigation culminating in two controlling decisions from this court  In re Medicare Reimbursement Litigation, 414 F.3d 7 (D.C.Cir.2005), and Monmouth Medical Center v. Thompson, 257 F.3d 807 (D.C.Cir.2001). We therefore provide only *60 the following brief overview of the applicable statutory and regulatory regime.
Under the Medicare Act, the Secretary of Health and Human Services (HHS) reimburses hospitals for covered inpatient services provided to Medicare beneficiaries. 42 U.S.C. § 1395ww. HHS administers these payments through the Centers for Medicare and Medicaid Services, formerly the Health Care Financing Administration (HCFA). To obtain reimbursement, hospitals submit yearly cost reports to fiscal intermediaries  typically private insurance companies acting on behalf of the Secretary. After auditing the cost report, the intermediary issues a Notice of Program Reimbursement (NPR), in which it determines the amount owed to the hospital for the cost reporting year at issue. 42 C.F.R. § 405.1803. Hospitals can appeal that determination to the Provider Reimbursement Review Board ("the Board") and then to federal district court. 42 U.S.C. § 1395oo(a), (f).
Hospitals serving a disproportionately high number of low-income Medicare patients receive increased reimbursements known as "disproportionate share hospital" (DSH) adjustments. Congress has set forth a formula for determining DSH adjustments based, in part, on the number of days that a hospital treated patients entitled to state Medicaid payments. Id. § 1395ww(d)(5)(F)(vi)(II). Previously, HCFA interpreted this statutory formula to include only those days for which hospitals actually received Medicaid payments  an interpretation that the Fourth, Sixth, Eighth, and Ninth Circuits struck down as inconsistent with the Medicare Act. Cabell Huntington Hosp., Inc. v. Shalala, 101 F.3d 984 (4th Cir.1996); Legacy Emanuel Hosp. & Health Ctr. v. Shalala, 97 F.3d 1261 (9th Cir.1996); Deaconess Health Servs. Corp. v. Shalala, 83 F.3d 1041 (8th Cir.1996) (per curiam); Jewish Hosp., Inc. v. Sec'y of Health & Human Servs., 19 F.3d 270 (6th Cir.1994). In 1997, acknowledging that its prior interpretation was "contrary to the applicable law in four judicial circuits," HCFA issued Ruling 97-2, which instructed intermediaries to include all Medicaid-eligible days in the DSH adjustment calculation, regardless of whether the hospital actually received payments for those days. Health Care Financing Administration Ruling 97-2 (Feb. 27, 1997) ("Ruling 97-2" or "HCFAR 97-2").
The two cases before us involve the intersection of Ruling 97-2 and HHS regulations authorizing the reopening of intermediary reimbursement determinations. Pursuant to 42 C.F.R. § 405.1885(a) (1997), as that regulation existed at all relevant times, an intermediary's reimbursement determination "may be reopened" if the affected hospital moves to do so "within 3 years of the date of the notice of the intermediary determination." Unlike NPR determinations themselves, an intermediary's decision whether to reopen a determination under this provision is both discretionary and unreviewable. Your Home Visiting Nurse Servs., Inc. v. Shalala, 525 U.S. 449, 452-56, 119 S.Ct. 930, 142 L.Ed.2d 919 (1999). Additionally, 42 C.F.R. § 405.1885(b) (1997)  the key provision at issue here  provides that a determination rendered by the intermediary "shall be reopened and revised by the intermediary if, within the aforementioned 3-year period, [HCFA] notifies the intermediary that such determination or decision is inconsistent with the applicable law, regulations, or general instructions issued by [HCFA]."
In Monmouth, the first of our two previous decisions regarding this issue, we concluded that Ruling 97-2 constitutes notice under section 405.1885(b) that HCFA's former method of calculating DSH adjustments *61 was "inconsistent with the applicable law." 42 C.F.R. § 405.1885(b). Accordingly, we held that because section 405.1885(b) speaks in mandatory terms, it imposes a nondiscretionary duty on the Secretary, enforceable through mandamus, to reopen NPRs decided within the three years before the issuance of Ruling 97-2  notwithstanding the fact that Ruling 97-2 itself states that the agency "will not reopen settled cost reports based on this issue." See Monmouth, 257 F.3d at 814-15. Then, in In re Medicare, we clarified that this clear duty to reopen applies to NPRs issued during the three years prior to Ruling 97-2 even for hospitals that had failed to appeal a cost report or request reopening: "given that section 405.1885(b) does not require hospitals to file anything at all to obtain relief, we see no basis for holding that only those hospitals that appealed or sought section 405.1885(a) reopening have a personal right to the reopening required by section 405.1885(b)." In re Medicare, 414 F.3d at 11.
Relying on our decisions in Monmouth and In re Medicare, the two hospitals in these consolidated appeals seek mandamus to compel the Secretary (through her intermediaries) to reopen their cost reports and apply the more favorable DSH calculation adopted in Ruling 97-2. See 28 U.S.C. § 1361. The first hospital, Baptist Memorial, challenges a 1993 NPR that determined, pursuant to HCFA's former eligible days calculation, that it was ineligible for a DSH adjustment for its FY 1991 cost report. In 1994, Baptist appealed that decision to the Board. While that appeal was still pending, HCFA issued Ruling 97-2. The Board then advised Baptist of the filing schedule for the appeal and warned that its case would be dismissed if Baptist missed the applicable deadlines. Despite this reminder, Baptist failed to submit its "position papers" on time, and the Board consequently dismissed its appeal for want of prosecution in 1998. Four years later, Baptist filed this mandamus action in the U.S. District Court for the District of Columbia, seeking an order compelling the Secretary to reopen and correct the 1993 reimbursement determination pursuant to the eligible but unpaid days calculation set forth in Ruling 97-2.
The second hospital before us, St. Agnes Medical Center, challenges its intermediary's 1992 NPR determination regarding its FY 1990 cost report. In 1995, St. Agnes asked the intermediary to reopen the cost report and provide a DSH adjustment, but the intermediary rejected that request. St. Agnes appealed that decision to the Board, and on June 4, 1997 (after Ruling 97-2's issuance), the parties settled, agreeing that the intermediary would reopen St. Agnes's cost report to apply a DSH adjustment. After doing so and applying the former eligible days calculation, however, the intermediary informed St. Agnes that it failed to meet the qualifying threshold for an adjustment. Then, in 1999, the Board dismissed St. Agnes's appeal on the ground that it lacked jurisdiction over that appeal in view of Your Home Visiting Nurse Services, Inc. v. Shalala, 525 U.S. at 453, 119 S.Ct. 930, in which the Supreme Court held that the Board lacks authority to review an intermediary's refusal under section 405.1885(a) to reopen a reimbursement determination. Seven years after the dismissal of its appeal, St. Agnes sought mandamus relief in the district court.
The district court dismissed both mandamus actions for lack of jurisdiction. Noting that the two hospitals sought reopening of NPRs issued more than three years prior to Ruling 97-2's issuance in 1997, the court concluded that neither hospital could show that it had a clear right to relief or that the Secretary had a nondiscretionary duty to act under the regulation *62  prerequisites for mandamus jurisdiction. See Power v. Barnhart, 292 F.3d 781, 784 (D.C.Cir.2002) (outlining requirements for mandamus relief). In reaching this conclusion, the district court also rejected the hospitals' argument that they were entitled to mandamus relief because they had jurisdictionally proper appeals pending when HCFA issued Ruling 97-2. Baptist Mem'l Hosp. v. Johnson, 603 F.Supp.2d 40, 45-46 (D.D.C.2009); St. Agnes Med. Ctr. v. Sebelius, 628 F.Supp.2d 78, 83-84 (D.D.C.2009).
Baptist and St. Agnes appealed the denials of their mandamus petitions. Because both cases require us to answer the same principal question  whether section 405.1885(b) mandates reopening of NPRs issued more than three years prior to issuance of Ruling 97-2 where the hospitals had appeals pending at that time  we consolidated the appeals.

II.
The Mandamus Act grants district courts original jurisdiction over "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. A court may grant mandamus relief "only if: (1) the plaintiff has a clear right to relief; (2) the defendant has a clear duty to act; and (3) there is no other adequate remedy available to plaintiff." Power, 292 F.3d at 784 (internal quotation marks omitted). We review a district court's determination whether a plaintiff has satisfied these standards de novo. In re Medicare, 414 F.3d at 10.
In Monmouth and In re Medicare, we held that the Secretary had a clear duty to reopen the hospitals' NPRs pursuant to section 405.1885(b) because the notice of inconsistency  i.e., Ruling 97-2  occurred within the three-year period after the date of the challenged reimbursement determinations. Baptist and St. Agnes concede, as they must, that unlike the hospitals in Monmouth and In re Medicare, they seek reopening of "intermediary determinations that were issued before the three-year reopening window, as measured from the issuance of HCFAR 97-2." Appellants' Br. 26. They nonetheless contend that the district court erred in dismissing their mandamus actions because Ruling 97-2's "appeal provision" imposes on the Secretary a nondiscretionary duty to reopen their cost reports. The portion of Ruling 97-2 on which the hospitals rely states:
We will not reopen settled cost reports based on this issue. For hospital cost reports that are settled by fiscal intermediaries on or after the effective date of this ruling, these [eligible but unpaid] days may be included. For hospital cost reports which have been settled prior to the effective date of this ruling, but for which the hospital has a jurisdictionally proper appeal pending on this issue pursuant to either 42 CFR 405.1811 or 42 CFR 405.1835, these [eligible but unpaid] days may be included for purposes of resolving the appeal.
Homing in on the last sentence of this paragraph, the hospitals argue that Ruling 97-2 creates a mandatory duty to reopen their cost reports because they had "jurisdictionally proper appeal[s]" pending before the Board when HCFA issued the 1997 ruling.
In arguing that the appeal provision compels the Secretary to reopen their cost reports, however, the hospitals lose sight of the fact that under Monmouth and In re Medicare it is section 405.1885(b), not Ruling 97-2, that creates the obligation to reopen. Ruling 97-2 merely serves as the notice of inconsistency that triggers the Secretary's duty to reopen and revise *63 NPR determinations. But that obligation  and thus the clear duty to act required for mandamus relief  itself derives from section 405.1885(b)'s "shall be reopened" language. And the scope of section 405.1885(b)'s mandate is clear: it expressly limits the duty to reopen to cases in which HCFA provides a notice of inconsistency to intermediaries within three years of the NPR. Ruling 97-2's appeal provision is therefore beside the point, as it does nothing to alter section 405.1885(b)'s three-year reopening limitation. See Monmouth, 257 F.3d at 814-15 ("[Section] 405.1885(b) impose[s] a clear duty on intermediaries to reopen DSH payment determinations for the hospitals. The portion of HCFAR 97-2 that conflicts with that duty is simply inapplicable."); see also 42 C.F.R. § 405.1885(a) ("No such determination or decision may be reopened after such 3-year period except as provided in paragraphs (d) and (e) of this section.").
As the district court explained, moreover, even if the appeal provision had any effect here, that provision says only that eligible but unpaid days "may" be included if a hospital has an appeal pending on the issue: "While the above paragraph [containing the appeal provision] plainly permitted the Secretary and the Review Board to rely on HCFAR 97-2's policy change when settling appeals pending at the time HCFAR 97-2 was issued, it does not require them to do so." Baptist, 603 F.Supp.2d at 46; see St. Agnes, 628 F.Supp.2d at 83. The hospitals respond that although the word "may" usually connotes a degree of discretion, in this context it actually means "must" or "shall." But we agree with the district court that the most natural reading of this provision is the one that is most obvious: "may" is permissive rather than obligatory. The appeal provision therefore cannot provide the "clear duty to act" necessary to sustain the hospitals' requests for mandamus relief. Power, 292 F.3d at 784 (internal quotation marks omitted).
Reinforcing this conclusion, the appeal provision specifies that eligible but unpaid days may be included "for purposes of resolving the appeal" under 42 C.F.R. §§ 405.1811 or 405.1835. In other words, the appeal provision is just that: it pertains to the resolution of appeals, not to the reopening of settled cost reports under section 405.1885. Because neither Baptist nor St. Agnes had any such appeal pending when it brought its mandamus action in the district court, there is no extant appeal to "resolv[e]" through application of the new eligible days calculation.
Baptist and St. Agnes further contend that even if Ruling 97-2 creates no duty to reopen, the filing of their appeals tolled the three-year reopening limitation. But because neither hospital pressed this argument in the district court, they cannot do so for the first time here. See Adams v. Rice, 531 F.3d 936, 945 (D.C.Cir.2008) (refusing to consider argument never made in district court).

III.
Having disposed of the principal argument shared by Baptist and St. Agnes, we turn to the arguments unique to each hospital.

Baptist Memorial
Baptist raises an alternative theory of mandamus relief based on a 1994 policy memorandum HCFA issued in the wake of the Sixth Circuit's decision in Jewish Hospital v. Secretary of Health & Human Services, 19 F.3d 270  the first of the four circuit court decisions striking down the former eligible days calculation as inconsistent with the Medicare Act. This "Sixth *64 Circuit Memorandum" informed the HCFA regional office of the Jewish Hospital opinion and instructed it to apprise intermediaries serving hospitals within the Sixth Circuit of the resulting "change in policy concerning DSH calculations." Located within the jurisdiction of the Sixth Circuit, Baptist argues that the Sixth Circuit Memorandum constitutes a notice of inconsistency for purposes of section 405.1885(b).
If, as Baptist alleges, the Sixth Circuit Memorandum qualifies as proper notice of inconsistency, then it would indeed trigger section 405.1885(b)'s duty to reopen. This is because HCFA issued the memorandum in 1994  comfortably within the three-year period following Baptist's 1993 NPR. Although it is unclear from the record whether HCFA ever conveyed the new policy articulated in the Sixth Circuit Memorandum to intermediaries (as required to qualify as notice under section 405.1885(b)), we need not decide whether the memo triggered a "clear right to relief" or "duty to act" (the first two requirements for mandamus relief) because Baptist has failed to show that there was "no other adequate remedy available" (the third requirement for mandamus relief). Power, 292 F.3d at 784 (internal quotation marks omitted).
Baptist filed its appeal with the Board just a few days after the Sixth Circuit issued its decision in Jewish Hospital  controlling authority directly supporting Baptist's argument that the intermediary should have calculated its DSH adjustment using eligible but unpaid days. And while that appeal was pending, HCFA issued the Sixth Circuit Memorandum, which adopted Jewish Hospital as binding on intermediaries. Yet instead of raising the Jewish Hospital decision in its appeal to the Board and then, if necessary, seeking subsequent court review pursuant to 42 U.S.C. § 1395oo(f), Baptist abandoned its appeal altogether. As the district court rightly concluded, Baptist has offered no "compelling reason for its failure to pursue these avenues of relief." Baptist, 603 F.Supp.2d at 47; see Heckler v. Ringer, 466 U.S. 602, 616, 104 S.Ct. 2013, 80 L.Ed.2d 622 (1984) ("The common-law writ of mandamus, as codified in 28 U.S.C. § 1361, is intended to provide a remedy for a plaintiff only if he has exhausted all other avenues of relief.").
Baptist insists that it did supply a valid reason for abandoning its appeal: "the Hospital reasonably believed that it was unnecessary for it to pursue its appeal of fiscal year 1991 before the [Board] because the Hospital was of the understanding that the intermediary was required to unilaterally reopen the cost report to make the DSH adjustment by including" eligible but unpaid days. Appellants' Br. 50 (internal quotation marks omitted). But for purposes of mandamus jurisdiction, the question is whether Baptist had an adequate remedy. It did  the administrative appeal that it subsequently abandoned. Even though this remedy may have been, in Baptist's view, redundant (because Baptist thought the intermediary was obligated to reopen the NPR on its own initiative), that hardly renders it inadequate. Having failed to pursue the adequate remedy afforded by the administrative and judicial appeal processes, Baptist cannot now seek to vindicate its alleged right to relief through mandamus.

St. Agnes
St. Agnes's alternative argument suffers from the same flaw. It contends that once the intermediary reopened its cost report pursuant to the 1997 settlement agreement, the intermediary was obligated to include eligible but unpaid days in the DSH calculation. According to St. Agnes, that obligation derives from three *65 sources: (1) Ruling 97-2; (2) the Ninth Circuit's decision in Legacy Emanuel Hospital & Health Center v. Shalala, 97 F.3d 1261  the third in the quartet of circuit court opinions striking down HCFA's former eligible days interpretation; and (3) the "Ninth Circuit Memorandum," a HCFA directive (analogous to the Sixth Circuit Memorandum discussed above) instructing the regional office to notify fiscal intermediaries serving hospitals in the Ninth Circuit, where St. Agnes is located, of the Legacy Emanuel decision. When calculating the DSH adjustment for the reopened cost report, however, the intermediary, allegedly in violation of all three of these authorities, used HCFA's former eligible days calculation. St. Agnes complains that it lacked any remedy for this violation because "once the Board had dismissed [its appeal] for lack of jurisdiction" pursuant to Your Home, it "was left without a further avenue to obtain the benefit to which it was entitled under the reopening." Reply Br. 31.
Your Home, however, only barred St. Agnes from seeking review of the intermediary's refusal to reopen the FY 1990 cost report; it did not prevent St. Agnes from challenging the reimbursement determination made by the intermediary after the intermediary reopened the cost report in 1997. As the Supreme Court explained, "an intermediary's affirmative decision to reopen and revise a reimbursement determination `shall be considered a separate and distinct determination' to which the regulations authorizing appeal to the Board are applicable." Your Home, 525 U.S. at 453, 119 S.Ct. 930 (quoting 42 C.F.R. § 405.1889). Although St. Agnes's intermediary may not have "revise[d]" the DSH adjustment, the Ninth Circuit has interpreted the appeal regulations as permitting Board review of "all matters the fiscal intermediary had reconsidered upon reopening the cost report," not just those cost items modified on reopening. French Hosp. Med. Ctr. v. Shalala, 89 F.3d 1411, 1420 (9th Cir.1996); see Edgewater Hosp., Inc. v. Bowen, 857 F.2d 1123, 1135 (7th Cir.1989) (noting that an intermediary's decision not to change challenged cost items "itself was a reconsideration" subject to appeal), amended by 866 F.2d 228 (7th Cir.1989).
Yet St. Agnes made no effort to appeal the intermediary's 1997 reimbursement determination to the Board, and it gives us no persuasive reason to believe it could not have done so. Nor did it take any other action to contest the implementation of the settlement agreement until it filed its mandamus action in the district court seven years later. Because St. Agnes, like Baptist, failed to seek relief through available administrative and judicial review procedures, it cannot do so now through mandamus.

IV.
For the foregoing reasons, we affirm the district court's dismissals of both mandamus actions.
So ordered.
