
573 F.3d 808 (2009)
Elouise Pepion COBELL, et al., Appellants/Cross-Appellees
v.
Kenneth Lee SALAZAR, Secretary of the Interior, et al., Appellees/Cross-Appellants.
No. 08-5500, 08-5506.
United States Court of Appeals, District of Columbia Circuit.
Argued May 11, 2009.
Decided July 24, 2009.
Dennis M. Gingold argued the cause for appellants/cross-appellees. With him on the briefs were Elliott H. Levitas and *809 David C. Smith. Keith M. Harper entered an appearance.
Alisa B. Klein, Attorney, U.S. Department of Justice, argued the cause for appellees/cross-appellants. With her on the briefs were Michael F. Hertz, Acting Assistant Attorney General, Jeffrey A. Taylor, U.S. Attorney, and Robert E. Kopp, Mark B. Stern, Thomas M. Bondy, Alisa B. Klein, Mark R. Freeman, and Samantha L. Chaifetz, Attorneys. Tracy L. Hilmer and James C. Kohn, Attorneys, U.S. Department of Justice, and R. Craig Lawrence, Assistant U.S. Attorney, entered appearances.
Merrill C. Godfrey argued the cause for movant-intervenor Osage Nation. With him on the brief was James P. Tuite.
Before: SENTELLE, Chief Judge, GINSBURG, Circuit Judge, and RANDOLPH, Senior Circuit Judge.
Opinion for the Court filed by Chief Judge SENTELLE.
SENTELLE, Chief Judge:
In this interlocutory appeal, both plaintiffs and defendants in protracted litigation over trust accounts held by federal officials on behalf of American Indians seek review of orders of the district court. The district court held the Department of the Interior to be in continuing breach of its duty to account for trust funds and that accounting for the funds was impossible; it ordered monetary relief to the members of the plaintiff class. On review, we hold that while the district court's analysis of duty and breach are generally correct, the court erred in freeing the Department of the Interior from its burden to make an accounting. We therefore vacate the district court's orders and remand for further proceedings.

I. Background
In 1996, beneficiaries of Individual Indian Money (IIM) trust accounts brought this class action against the Secretary of the Interior, the Secretary of the Treasury, and the Assistant Secretary of the Interior for Indian Affairs, alleging that those officials had violated their fiduciary duties as trustees acting on behalf of the United States. See Cobell v. Babbitt, 30 F.Supp.2d 24, 29 (D.D.C.1998) (Cobell I). The bulk of the trust assets "are the proceeds of various transactions in land allotted to individual Indians under the General Allotment Act of 1887, known as the `Dawes Act.'" Cobell v. Norton, 392 F.3d 461, 463 (D.C.Cir.2004) (Cobell XIII) (citing 24 Stat. 388 (codified as amended at 25 U.S.C. § 331 et seq. (§§ 331-333 repealed 2000))). In bringing this action, appellants rely upon the American Indian Trust Fund Management Reform Act of 1994, Pub.L. No. 103-412, 108 Stat. 4239 (codified as amended at 25 U.S.C. § 162a et seq.; id. at §§ 4001-4061) (1994 Act). That statute requires the Secretary of the Interior to "account for the daily and annual balance of all funds held in trust by the United States for the benefit of ... an individual Indian which are deposited or invested pursuant to the Act of June 24, 1938 (25 U.S.C. 162a)." 25 U.S.C. § 4011(a). The plaintiffs initially sought an accounting of the trust funds but did not seek payment of any money beyond "court costs, experts' costs, and attorneys' fees." Cobell I, 30 F.Supp.2d at 29.
Plaintiffs and defendants cross appeal from two orders of the district court. The first, Cobell v. Kempthorne, 532 F.Supp.2d 37, 39 (D.D.C.2008) (Cobell XX), held that the Department of the Interior continued to breach its duty to account for trust funds as identified in Cobell v. Babbitt, 91 F.Supp.2d 1, 58 (D.D.C.1999) (Cobell V), and affirmed by this court in Cobell v. *810 Norton, 240 F.3d 1081 (D.C.Cir.2001) (Cobell VI). Cobell XX further held that accounting for the funds was impossible "as a conclusion of law" because the government could not "achieve an accounting that passes muster as a trust accounting" given inadequate present and (likely) future funding from Congress. 532 F. Supp 2d at 104 n. 19. The second order of the district court, Cobell v. Kempthorne, 569 F.Supp.2d 223, 238, 251-52 (D.D.C.2008) (Cobell XXI), granted equitable restitution to the plaintiff class based on the unproven shortfall of the trust's actual value as compared with its statistically likely value. The district court stressed that breaching the duty to account did not generate the government's financial liability. Id. at 243. Rather, the government's "failure properly to allocate and pay trust funds to beneficiaries" gave rise to "restitution or disgorgement of the very money that ha[d] been withheld." Id. Accordingly, the court awarded $455,600,000 to the plaintiff class in what it called a restitutionary award. Id. at 226.
Soon after issuing Cobell XXI, the district court certified an immediate interlocutory appeal from both decisions under 28 U.S.C. § 1292(b). Order (Sept. 4, 2008). All plaintiffs and all defendants petitioned for permission to appeal, and this court granted the petitions. Orders (Nov. 21, 2008).
We now hold that the district court correctly held that the 1994 Act and Cobell VI required a full accounting, but erred in holding that an accounting cannot be conducted because, in the district court's view, Congress will never appropriate the funds necessary to conduct such an accounting. The statute gives the plaintiff class a right to an accounting. Sitting in equity, the district court has the authority to approve a plan that efficiently uses limited government resources to achieve that goal. It is within the power of the district court to order an accounting without requiring Interior to perform analyses the costs of which exceed the benefits payable to individual American Indians. It would indeed be "nuts" to spend billions to recover millions. Cobell XX, 532 F.Supp.2d at 86. A court sitting in equity may avoid reaching that absurdity.

* * *
As this case enters its thirteenth year, it becomes increasingly difficult to summarize its factual and procedural background. See Cobell XX, 532 F.Supp.2d at 103 & n. 20 (collecting quotations from Charles Dickens's Bleak House); id. at 39-43 (attempting such a summary). Cobell VI contains a general description of how funds came to be deposited in the IIM accounts. 240 F.3d at 1086-88. For a summary of their early mismanagement and the government's early attempts at reform, see id. at 1089-90.
Since passage of the 1994 Actand the filing of this lawsuitthe Department of the Interior has had mixed success in its efforts to account for the trust funds. Cobell XX, 532 F.Supp.2d at 43-56, provides a good summary of the evolution of the current historical accounting project. Apart from Interior's independent efforts, the district court has frequently issued injunctions specifying the terms of an accounting that it held were required by the 1994 Act. In 1999, the district court issued an eight-point injunction declaring the government in violation of the 1994 Act and in breach of trust. Cobell V, 91 F.Supp.2d at 58. The injunction ordered the defendants "to provide plaintiffs an accurate accounting of all money in the IIM trust held in trust for the benefit of plaintiffs, without regard to when the funds were deposited," and laid out a general plan for compliance. Id. We affirmed the district court's order in 2001. Cobell VI, 240 F.3d at 1110.
*811 In 2003, the district court issued a nine-page injunction. See Cobell v. Norton, 283 F.Supp.2d 66, 287-95 (D.D.C.2003) (Cobell X). That injunction called for a detailed accounting of "all funds deposited or invested in," id. at 288, or "assets held by[,] the Trust since the passage of the General Allotment Act of 1887," id. at 289, as well as money held by Indian tribes, accounts of deceased beneficiaries, and all property escheated from the trust. Id. at 288-89. When performing this accounting, Interior was prohibited from "mak[ing] use of any statistical sampling." Id. at 289. In Cobell XIII, 392 F.3d at 464-68, we vacated the "historical accounting" portions of Cobell X's injunction, relying on the appropriations language of the Department of the Interior and Related Agencies Appropriations Act of 2004, Pub L. No. 108-108, 17 Stat. 1241. That act, passed by Congress in November 2003, conditioned the appropriation of Indian trust money on the requirement that nothing in the 1994 Act, "or in any other statute, and no principle of common law, sh[ould] be construed or applied to require the Department of the Interior to commence or continue historical accounting activities with respect to the Individual Indian Money Trust until" (a) Congress amended the 1994 Act to "delineate [Interior's] specific historical accounting obligations" or (b) "December 31, 2004." 117 Stat. at 1263.
After 2005 arrived without congressional action, the district court reissued the injunction that had been vacated by Cobell XIII. Reasoning that "December 31, 2004 ha[d] come and gone" with "no legislative solution," the district court held itself "bound, by its findings of fact and conclusions of law" in Cobell X, "to reissue without modification the `historical accounting' provisions of its structural injunction." Cobell v. Norton, 357 F.Supp.2d 298, 300 (D.D.C.2005) (Cobell XIV). We again vacated the district court's injunction. See Cobell v. Norton, 428 F.3d 1070, 1074-77 (D.C.Cir.2005) (Cobell XVI). We explained that the 1994 "Act's general language doesn't support the inherently implausible inference that it intended to order the best imaginable accounting without regard to cost." Id. at 1075. Because of the unique nature of this trust, we held that "the common law of trusts doesn't offer a clear path for resolving" the "ambiguities" involved in setting the parameters of an accounting. Id. at 1074. And because "Congress was, after all, mandating an activity to be funded entirely at the taxpayers' expense," we held that the 1994 Act did not "grant courts the same discretion that an equity court would enjoy in dealing with a negligent trustee" to order "the best imaginable accounting without regard to cost." Id. at 1075. Congress's limited appropriation undercut any "mandate to indulge in cost-unlimited accountingin fact, [it] suggest[ed] quite the opposite." Id.
When we vacated the district court's injunction for abuse of discretion, we noted in particular that the injunction "caused the cost ... to rise by more than an order of magnitude, from $335 million over five years to more than $10 billion." Id. at 1077. We then specifically approved the use of statistical sampling on the rationale that for some transactions, "the average cost of accounting, per transaction, would exceed the average value of the transactions." Id. at 1078. We now take that reasoning a step further, and instruct the district court to use its equitable power to enforce the best accounting that Interior can provide, with the resources it receives, or expects to receive, from Congress. Therefore we vacate the district court's orders and remand for proceedings consistent with this opinion.

II. Analysis
Before beginning our analysis, we want to commend the district court for its efforts *812 to cut through this Gordian knot in Cobell XX and Cobell XXI. While we vacate the district court's orders, including its holding of impossibility, we do so with substantial sympathy, recognizing that our precedents do not clearly point to any exit from this complicated legal morass.

A. The District Court's Analysis
Bowing to our directive in Cobell v. Kempthorne, 455 F.3d 301 (D.C.Cir.2006) (Cobell XVII)that because "both the APA and the common law of trusts apply in this case[,] the specific question to be addressed determines which body of law becomes most prominent," id. at 303-04 the district court sought to determine "which body of law [wa]s more prominent with respect to specific aspects of Interior's 2007 accounting plan," Cobell XX, 532 F.Supp.2d at 89. Most importantly, the district court divided the issues into those relating to the methodology and to the scope of the accounting. Id. The district court correctly held that Interior's methodology was "owed the greatest deference," id. at 89, because it "ar[ose] out of an administrative balancing of cost, time, and accuracy," id. at 91. See also Cobell XVII, 428 F.3d at 1076 (administrative deference owed when "choices at issue required both subject-matter expertise and judgment about the allocation of scarce resources"). In contrast, the court observed that the scope "is the result ... of a legal interpretation of the 1994 Act and other statutes governing the IIM trust." Cobell XX, 532 F.Supp.2d at 89. It further noted that scope is not "only a temporal matter. It also relates to the elements that are present within and missing from the statements of account Interior proposes to issue...." Id. at 90. That said, the court went on to conclude that Interior's choices on scope, particularly as to the latter aspects, "were not dictated by administrative cost-benefit analyses to which judicial deference is owed...." Id. In that conclusion, the district court went too far.
We recognize, as did the district court, that the courts face two mandates of deference in construing the relevant statutes at issue in this case. First, there is the familiar Chevron deference upon which the district court relied in reviewing Interior's methodology. However, as the court observed, Chevron deference can be "`trumped by the requirement that statutes are to be construed liberally in favor of the Indians, with ambiguous provisions interpreted to their benefit.'" Id. at 89 (quoting Cobell XVIII, 455 F.3d at 304, and collecting other citations). Nonetheless, Chevron deference does not disappear from the process of reviewing an agency's interpretation of those statutes it is trusted to administer for the benefit of the Indians, although that deference applies with muted effect. Granted, the Indians' benefit remains paramount. But where Congress has entrusted to the agency the duty of applying, and therefore interpreting, a statutory duty owed to the Indians, we cannot ignore the responsibility of the agency for careful stewardship of limited government resources. Applying even a muted Chevron deference leads us to a different conclusion than that reached by the district court.
In Cobell VI, we observed that "[u]nder traditional equitable principles, `[t]he trustee's report must contain sufficient information for the beneficiary readily to ascertain whether the trust has been faithfully carried out.'" 240 F.3d at 1103 (quoting White Mountain Apache Tribe of Arizona v. United States, 26 Cl.Ct. 446, 449 (Cl.Ct. 1992)). The district court's order we affirmed in Cobell VI "explicitly left open the choice of how the accounting would be conducted, and whether certain accounting methods, such as statistical sampling or something else, would be appropriate." *813 240 F.3d at 1104. In Cobell XVII, we opined that "neither congressional language nor common law trust principles (once translated to this context) establish a definite balance between exactitude and cost." 428 F.3d at 1076. While we understand that it may not have been clear to the Cobell XX court that this balance applied beyond the accounting methodology, we now hold that the scope of the accounting must also be balanced in equity.
Therefore, the district court was not completely correct when it said that "the proper scope of the accounting obligation.... is the result ... of a legal interpretation of the 1994 Act and other statutes governing the IIM trust." Cobell XX, 532 F.Supp.2d at 89 (second emphasis added). The district court was correct to the extent that the scope of the accounting is derived from statutory law. But when Congress affords courts equitable jurisdictionas it has done in this caseit draws on a tradition of flexibility, not rigidity, in equity. The unique nature of this trust has been emphasized by the district court. See Cobell XXI, 569 F.Supp.2d at 225, 249; Cobell XX, 532 F.Supp.2d at 90. Also, Cobell XVII explained that congressional appropriations "unequivocally control what may be spent on historical-accounting activities...." 428 F.3d at 1075. "The essence of equity jurisdiction has been the power of the Chancellor to do equity and to mould each decree to the necessities of the particular case." Hecht Co. v. Bowles, 321 U.S. 321, 329, 64 S.Ct. 587, 88 L.Ed. 754 (1944). The unique nature of this trust requires the district court to exercise equitable powers in resolving the paradox between classical accounting and limited government resources. It must "mould [its] decree to the necessities of the particular case." Id. Therefore, the district court was incorrect insofar as it assumed that the scope of the accounting obligation could not be adjusted in equity.
The plaintiffs are entitled to an accounting under the statute. 25 U.S.C. § 4011(a). The district court sitting in equity must do everything it can to ensure that Interior provides them an equitable accounting. The district court's holding of impossibility contradicts the requirement of an equitable accountingone that makes most efficient use of limited government resources. Given the realities of congressional appropriations, it would be inequitable for Interior to throw up its hands and stop the accounting. This is what the district court declared Interior should do in Cobell XX, leading to the money judgment of Cobell XXI. That judgment was substantial, but without an accounting, it is impossible to know who is owed what. The best any trust beneficiary could hope for would be a government check in an arbitrary amount. Even if this did justice for the class, it would be inaccurate and unfair to an unknown number of individual trust beneficiaries. There will be uncertainty in any accounting for this trust. Interior's job is to minimize that uncertainty with a finite budget. Equity requires the courts to assure that Interior provides the best accounting it can.

B. An Equitable Accounting
The proper scope of the accounting ultimately remains a question for the district court, but we will provide as much guidance as we can on appropriate methodology, and principles to guide the analysis of unforeseen circumstances. The overarching aim of the district court should be for Interior to provide the trust beneficiaries the best accounting possible, in a reasonable time, with the money that Congress is willing to appropriate.
In Cobell XVII, we made clear that an equitable accounting may include the use of statistical sampling when verifying transactions. See 428 F.3d at 1077-78. A *814 primary reason for this decision was that, "for the subset of transactions valued at less than $500, Interior estimated that the average cost of accounting, per transaction, would exceed the average value of the transactions." Id. at 1078. Because of this, Interior proposed to study only "about 0.3% of the roughly 25 million transactions under $500." Id. We now instruct the district court to extend this reasoning to the rest of the accounting. Departing from this approachthat is, by sticking to the ideal concept of a complete historical accountingwould render the accounting impossible (or, what is functionally the same, it "would not be finished for about two hundred years, generations beyond the lifetimes of all now living beneficiaries," id. at 1076).
The equitable approach we envision is illustrated by so-called Youpee escheatments. The Dawes Act, and subsequent legislation, allotted land to individual Indians that could not be sold or leased without permission of the government. See Cobell XX, 532 F.Supp.2d at 40-41. When these allotments were "divided and divided again by inheritance through succeeding generations," many individuals owned fractional, undivided interests in the land that "caus[ed] enormous administrative difficulties" for the government. Id. at 41. The Indian Land Consolidation Act, Pub.L. No. 97-459, tit. II, 96 Stat. 2517 (1983), tried to consolidate these holdings by causing them to escheat to the Indian tribes, but the escheatments were held to be unconstitutional takings in Hodel v. Irving, 481 U.S. 704, 718, 107 S.Ct. 2076, 95 L.Ed.2d 668 (1987). An amended statute was similarly rejected in Babbitt v. Youpee, 519 U.S. 234, 117 S.Ct. 727, 136 L.Ed.2d 696 (1997). See Cobell XX, 532 F.Supp.2d at 79-80. Small payments are now owed for 775,000 fractional land interests, according to estimates by the Department of the Interior. Id. at 80. Interior considers calculating these payments to be "an accounting for land" and so argues they should be excluded from the historical accounting project, which accounts only for funds. Id.
The government may be correct, but for the wrong reason. To determine whether the accounting should cover the escheatments, the district court should ask the practical question of whether the cost to account will exceed the amount recovered by class beneficiaries. As the district court observed, escheated "interests are tiny, generally of very low value, and the cost of reversing the escheatments is high." Id. The district court should exercise its equitable power to ensure that Interior allocates its limited resources in rough proportion to the estimated dollar value of payments due to class members. It should also consider low-cost statistical methods of estimating benefits across class sub-groups.
Another illustration of the need for a flexible approach involves administrative fees. Interior often charged trust beneficiaries administrative fees "in connection with the probate process," when the government sold timber on trust land, or when the government leased or sold trust land. Id. at 79. These fees were subtracted before money was deposited into beneficiary accounts, and, so the government argues, they should be excluded from any accounting. Again the government is probably right for the wrong reason. Common sense should guide the district court's analysis in equity. Like escheatments, "[a]dministrative fees ... likely amount to a tiny fraction of the monies that pass through the IIM trust." Id. at 96. If accounting for them causes an enormous increase in costbecause, for instance, Interior has to integrate several new systems of records with the IIM trustand only a small effect on the ultimate balances, then the district court is free to approve of Interior's low-cost ways *815 to avoid this. The district court would be within bounds to accept a reasonable simplification of accounting for administrative fees, possibly extending to sampling and even exclusions. As in the case of escheatments, these modifications and exclusions should be made considering whether the cost to account exceeds a potential recovery for the class.
Just as equity affects the substance of the accounting, so it affects which accounts are subject to the accounting. First, we consider the legal case: The 1994 Act only requires accounting of "funds held in trust by the United States for the benefit of ... an individual Indian which are deposited or invested pursuant to the Act of June 24, 1938 (25 U.S.C. 162a)." 25 U.S.C. § 4011(a). The district court ordered accounting even for accounts closed before the 1994 Act was passed. See Cobell XX, 532 F.Supp.2d at 98. Its "rationale for including predecessor accounts in the historical accounting process" was "that beneficiaries are entitled to know where their money came from." Id. This is true, the district court held, because "the probate process does not produce an accounting." Id. The district court recognized that Interior's duty did not extend to "every beneficiary who ever walked the earth." Id. But it erred by including within the plaintiff class heirs to money from closed accounts. The statute calls for an accounting of "the daily and annual balance of all funds held in trust" that "are deposited or invested" by the United States for the Indians. 25 U.S.C. § 4011(a) (emphasis added). Closed accounts no longer have daily or annual balances, nor are they deposited or invested. And, as the government rightly points out, "the very point of probate is to produce a final determination of the assets of the estate, so that the assets may be distributed among heirs and creditors."
This is another instance in which the limited resources of the historical accounting project may be better spent elsewhere. Accounting for closed accounts, dealing with probate and probate regulations, and considering the impact of the IIM trust on a host of heirs and creditors could needlessly further complicate an already complicated process. The purpose of an equitable accounting, as we have tried to articulate, is for Interior to concentrate on picking the low-hanging fruit. We must not allow the theoretically perfect to render impossible the achievable good.

III. Conclusion
We vacate the orders of the district court and remand for further proceedings consistent with this opinion.[1]
It is so ordered.
NOTES
[1]  We are hearing this case on interlocutory appeal. It does not appear that the issues raised by intervenor Osage Nation are yet ripe for review.
