ROGERS, Circuit Judge:

This is an appeal from the approval of a class action settlement agreement related to the Secretary of the Interior's breach of duty to account for funds held in trust for individual Native Americans. Class member Kimberly Craven challenges the fairness of the settlement, contending principally that an impermissible intra-class conflict permeates the scheme to compensate class members for surrendering their established right to injunctive relief and that this conflict undermines the commonality, cohesiveness, and fairness required by Federal Rule of Civil Procedure 23 and due process. The record, however, fails to confirm either the existence of the purported intra-class conflict or a violation of due process. Rather, the record confirms that the two plaintiff classes possess the necessary commonality and adequate representation to warrant certification, and that the district court, therefore, did not abuse its discretion in certifying the two plaintiff classes in the settlement or in approving the terms of the settlement as fair, reasonable, and adequate pursuant to Rule 23(e). Accordingly, we affirm the judgment approving the class settlement agreement.

I.

In 1996, Eloise Cobell and four other Native Americans filed a class action alleging a breach of fiduciary duties by the Secretary in managing the class members' "Individual Indian Money" ("IIM") trust accounts. "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. Salazar ("Cobell XXII"), 573 F.3d 808, 809 (D.C.Cir.2009) (citation omitted). The class, certified pursuant to Federal Rule of Civil Procedure 23(b)(1)(A) and (b)(2), sought injunctive and declaratory relief in the form of an historical accounting. Id.1 Their right to an historical accounting arose under the American Indian Trust Fund Management Reform Act of 1994 ("the 1994 Act"), 25 U.S.C. § 162a et seq. (2006); id. §§ 4001-4061. Cobell XXII, 573 F.3d at 810. The Act did not specify, however, the proper scope of such an accounting or the methodology by which it could be accomplished. Id. at 813; Cobell XX, 532 F.Supp.2d at 42. During the initial stages of the litigation, the Secretary proposed several plans for accomplishing an accounting. See Cobell XX, 532 F.Supp.2d at 47-56. For example, in a 2002 report to Congress, the Secretary described plans "to conduct a transaction-by-transaction reconciliation of all funds in the IIM accounts through December 31, 2000," and to provide historical statements of account for each account. Id. at 48. The estimated cost was $2.425 billion. Id. Congress "request[ed] that the Secretary `promptly consider ways to reduce the costs and the length of time necessary for an accounting . . . [including] alternative accounting methods.'" Id. The Secretary then developed a plan in 2003, which was to rely on statistical sampling and use only limited transaction-by-transaction reconciliation, at an estimated cost of $335 million. Id. at 48-49. "Between 2003-2007, however, not only did Interior receive only $127.1 million in appropriations for its IIM historical accounting work, but it also discovered that the accounting process it had envisioned would be both more costly and more time-consuming than it had anticipated." Id. at 56. Consequently, as the litigation entered its eleventh year, the issue of the proper scope and methodology of an historical accounting had yet to be resolved. In October 2007, the district court held a trial to address these and other questions.

At trial, the Secretary offered evidence regarding the latest plan ("the 2007 Plan") for accomplishing an historical accounting in compliance with the 1994 Act. The 2007 Plan relied on statistical sampling for account and transaction reconciliation to an even greater extent than the 2003 Plan. In addition, the total number of transactions to be reconciled was significantly reduced, and the provision of asset statements to account beneficiaries was eliminated. See id. at 56-58. The Secretary's explanation for these changes to the scope and methodology of the proposed accounting echoed those offered in 2003 for tailoring the 2002 proposal: "Original cost and time estimates were off by several multiples, and Congress failed to appropriate the funds Interior had requested and expected." Id. at 58. The 2003 Plan was now estimated to cost $1.675 billion to complete, with an average cost of $3,000 to $3,500 for reconciliation of a single transaction. Id. In contrast, the Secretary estimated completion of the 2007 Plan would cost $271 million. Id. at 81. Despite the reduced ambitions of the 2007 Plan, the average cost of the accounting for a single transaction still would likely exceed the average value of that transaction, id. at 92, and, more significantly, the 2007 Plan would "not provide beneficiaries with information about the assets from which IIM funds ha[d] been derived," id. at 98.

Given this state of affairs and the likelihood of many more years of litigation, the parties entered into settlement negotiations in the summer of 2009. On December 7, 2009, the parties entered into a class settlement agreement. See Class Action Settlement Agreement, Ex. 2 to Joint Mot. for Prelim. Approval of Settlement, Cobell v. Salazar (No. 1:96-cv-01285) (Dec. 10, 2010). We describe its basic parts:

First, an amended complaint would be filed setting forth two classes:

The settlement envisioned that the Historical Accounting Class would be certified pursuant to Rule 23(b)(1)(A) and 23(b)(2), in the alternative, with no individual right to opt out of the class; the Trust Administration Class would be certified pursuant to Rule 23(b)(3) with an opt-out right. Id. § B ¶ 4.b.

Second, the Secretaries of Interior and Treasury would deposit $1.412 billion into a settlement fund. Id. § E ¶ 2.a. From this fund, each member of the Historical Accounting Class would receive $1,000, id. § E ¶ 3.a, in exchange for the release of the Secretary of Interior's "obligation to perform a historical accounting of [the class member's] IIM Account or any individual Indian trust asset," id. § I ¶ 1. The Trust Administration Class members would receive a baseline payment of $500 plus an additional pro rata share of the remaining settlement funds in accordance with an agreed-upon compensation formula. Id. § E ¶ 4.b. The Trust Administration Class payment would release the Secretary from liability arising out of any past mismanagement of IIM accounts and trust properties. The scope of that release would not be unlimited: for example, claims for payment of existing account balances, breach-of-trust claims arising after September 30, 2009, and water-rights claims would fall outside of its scope. Id. § I ¶¶ 2-3.

Third, in addition to the class and compensation structure, the proposed settlement provided for:

The proposal also stated that the class settlement agreement was contingent upon the enactment of legislation by Congress to authorize certain aspects of the settlement. Id. § B ¶ 1.

In 2010, Congress enacted the Claims Resolution Act of 2010 ("the CRA"), Pub.L. No. 111-291, 124 Stat. 3064 (Dec. 8, 2010), which "authorized, ratified, and confirmed" the proposed settlement, id. § 101(c)(1). It also authorized the district court to certify the Trust Administration Class without regard to the requirements of the Federal Rules of Civil Procedure, and provided that such a certification would be treated as a certification pursuant to Rule 23(b)(3). Id. § 101(d)(2). The CRA appropriated funds including funds for the settlement and land-consolidation funds. Id. § 101(e)(1)(C)(I), (j)(1)(A). Settlement funds received by class members would be tax-exempt under the Internal Revenue Code. Id. § 101(f). Congress also increased the total amount of the settlement fund by $100 million, from $1.412 billion to $1.512 billion, id. § 101(j)(1)(A), resulting in approximately a $300 increase in the baseline payment (from $500 to $800) due members of the Trust Administration Class.4

On December 10, 2010, the parties filed a joint motion for preliminary approval of the class settlement agreement, which the district court granted on December 21, 2010. The district court also certified the Historical Accounting Class pursuant to, in the alternative, Rule 23(b)(1)(A) and (b)(2), and the Trust Administration Class pursuant to, in the alternative, CRA § 101(d)(2) and Rule 23(b)(3). Appellant Kimberly Craven and ninety-one other class members filed timely objections. At a fairness hearing on June 20, 2011, the district court heard testimony from objecting class members, including Craven's intra-class conflicts objections, along with arguments in support of the settlement agreement by counsel for the plaintiff class and the Secretary. At the close of the hearing the district court explained why it concluded the settlement was fair, reasonable, and adequate. We summarize relevant parts.

To begin, the district court acknowledged the objectors' concerns and that the settlement "may not be . . . as fortuitous as some wished and do[es not] provide redress for their wrongs." Fairness Hr'g Tr. at 217. Nonetheless, the district court explained that it was "not persuaded that striking a different balance would have been either achievable in the negotiating process or more favorable to more members of the class," id., nor "that a better result would have been achieved by taking this case to trial," id. at 218. First, the parties were facing "years of litigation . . . with rather dubious chances of ultimate success." Id. at 213. They had "found a way out of the morass that the Court of Appeals said [it] saw no easy exit from," and "after 15 years of bitter litigation [the parties had] . . . entered into a settlement agreement to resolve the issues in this case, . . . not to resolve every single claim that the Native Americans may have against the government." Id. at 214. Second, "[t]his settlement at least now provides some measure of certainty for most class members," whereby "[t]he vast majority of class members are entitled to automatic recovery under the historical accounting, and . . . those under the trust accounting would [be] provide[d] other monies that they can show they are due." Id. at 217. The settlement does so, moreover, in the absence of evidence of an intra-class conflict among the Historical Accounting Class by providing a non-damages payment of $1,000 to each class member. As for the Trust Administration Class, it has the commonality, numerosity, and typicality required by Rule 23. See id. at 233. Third, the settlement is reasonable and adequate because it "affords substantial benefits," with "a total settlement of $3.4 billion." Id. at 235. Obtaining Congressional approval and avoiding Presidential disapproval of the settlement was, the district court observed, "a remarkable accomplishment by all sides." Id. at 215.

By order of July 27, 2011, the district court granted final approval to the class settlement agreement that the lawsuit be settled and that the United States pay $3.412 billion—$1.512 billion to the settlement fund and $1.9 billion to the land-consolidation fund—in accordance with the terms of the settlement agreement and the CRA. Among other actions, the order set forth the scope of the two plaintiff classes and their respective claim releases, listed the individuals who had chosen to opt out of the Trust Administration Class, and awarded attorneys' fees and incentive payments to the remaining class representatives, while denying most requested additional expenses.5 A final judgment was signed and entered August 4, 2011. Craven appeals the judgment and related orders.

II.

A.

As an initial matter, Craven contends that the law of the case bars approval of the settlement agreement. She points to Cobell XXII, where this court vacated the judgment in favor of the plaintiff class and the order of a restitution award, holding that such an award would be arbitrary, inaccurate, and unfair to some class members in the absence of an historical accounting, 573 F.3d at 813. A lump-sum award, whose magnitude was of uncertain origin, the court stated, was an improper equitable judgment for the class's claim; "without an accounting, it is impossible to know who is owed what," and so "[t]he best any trust beneficiary could hope for would be a government check in an arbitrary amount." Id. Although Cobell XXII did address the issue of a remedy for the historical-accounting claim, the law-of-the-case doctrine has no application here.

Under the law-of-the-case doctrine, "the same issue presented a second time in the same case in the same court should lead to the same result." LaShawn A. v. Barry, 87 F.3d 1389, 1393 (D.C.Cir.1996) (en banc) (emphasis in original). Cobell XXII involved the same case, the same court, and the same parties as the current appeal, but the court's holding arose in a different context at an earlier stage of the litigation and the statements with regard to its holding spoke to a different issue— one that did not involve the terms of the class settlement agreement now under review. The court did not address, nor could it given the stage of the proceedings, the propriety or fairness of a two-class settlement involving pro rata as well as per capita payments. The distribution method for the lump-sum award had not yet been determined and so could not have been at issue in Cobell XXII, see Cobell v. Kempthorne ("Cobell XXI"), 569 F.Supp.2d 223, 253 (D.D.C.2008). Furthermore, the factors that guided the exercise of the district court's equitable power in addressing the claims for injunctive and declaratory relief under review in Cobell XXII, are distinct from those that govern the district court's approval of a settlement. Compare Cobell XXII, 573 F.3d at 813 (discussing the interplay of the 1994 Act and equitable principles in determining scope of an historical accounting) with FED. R. CIV. P. 23(e) (setting the procedure for approving a class settlement).

The class settlement agreement was the result of discussions post-dating Cobell XXII in which the parties, facing nigh insurmountable obstacles to achieving their original goal, decided to pursue another approach to resolving their protracted differences. Given the distinction between Cobell XXII and the current appeal, the law of the case does not foreclose approval of the class settlement agreement. To the extent Craven suggests that the lawsuit could be settled only for some type of historical accounting but not for monetary relief, her contention fails, see infra Part II.B; to the extent she contests the fairness of the distribution scheme, her contentions also fail, see infra Part II.C.

B.

Craven contends with respect to the Historical Accounting Class that "a mandatory [Rule] 23(b)(2) class settlement without [an] opt-out right is inappropriate where relief is predominantly monetary, especially when individual class members are required to waive rights to injunctive relief already won in litigation." Appellant's Br. at 28 (capitalization removed). This argument mischaracterizes the Historical Accounting Class.

Rule 23(b)(2) provides for class certification where "the party opposing the class has acted or refused to act on grounds that apply generally to the class, so that final injunctive relief . . . is appropriate respecting the class as a whole." FED. R. CIV. P. 23(b)(2). Just such a circumstance presents itself here: the Secretary refused to provide an historical accounting to IIM account holders; their claim for injunctive and declaratory relief in Count I of the amended complaint applied to the Historical Accounting Class as a whole.

Craven disagrees. The $1,000 per capita settlement payment, she maintains, monetizes the historical-accounting claims so that what was a uniform, indivisible remedy becomes divisible and individualized, and therefore certification of the Historical Accounting Class pursuant to Rule 23(b)(2) is precluded by Wal-Mart Stores, Inc. v. Dukes, ___ U.S. ___, 131 S.Ct. 2541, 2557-58, 2560, 180 L.Ed.2d 374 (2011). This is so, Craven says, because the historical accounting has greater value to class members with significant trust-mismanagement claims, who may use the information from the accounting to obtain substantial monetary relief, than to those with negligible trust-mismanagement claims for whom the accounting may provide little or no benefit. In other words, because some plaintiffs stand to gain more from claims based on the information an historical accounting would produce, the injunctive relief sought is worth more to them than it is to other class members.

Assuming that the $1,000 per capita settlement payment monetized the requested injunctive relief, certification of the Historical Accounting Class as a Rule 23(b)(2) class was nonetheless appropriate because of the unusual circumstances surrounding this litigation. Craven's argument ignores that the record developed through extensive and hard-fought litigation indicates that the different interests she alleges likely do not exist and that even if they do exist, they would not be revealed by the type of sampling-heavy accounting that would almost certainly occur if the plaintiff class prevailed in the litigation. See Fairness Hr'g Tr. at 213, 218; Cobell XX, 532 F.Supp.2d at 56, 103. Interior had performed a fairly extensive accounting in the course of the litigation but found only minor discrepancies. At trial, the district court observed that "one permissible conclusion from the record would be that the [Secretary] has not withheld any funds from plaintiffs' accounts." Cobell XXI, 569 F.Supp.2d at 238. This court's decision in Cobell XXII placed significant limits on the Secretary's accounting duty, clarifying that Interior need only provide "the best accounting possible . . . with the money that Congress is willing to appropriate." 573 F.3d at 813. Given that any additional accounting funded by Congress would likely rely heavily on statistical sampling, even if latent intraclass conflicts did exist, they would be unlikely ever to be discovered. All of this suggests that the information produced from an historical accounting is not likely to be worth significantly more to some class members than to others, and thus the $1,000 settlement payment is properly viewed as nonindividualized and does not run a foul of Wal-Mart.6

Moreover, this case is extraordinary in that Congress not only expressly authorized, ratified, and confirmed the settlement, but also appropriated $3.4 billion to fund it. Although Congress made no express findings about the propriety of (b)(2) certification of the Historical Accounting Class, given the lengthy litigation and the limited funds available for further accounting, Congress's judgment that uniform payments would adequately compensate class members for an accounting right that it created carries significant weight and sets this case apart from others.

C.

Craven also contends that the Trust Administration Class's distribution scheme is unfair under Federal Rule of Civil Procedure 23(e) "because it bears no relation to the underlying claims and perversely undervalues the claims of the most injured class members while providing windfalls to class members who have suffered little or no injury." Appellant's Br. at 23 (capitalization removed). Her challenge rests again on an alleged intra-class conflict that arises from the distribution scheme's under- and over-compensation of class members. Although disclaiming any suggestion that Rule 23(e) fairness requires a perfect allocation of payments among individual class members, see Appellant's Br. at 25, Craven nevertheless maintains that under the existing distribution formula, some members of the Trust Administration Class likely possess more valuable claims than do others and therefore the per capita baseline payment under-compensates the former while over-compensating the latter, an inequity that the pro rata payment does not remedy. As the district court found, however, the distribution scheme is fair, Fairness Hr'g Tr. at 219, and "[i]t is hard to see how there [c]ould be a better result," id. at 218, because Craven offers no persuasive evidence to support her claim of unfair compensation. Absent such evidence, Craven's intra-class conflict contention cannot undermine the overall fairness of the distribution scheme and she thus fails to demonstrate an abuse of discretion by the district court. See Richards v. Delta Air Lines, Inc., 453 F.3d 525, 530 (D.C.Cir. 2006); Pigford v. Glickman, 206 F.3d 1212, 1216 (D.C.Cir.2000).

1. The Secretary initially questioned Craven's standing to present this challenge because he understood her to claim only injuries to third parties and not to herself. See Appellees' Br. at 43 n.7. Craven's declaration disposes of that conjecture; it identifies how she is personally injured as a result of the district court's certification of both classes.7 Craven Decl. ¶¶ 6-7, 11; see also 28 U.S.C. § 1653; Am. Library Ass'n v. FCC, 401 F.3d 489, 494 (D.C.Cir.2005). Moreover, the Secretary's suggestion overlooks the fact that the two major components of the settlement—the Historical Accounting Class and the Trust Administration Class—are inextricably intertwined. The historical accounting that the plaintiff class sought—but which is taken away by the settlement—would have provided evidence of the value of each class member's IIM account and thereby shown, among other things, whether there was an intra-class conflict. The settlement agreement makes the challenges unseverable. See Class Action Settlement Agreement, § M ¶ 6. Craven thus has established a non-speculative basis for asserting an "injury in fact," Lujan v. Defenders of Wildlife, 504 U.S. 555, 560, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992), that gives her standing to challenge not only the certification of the Historical Accounting and Trust Administration Classes but also the fairness of the Trust Administration Class's distribution scheme. Any other conclusion would prove a bitter irony for those who have lost their earned right to an historical accounting under the 1994 Act. See Union Asset Mgmt. Holding A.G. v. Dell, Inc., 669 F.3d 632, 637-39 (5th Cir.2012) (citing Devlin v. Scardelletti, 536 U.S. 1, 6-7, 122 S.Ct. 2005, 153 L.Ed.2d 27 (2002)); cf. In re Vitamins Antitrust Class Actions, 215 F.3d 26, 28-29 (D.C.Cir.2000).

2. Although Craven has standing to challenge the fairness of the distribution scheme on the basis of the alleged intra-class conflict, her contention fails on the merits. As an initial matter, Craven's discussion of a hypothetical conflict is an inadequate basis for vacating the class settlement agreement. See Eubanks v. Billington, 110 F.3d 87, 98 (D.C.Cir.1997). And her concrete examples fare no better. Craven references congressional testimony (attached to a supplemental brief that the district court struck as untimely, see infra Part II.E) regarding the value of potential claims held by a particular class member. Other evidence indicates that the class member's ancestor likely released his claim to oil and gas royalties in exchange for a lump-sum payment from his tribe when the tribal council, pursuant to a 1919 congressional Indian Appropriations Act, asserted tribal mineral rights.8 See also Cobell XX, 532 F.Supp.2d at 95-97. Even assuming those claims survived, that class member, like any other class member who is allegedly under-compensated by the distribution formula, could have opted out of the Trust Administration Class; the record indicates the class member at issue declined to do so.

Indeed, the existence of the opt-out alternative effectively negates any inference that those who did not exercise that option considered the settlement unfair. The district court, although acknowledging the possibility that some class members may not have read or fully understood the settlement-notice documents, was satisfied that the opt-out provision fulfilled its purpose of protecting objecting class members, Fairness Hr'g Tr. at 225, finding that the "extensive and extraordinary notice" procedures, id. at 230, ensured "hundreds of thousands" of class members "knew about th[e] settlement and understood what they were getting into and approved it," id. at 238. Craven does not suggest these findings are clearly erroneous. See FED. R. CIV. P. 52; In re Vitamins Antitrust Class Actions, 327 F.3d 1207, 1209 (D.C.Cir.2003).

Other portions of the record also contradict the inequity Craven alleges. The historical-accounting records examined thus far have revealed only minor errors in trust accounting. In 2007, Interior reported that it successfully traced 94.7% of over 47 million IIM transactions occurring between 1985 and 2007,9 "reflect[ing] the reality that, in the absence of some kind of equitable evidentiary presumption in favor of the plaintiffs, one permissible conclusion from the record would be that the government has not withheld any funds from plaintiffs' accounts," Cobell XXI, 569 F.Supp.2d at 238.

Craven's attempt to support her intra-class conflict attack by turning, in her reply brief, to the accounting received by the class representatives is not well taken. She maintains that, prior to the settlement agreement, the class representatives received historical accountings that showed their trust claims to be of little value; their interests therefore were in conflict with those of the rest of the class members who did not know how they would fare under the distribution scheme. First, as discussed, few if any class members are likely to have trust claims of substantial value. Second, even assuming Craven is properly responding to Plaintiffs-Appellees' argument that there is no conflict among unnamed class members, see Am. Wildlands v. Kempthorne, 530 F.3d 991, 1001 (D.C.Cir.2008), and that Craven could show that the distribution scheme did over-compensate the class representatives, she has still failed to present persuasive evidence of class members who are under-compensated by the distribution scheme and thus failed to demonstrate the alleged conflict. Craven's evidence also does not establish that the distribution scheme over-compensates the class representatives. Only a partial accounting of the class representatives' IIM accounts was performed in 2001, which revealed "small variances" in the analyzed transactions. Cobell XX, 532 F.Supp.2d at 50. The class representatives thus stand in the same position as all other class members—lacking the historical accounting to which they are entitled under the 1994 Act and therefore lacking accurate information from the Secretary of the value of their claims.

Furthermore, as mentioned, the record indicates that any feasible accounting would be unlikely to provide evidence of the alleged intra-class conflict. Craven's position leaves this problem unaddressed, neglecting to account for the changed circumstances during the fifteen years between the commencement of this litigation and its settlement in 2011. By the time the parties entered settlement negotiations following Cobell XXII, it had become clear that the Secretary would be unable to perform an accounting of the IIM trust under the 1994 Act with the degree of accuracy desired by the plaintiff class. See Cobell XXII, 573 F.3d at 813-15; Cobell XX, 532 F.Supp.2d at 103. Trust records had been lost or destroyed, Cobell XX, 532 F.Supp.2d at 45-46, fractional ownership rendered accounting difficult, see Cobell XXI, 569 F.Supp.2d at 249, and changes to Interior's trust-accounting system had complicated accounting efforts, see Cobell XX, 532 F.Supp.2d at 43-44; HISTORICAL RESEARCH ASSOCS., supra note 8, at 25 (Pls.-Appellees' App'x 119). Preliminary work had revealed that even a partially complete accounting would be prohibitive in cost, see Cobell XX, 532 F.Supp.2d at 81-82; the record was clear "on the tension between the expense of an adequate accounting and congressional unwillingness to fund such an enterprise," id. at 103 n. 21. In view of these realities, this court in July 2009 instructed "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." Cobell XXII, 573 F.3d at 811. This instruction underscored the reality that the original goal of the litigation—a complete historical accounting for each class member—would not be realized. Instead, any historical accounting that would result from continued litigation would likely be severely limited in scope, heavily restrained by cost, and thus unlikely to reveal the existence of—much less remedy—the intra-class conflict Craven alleges.

Viewed, then, not in the hypothetical light cast by Craven's challenge, but in the actual light illuminating the parties' negotiations, the district court reasonably concluded that the class settlement agreement offered a fair resolution of the plaintiff classes' claims free of impermissible intra-class conflict.

D.

Additionally, Craven challenges the certification of the Trust Administration Class as inconsistent with constitutional due process. She maintains that the commonality and cohesiveness requirements of Rule 23 are of constitutional magnitude inasmuch as they inform adequacy of representation, which is a clear constitutional pre-requisite to class certification. She relies on Phillips Petroleum Co. v. Shutts, 472 U.S. 797, 811-12, 105 S.Ct. 2965, 86 L.Ed.2d 628 (1985), involving claims for money damages, as well as Hansberry v. Lee, 311 U.S. 32, 37, 61 S.Ct. 115, 85 L.Ed. 22 (1940), involving injunctive relief, and points to this court's acknowledgment of the due-process implications of adequate representation in National Association for Mental Health, Inc. v. Califano, 717 F.2d 1451, 1457 (D.C.Cir.1983), and Phillips v. Klassen, 502 F.2d 362, 366 (D.C.Cir.1974). Craven fails, however, to show that certification of the Trust Administration Class violated due process.

Where money damages are sought, due process requires: (1) adequate notice to the class; (2) an opportunity for class members to be heard and participate; (3) the right of class members to opt out; and (4) adequate representation by the lead plaintiff(s). Phillips Petroleum, 472 U.S. at 811-12, 105 S.Ct. 2965. Given the district court's findings regarding the extensive notice of the proposed settlement that was provided to class members, the opportunity for class members to present their objections and participate in the fairness hearing, and the right to opt out, Craven's due-process objection boils down to a challenge to the adequacy of class representation. As Craven suggests, the adequate-representation element of due process overlaps with Rule 23(a)'s requirement that "there are questions of law or fact common to the class," FED.R.CIV.P. 23(a)(2). See Amchem Prods., Inc. v. Windsor, 521 U.S. 591, 626 n. 20, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997). Under Rule 23(a), commonality requires that plaintiffs advance a "common contention" that "must be of such a nature that it is capable of classwide resolution—which means that determination of its truth or falsity will resolve an issue that is central to the validity of each one of the claims in one stroke." Wal-Mart, 131 S.Ct. at 2551. The Trust Administration Class satisfies this requirement. Although Craven characterizes the Class as "sprawling" and encompassing "dozens of wildly different theories of liability," Appellant's Br. at 42, all of the class members' trust claims revolve around resolution of a single issue—the extent of the Secretary's fiduciary obligation as trustee of the IIM accounts. To the extent Craven's commonality objection rests on the purported intra-class conflict between over- and under-compensated class members, her contention fails for lack of persuasive evidentiary support, see supra Part II.C.2.

Nor, as Craven maintains, did the district court's award of incentive payments to class representatives create an impermissible conflict requiring decertification of either class. To the extent Craven's argument that the incentive awards create an intra-class conflict hinges on the size of the incentive awards, her brief focuses on the class representatives' request, not on the terms of the class settlement agreement, the district court's findings, or the district court's actual award. Although the district court acknowledged in ordering the incentive payments that such awards "are routinely provided to compensate named plaintiffs for the services they provide and the risks they incur[ ] during the course of class-action litigation," Fairness Hr'g Tr. at 238, the class settlement agreement provided no guarantee that the class representatives would receive incentive payments; it left that decision and the amount of any such payments to the discretion of the district court. The Secretary's opposition to the magnitude of the class representatives' proposed incentive payments highlighted the uncertain status of such payments at the time of the settlement. In describing Ms. Cobell's singular, selfless, and tireless investment of time, energy, and personal funds to ensure survival of the litigation as meriting an incentive award, the district court found such contributions undermined any attempt to imply that Ms. Cobell had improperly colluded with the Secretary to settle prematurely in order to collect a fee. See id. at 239. It also denied altogether the class representatives' request for expenses incurred prior to December 7, 2009 (the date of the settlement agreement), finding that, with the exception of Ms. Cobell, they had failed to show directly-incurred expenses; with regard to Ms. Cobell, her expenses were incorporated into her incentive payment.

Craven thus fails to show either an error of law or clear factual error in the district court's due-process analysis.

E.

Craven's other challenges also fail. First, the district court's reference to the small number of objectors was one of many observations, not a dispositive finding in its fairness analysis amounting to legal error. Nothing in the district court's observation was inconsistent with the caution that should be exercised in "inferring support from a small number of objectors to a sophisticated settlement," In re Gen. Motors Corp. Pick-Up Truck Fuel Tank Prods. Liab. Litig., 55 F.3d 768, 812 (3d Cir.1995). See also In re Gen. Motors Corp. Engine Interchange Litig., 594 F.2d 1106, 1137 (7th Cir.1979).

Second, Craven fails to show that any prejudice resulted from the district court's striking of her supplemental brief as untimely, so the error, if any, was harmless. See Burkhart v. Wash. Metro. Area Transit Auth., 112 F.3d 1207, 1214 (D.C.Cir.1997). The district court allowed Craven's counsel to present those arguments at the fairness hearing. See Fairness Hr'g Tr. at 77-78. Even now Craven fails to identify any argument in her supplemental brief that was not presented to the district court.

Finally, Craven's general objection to the fairness of the class settlement agreement focuses on the information-deficit concern discussed previously: without an historical accounting, it is impossible to tell whether some members are being over-compensated while others are being under-compensated, and yet class members are being forced to surrender their right to an historical accounting and are thereby left without the information needed to establish the value of their claims. The protracted and contentious nature of this litigation underscores the reasonableness of the district court's evaluation of the fairness and adequacy of the class settlement agreement under Rule 23(e). Congress had shown no inclination to fund the historical accounting to which the plaintiff class was entitled under the 1994 Act. The question was could the class nonetheless benefit appropriately without it. Class counsel acknowledged that, despite significant work with existing data, efforts had failed to show significant accounting errors in the IIM accounts, see Cobell XXI, 569 F.Supp.2d at 238. The class settlement agreement was the result of an arms-length negotiation. What interests it protected and what benefits it provided were weighed by the district court, and considered in view of the class-member objections. The settlement acknowledged the plaintiff class' entitlement to an historical accounting and that the United States would pay for the surrender of that right and for trust claims in accordance with an agreed-upon formula. The settlement further provided that the Secretary would attempt to purchase fractional ownership shares to enable accurate accounting in the future in fulfillment of the Secretary's trust responsibilities. Congress has approved the settlement and appropriated the necessary funds. For Craven to characterize the settlement as "tak[ing] shortcuts to solve the problem at the expense of individual rights," Appellant's Br. at 13, and "tak[ing] a series of impermissible shortcuts that abuse the class action process to settle this case," id. at 15, is to ignore the history of this hard-fought litigation and the obstacles to producing an historical accounting.

Accordingly, we hold that in approving the class settlement agreement pursuant to Rule 23(e) the district court did not abuse its discretion in focusing on the significant benefits for each class member in view of the realities facing them after fifteen years of litigation, including multiple appeals, and we affirm the judgment certifying the two classes, approving the terms of the settlement, and encompassing the provisions of the July 27, 2011 order.