concurring in part and dissenting in part:
The Supreme Court has held that the Oneida Indian Nation has “a federal common-law right to sue to enforce [its] aboriginal land rights.” County of Oneida, N.Y. v. Oneida Indian Nation of N.Y. State, 470 U.S. 226, 235, 105 S.Ct. 1245, 84 L.Ed.2d 169 (1985) (“Oneida II”); see also Oneida Indian Nation of N.Y. State v. County of Oneida, N.Y., 414 U.S. 661, 674, 94 S.Ct. 772, 39 L.Ed.2d 73 (1974) (“Oneida I”). It has done so acknowledging that, while “[o]ne would have thought that claims dating back for more than a century and a half would have been barred long ago,” “neither petitioners nor we have found any applicable statute of limitations or other relevant legal basis for holding that the Oneidas’ claims are barred or otherwise have been satisfied.” Oneida II, 470 U.S. at 253, 105 S.Ct. 1245. And yet, after thirty-five years of litigation, including two trips to the Supreme Court and the intervention of the United States on plaintiffs’ behalf, the majority forecloses the Oneidas from obtaining any remedy in this action.
Like the majority, I accept that, in light of the decision in Cayuga Indian Nation of N.Y. v. Pataki, 413 F.3d 266 (2d Cir.2005), plaintiffs’ claims that hinge on their possessory rights to the land fail. Unlike the majority, I conclude that Cayuga does not foreclose plaintiffs’ non-possessory claims. Consequently, I dissent.
I.
The plaintiffs—the Oneida Indian Nation and the United States—-both present two cognizable non-possessory claims. First, the United States emphasizes its federal common law claim against the State for violating the Nonintercourse Act, 25 U.S.C. § 177, when the State failed to pay the Oneidas a fair price for their land. (The Oneidas also assert a claim under the Nonintercourse Act.) This claim is consistent with the Act’s “obvious purpose”: “to prevent unfair, improvident, or improper disposition by Indians of lands owned or possessed by them .... ” Fed. Power Comm’n v. Tuscarora Indian Nation, 362 U.S. 99, 119, 80 S.Ct. 543, 4 L.Ed.2d 584 (1960). Put differently, the United States seeks to vindicate not its right under the Act to stop sales without its approval, but its right to ensure that when the Oneidas sold their land, they would receive a fair price. See U.S. v. Oneida Nation of N.Y., 201 Ct.Cl. 546, 477 F.2d 939, 943 (1973) (noting that the United States’ responsibiL ity under the Nonintercourse Act “was not merely to be present at the negotiations or to prevent actual fraud, deception, or duress alone; improvidence, unfairness, the receipt of unconscionable consideration would likewise be of federal concern.”) (internal quotation marks omitted) (emphasis in original).
Unquestionably, the United States may sue New York for a violation of a federal statute. See Cramer v. United States, 261 U.S. 219, 233, 43 S.Ct. 342, 67 L.Ed. 622 (1923) (“The United States may lawfully maintain suits in its own courts to prevent interference with the means it adopts to exercise its powers of government and to carry into effect its policies.”) (internal quotation marks omitted). In other words, the United States has both an interest in this suit as trustee for the Native Americans, and an independent interest in ensuring that the State complies with the Nonintercourse Act. See United States v. Minnesota, 270 U.S. 181, 194, 46 S.Ct. 298, 70 L.Ed. 539 (1926) (holding that the United States’ interest in an Indian claims suit *142“arises out of its guardianship over the Indians, and out of its right to invoke the aid of a court of equity in removing unlawful obstacles to the fulfillment of its obligations, and in both aspects the interest is one which is vested in it as a sovereign.”)
In my view, both the United States and the Oneidas also assert a claim arising under federal common law which, as articulated by Judge Kahn, is a contract claim based on uneonseionability.1 The majority does not challenge that the contract claim has been adequately pled in the Oneidas’ complaint, but takes the position that the United States’ amended complaint itself lacks sufficient factual allegations to support the claim. Because of disparities between the two complaints, the majority concludes that the Oneida Nation cannot take advantage of the United States’ intervention to overcome the State’s sovereign immunity. See Alabama v. North Carolina, -U.S.-, 130 S.Ct. 2295, 2315, 176 L.Ed.2d 1070 (2010) (concluding that a State’s sovereign immunity is not compromised “by an additional, nonsovereign plaintiffs bringing an entirely overlapping claim for relief that burdens the State with no additional defense or liability.”).2
If the majority finds the United States’ amended complaint insufficient, then we should deem the United States’ complaint constructively amended. See Wahlstrom v. Kawasaki Heavy Indus., Ltd., 4 F.3d 1084, 1087 (2d Cir.1993).3 Judge Kahn found that the Oneida Nation’s complaint set forth adequate facts to support its nonpossessory contract claim, a finding the majority does not dispute. The State, therefore, had full notice of the claim, and it never argued below that the parties’ complaints were inconsistent; in fact, in its summary judgment briefing, the State described the complaints as “parallel.” The State chose to bring its dispositive motion as one for summary judgment, where the theories of the case and issues would be more clearly defined than at the pleading *143stage. See Swierkieiwicz v. Sorema N.A., 534 U.S. 506, 512, 122 S.Ct. 992, 152 L.Ed.2d 1 (2002) (“[Fed.R.Civ.P.’s 8(a)(2)’s] simplified notice pleading requirement relies on liberal discovery rules and summary judgment motions to define disputed facts and issues and to dispose of unmeritorious claims.”). And even after plaintiffs squarely presented the State with their non-possessory theories, the State avowed that no further discovery was necessary. All parties briefed the availability of non-possessory claims and damages extensively in their briefs on appeal. Consequently, the State would suffer no unfair prejudice; it had full knowledge of the facts and legal theories relied upon by both plaintiffs at the time of the summary judgment motion, and, given that it did not raise any disparities between the two complaints, or sovereign immunity issues, before the district court, cannot plausibly claim that it would have supported the motion any differently had there been no disparities.4
In addition to finding the United States’ pleading insufficient, the majority also reasons that the United States “disavows” such a claim in its briefs to this court. This miseharaeterizes the United States’ position. The United States asserted at oral argument that there is both a federal common law contract claim and a common law Nonintercourse Act claim. Clearly the United States prefers its Nonintercourse Act claim, under which, it argues, it would not have to prove “gross inadequacy of consideration” or the “inferiority of the Oneida Indian Nation’s negotiating position” to prevail. But there is nothing in its briefs or statements at oral argument that “disavows” the contract claim.5
In any event, whether the claim is premised on contract law or the Nonintercourse Act, the remedy would, as Judge Kahn acknowledged, be the same: “the difference between the fair market value of the land at the time and the consideration received by the Oneida Indian Nation minus any offsets, including, but not limited to, sales costs incurred by the State.” Oneida Indian Nation of N.Y. v. N.Y., 500 F.Supp.2d 128, 144, 139 n. 4 (N.D.N.Y.2007) (noting that “an analysis of Plaintiffs’ common law claims would be part of the determination of a remedy that would be commensurate with vindicating any viola*144tions of the Nonintercourse Act.”).6 Voluminous evidence of unfair compensation was before the district court. See id. at 145. An expert reviewed the State’s records of proceeds it obtained from sales of the Oneida land to show the gross disparity between the price the State paid the Oneidas for their land and the price the State received after a quick resale. Judge Kahn also noted “previous rulings that the State paid the Oneida Indian Nation ‘approximately fifty cents per acre’ in 1795 to purchase about a third of the reservation and resold the land to ‘white settlers for about $3.53 per acre.’ ” See id. at 145 (quoting Oneida Indian Nation of N.Y. State v. Oneida County, 719 F.2d 525, 529 (2d Cir.1983)). Taken together, this evidence “suggests that there are material facts indicating that the consideration paid to the Oneida Indian Nation by the State was significantly under the then-fair market price.” Id. Remedying the disparity would both cure the unconscionability of the original contract and disgorge the benefits the State gained by the contract in violation of federal law. See Dan B. Dobbs, Law of Remedies, § 4.1, at 552 (2d ed.1993) (the “purpose [of restitution] is to prevent the defendant’s unjust enrichment by recapturing the gains the defendant secured in a transaction.”)
II.
Determining whether plaintiffs have alleged cognizable claims is only the first part of the inquiry; the court must also consider whether both the claims and remedies the plaintiffs assert are precluded by the equitable defense articulated in City of Sherrill, N.Y. v. Oneida Indian Nation of N.Y., 544 U.S. 197, 125 S.Ct. 1478, 161 L.Ed.2d 386 (2005) (“Sherrill”), and Cayuga. Sherrill was an extraordinary case. The Oneida Nation claimed that it was exempt from paying property taxes to the City of Sherrill for land that was part of the Oneidas’ historic reservation, but which had been sold by them years before, and then reacquired. Plaintiffs argued that they had regained sovereignty over the land they purchased in the open market. See 544 U.S. at 213, 125 S.Ct. 1478. The Court rejected their “unification theory,” explaining that the “standards of federal Indian law and federal equity practice” precluded the Oneida Nation from “rekindling embers of sovereignty that long ago grew cold.” Id. at 214, 125 S.Ct. 1478. The Court noted that “the question of damages for the Tribe’s ancient dispossession is not at issue in this case, and we therefore do not disturb our holding in Oneida II.” Id. at 221, 125 S.Ct. 1478. “However,” the Court concluded, “the distance from 1805 to the present day, the Oneidas’ long delay in seeking equitable relief against New York or its local units, and developments in the City of Sherrill spanning several generations ... render inequitable the piecemeal shift in governance this suit seeks unilaterally to initiate.” Id.
In Cayuga, this court applied Sherrill’s equitable defense to bar the Cayugas’ possessory land claims. The Cayugas had filed suit in 1980, alleging that the cession of certain tribal lands to the State of New York in 1795 and 1807 was never ratified by the federal government. For these violations, they, later joined by the United States, sought actual possession of their ancestral reservation land. After ruling for the Cayugas on the liability issues, the *145district court decided a series of issues concerning the appropriate remedy. The court concluded that ejectment was a drastic, inappropriate remedy that would “result in widespread disruption not only to the Counties and those residing therein, but to the State of New York as a whole.” Cayuga Indian Nation of N.Y. v. Cuomo, 1999 WL 509442 at *29-30 (N.D.N.Y. July 1, 1999). The district court submitted the issue of monetary damages to a jury and the jury awarded the Cayugas damages “for loss of use and possession” of the land. See Cayuga Indian Nation of N.Y. v. Pataki, 165 F.Supp.2d 266, 273 (N.D.N.Y.2001).
The Second Circuit reversed. It understood Sherrill as holding “that equitable doctrines, such as laches, acquiescence, and impossibility, can, in appropriate circumstances, be applied to Indian land claims, even when such a claim is legally viable and within the statute of limitations.” Cayuga, 413 F.3d at 273. It also held that Sherrill’s equitable considerations applied equally to the district court’s “monetization” of their ejectment claim, reasoning that the main concern underlying Sherrill’s decision was the “disruptive nature of the claim itself.” Id. at 274. Therefore, despite Sherrill’s emphasis that the question of rights was “very different” from the question of remedy, 544 U.S. at 213, 125 S.Ct. 1478, the Cayuga court held that “[wjhether characterized as an action at law or in equity, any remedy flowing from this possessory land claim, which would call into question title to over 60,000 acres of land in upstate New York, can only be understood as a remedy that would similarly ‘project redress into the present and future.’ ” Cayuga, 413 F.3d at 275 (emphasis added) (quoting Sherrill, 544 U.S. at 202, 125 S.Ct. 1478).
The plaintiffs’ claims at issue here— whether premised on the Nonintercourse Act or contract law—are wow-possessory and do not “project redress into the present and future.” The Nonintercourse Act claim seeks restitution of the State’s profits from the State, a common remedy for violations of federal law, and one that does not implicate land ownership, much less possession. See, e.g., Securities and Exchange Comm’n. v. Texas Gulf Sulphur Co., 446 F.2d 1301, 1307 (2d Cir.1971) (“[T]he Supreme Court has upheld the power of the government without specific statutory authority to seek restitution ... as an ancillary remedy in the exercise of the courts’ general equity powers to afford complete relief.”). As for the contract claim, a finding that a term in the contract was unconscionable does not require “voiding” the underlying title, as the majority suggests. Even while acknowledging the “substantial flexibility” courts have to remedy such claims, the majority asserts that “the traditional remedy for a claim of unconscionability is to deny enforcement of the relevant contract.” Therefore, the majority concludes, “[t]he claim [of unconscionability] and its attendant remedy would again necessarily call into question and disrupt settled expectations regarding the ownership of land stemming from the original transfer of title to New York [.]”
But we are not constrained to provide only a “traditional” remedy for any violation; to the contrary, judgments “should grant the relief to which each party is entitled, even if the party has not demanded that relief in its pleadings.” Fed.R.Civ.P. 54. As the majority itself notes, in remedying an unconscionability claim, courts can choose, as Judge Kahn did, to reform the contract, rather than void it. This has the effect of denying enforcement of the unconscionable provision'—-in this case, the price—while preserving the rest of the contract, including the transfer of title.
*146I do not agree with the implication that a claim is possessory if even one potential remedy would question title. In United States v. Mottaz, 476 U.S. 834, 106 S.Ct. 2224, 90 L.Ed.2d 841 (1986), a plaintiff alleged that the United States had unlawfully sold her interest in her land and sought the market value of the land as the remedy. The plaintiffs position was that the Quiet Title Act, 28 U.S.C. § 2409a(a), which governs actions to “adjudicate a disputed title to real property in which the United States claims an interest,” did not apply to her case. The Court disagreed, holding that, in “demand[ing] damages in the amount of the current market value of her interests,” the plaintiff sought “a declaration that she alone possessed] valid title to her interests ... and that the title asserted by the United States is defective. ...” Id. at 842, 106 S.Ct. 2224 (emphasis in original). Therefore, the Quiet Title Act applied, and, because the plaintiff had not filed within the limitations period of that Act, her claim was defective. The Court, however, acknowledged that, if she had sought merely a share of the proceeds, rather than the current fair market value of her land, “a claim for monetary damages in that amount would involve a concession that title had passed ... and that the sole issue was whether [she] was fairly compensated for the taking of her interests in the allotments.” Id. This reasoning applies to the plaintiffs in this case: their claim, and their requested remedy, necessarily concedes that title has validly passed.
The majority distinguishes Mottaz by stating that awarding relief in this case “would not involve ‘concession[s] that title [has] passed’ but rather would establish that it had not, but that return of the property was impossible as a remedy under the circumstances.” In doing so, the majority refers to plaintiffs’ requests for “fair compensation” and “restitution” as “substitute remedies,” apparently to liken what is sought here to the monetization found improper in Cayuga. But these are not “substitute remedies”—a term that is the majority’s own, and not that of the plaintiffs or the district court—but separate claims with separate remedies pled in the complaint. See Fed.R.Civ.P. 8(d) (“A party may set out 2 or more statements of a claim or defense alternatively or hypothetically. ...”).
The suggestion that plaintiffs raised these non-possessory claims .and remedies only “to cast their claims in such a way as to avoid Cayuga’s equitable defense” is not to the point. Unlike the majority, I do not fault the Oneidas for adjusting their claims to recognize the changing legal landscape. It shows no disrespect to precedent to acknowledge that Cayuga significantly changed that landscape. Cayuga not only applied laches to bar Indian land claims, as well as remedies, relying on Sherrill, but it also applied laches to the United States’ claims.7 After thirty-five years of litiga*147tion in this case, and intervening appeals in two other cases, Sherrill and Cayuga, it is not surprising or improper that plaintiffs would reevaluate and refine their positions.
At its broadest reading, Cayuga limits only recovery for all possessory claims; while Cayuga found that both legal and equitable claims could be possessory in nature, and therefore subject to equitable defenses based on disruption to settled expectations regarding land title, Cayuga does not compel us to find, or even suggest, that non-possessory claims are to be treated as possessory. This is particularly true here where the United States seeks to vindicate a right that is not possessory in any sense: the right to sue for a violation of its statute.
III.
Finally, and perhaps most importantly, we must not forget the actual concerns Cayuga and Sheriill addressed. In Cayuga, the court wrote that “[ijnasmuch as the instant claim, a possessory land claim, is subject to the doctrine of laches, we conclude that the present case must be dismissed because the same considerations that doomed the Oneidas’ claim in Sherrill apply with equal force here.” Cayuga, 413 F.3d at 277. A claim for actual possession, as involved in Cayuga, or monetization of the possessory claim, as the district court granted the Cayugas, was found to presuppose that no title ever passed to the State. This in turn introduced difficult present-day complications that would affect innocent third-party purchasers and the current value of the developed land. These were among the considerations that had led the Supreme Court in Sherrill to reject the restoration of sovereignty to the Oneidas.
The nonpossessory claims and remedy involved here implicate none of these concerns. Present-day land considerations are irrelevant to the question of whether the State should disgorge the profit it earned from violating a United States statute. To calculate a restitution or fair compensation remedy, the court would not have to consider improvements to the land, settled expectations of innocent parties, or the “distinctly non-Indian character of the area and its inhabitants.” Sherrill, 544 U.S. at 202, 125 S.Ct. 1478. The distance in time matters little in this case because the damages calculation, with the exception of interest, would be no different than if this claim had been brought immediately after the alleged sales by the State.8 In other words, a fair compensation remedy would not upset present-day expectations because it has nothing to do with the present at all.
Cayuga held that “the import of Sherrill is that ‘disruptive,’ forward-looking claims, a category exemplified by possessory land claims, are subject to equitable defenses, including laches.” Cayuga, 413 F.3d at 277. Nothing in Cayuga or Sherrill prohibits the purely backward-looking, nonpossessory claims asserted here and the *148remedy described by Judge Kahn. What Cayuga was concerned about—whether labeled a claim or remedy—was avoiding undue disturbance of ancient land titles and settled expectations regarding them. The claims and remedy recognized by the district court in this case, and pursued now by the Oneidas and by the United States, involve no such disturbance. With this decision, the majority forecloses plaintiffs from bringing any claims seeking any remedy for them treatment at the hands of the State. This is not required by Sherrill or Cayuga, and is contrary to the spirit of the Supreme Court’s decisions in this very case. Therefore, I dissent and would affirm Judge Kahn’s carefully considered decision and order denying summary judgment to the State.
.In finding a cognizable federal contract law claim of uneonseionability, Judge Kahn drew analogies from the body of law federal courts have developed relating to Indian claims seeking fair compensation from the United States. Oneida Indian Nation of N.Y. v. N.Y., 500 F.Supp.2d 128, 140-45 (N.D.N.Y.2007). In particular, he noted that when Congress, in 1946, enacted the Indian Claims Commission Act ("the ICCA”) "to hear and determine all tribal claims against the United States that accrued before August 13, 1946,” it included "claims which would result if the treaties, contracts and agreements between the claimant and the United States were revised on the ground of fraud, duress, [or] unconscionable consideration....” Id. at 140-41. Judge Kahn explained that, “[w]hile claims based on unconscionable consideration were brought pursuant to statutory right, the Court of Claims fashioned a common law rule based on preexisting precedents to determine when Indian claimants could prevail on related claims.” Id. at 142. Caselaw developed in the Court of Claims, he reasoned, "supports a holding that when the record shows that an agreement resulted in a gross disparity between the fair market value and the price paid for the land transferred, a claim of unconscionable consideration presumptively exists and supports the revision of contract.” Id.
. The majority does not dispute that the Non-intercourse Act claim was pled by the United States and therefore does not present sovereign immunity issues.
. Federal Rule of Civil Procedure 15(b)(2) provides that "[w]hen an issue not raised by the pleadings is tried by the parties' express or implied consent, it must be treated in all respects as if raised in the pleadings.” Although this rule technically does not apply on appeal, appellate courts, using Fed.R.Civ.P. 15(b) "by way of analogy,” permit constructive amendment of pleadings "when the effect will be to acknowledge that certain issues upon which the lower court’s decision has been based or consistent with the trial court’s judgment have been litigated.” 6A Charles A. Wright, Arthur R. Miller & Maiy Kay Kane, Federal Practice and Procedure § 1494 (3d ed.2010).
. Constructive amendment in these circumstances is consistent with our federal rules’ instruction that "[pjleadings must be construed so as to do justice.” Fed.R.Civ.P. 8(e). “This provision is not simply a precatory statement but reflects one of the basic philosophies of practice under the federal rules.” 5 Charles A. Wright & Arthur R. Miller, Federal Practice and Procedure § 1286 (3d ed.2010). "One of the most important objectives of the federal rules is that lawsuits should be determined on their merits and according to the dictates of justice, rather than in terms of whether or not the averments in the paper pleadings have been artfully or inartfully drawn.” Id. Where, as here, a defendant has suffered no prejudice, constructive amendment is entirely compatible with this objective.
. Judge Kahn premised the Oneidas' and the United States’ non-possessory claim on the contract claim rather than the Nonintercourse Act. This was because he found that “the Circuit recognized an implied right of action [under the Nonintercourse Act] that was possessory in nature,” and that the federal common law claim was, therefore, "on stronger ground.” 500 F.Supp.2d at 139 n. 4. Although this court did, in fact, suggest that an implied right of action under the Nonintercourse Act would be possessory, it did so when only the Counties, and not the State, were the defendants in this case. See Oneida Indian Nation of N.Y. v. Oneida County, 719 F.2d 525, 540 (2d Cir.1983). Because the Counties were not involved in the land transactions, the Oneida Nation could assert only possessory remedies against them. Therefore, non-possessory claims were never at issue until now.
. The Nonintercourse Act "contains no remedial provision.” See Oneida II, 470 U.S. at 238-39, 105 S.Ct 1245. Therefore, the court may "presume the availability of all appropriate remedies unless Congress has expressly indicated otherwise.” Franklin v. Gwinnett Cnty. Pub. Sch., 503 U.S. 60, 66, 112 S.Ct. 1028, 117 L.Ed.2d 208 (1992).
. I need not address the applicability of this aspect of Cayuga’s holding to the present case because I do not agree with the majority that Sherrill’s equitable defenses apply to the nonpossessory claims. However, it is worth noting that the Cayuga majority acknowledged that "laches is not available against the federal government when it undertakes to enforce a public right or protect the public interest.” Cayuga, 413 F.3d at 279 n. 8. Reasoning that "the United States intervened in [Cayuga] to vindicate the interest of the Tribe, with whom it has a trust relationship,” the majority in Cayuga held that the United States was subject to a laches defense because, it concluded, that case did not involve the enforcement of a public right or the protections of a public interest. Id. at 278, 279 n. 8. In this case, as described above, the United States has two independent roles: as trustee for the Oneidas, and as a sovereign. The United States’ role as a sovereign enforcing its own statute by definition "involve[s] the enforcement of a public right or the protections of a public *147interest.” Thus, the question of laches does not rest "on facts virtually indistinguishable” to those in Cayuga, as the majority suggests; the different claims call for a different analysis.
. Of course, the distance in time affects prejudgment interest. But, as Judge McCurn recognized in Cayuga, prejudgment interest is an equitable matter. See Cayuga Indian Nation of N.Y., 165 F.Supp.2d at 297. The particulars of Judge McCurn’s analysis have never been addressed by this Court, and there is no reason to believe that the district court, on remand, and then this Court, on appeal, could not address the equities of prejudgment interest if damages were awarded. But the potential for a large award, without more, cannot itself be treated as so disruptive as to justify dismissal of a legally sound claim.