J. Richard ERNST, William T. Ervin, James E. Wilson, and John Patrick O'Brien, on behalf of themselves and all others similarly situated, Plaintiffs-Appellants, v. Jay B. RISING, Treasurer of the State of Michigan; Christopher M. DeRose, Director, Department of Management and Budget Office of Retirement Systems; George M. Elworth, Member, Michigan Judges Retirement Board; Mark Haas, Member, Michigan Judges Retirement Board; Alton Davis, Member, Michigan Judges Retirement Board; Francis Spaniola, Member, Michigan Judges Retirement Board; and Chris J. Swope, Member, Michigan Judges Retirement Board, Defendants-Appellees, 427 F.3d 351

SUTTON, J., delivered the opinion of the court, in which BOGGS, C.J., SUHRHEINRICH, BATCHELDER, GILMAN, GIBBONS, and COOK, JJ., joined and in which ROGERS, J., joined as to Parts I—III and V, and dissented from

Part IV. CLAY, J., (pp. 373-81), delivered a separate dissenting opinion, in which MARTIN, DAUGHTREY, MOORE, and COLE, JJ., joined and in which ROGERS, J., joined as to

Part II only. OPINION SUTTON, Circuit Judge. Four state-court judges from Michigan filed this lawsuit under 42 U.S.C. § 1983, the Equal Protection Clauses of the United States and Michigan Constitutions, and Michigan common law, claiming that state-court judges based in Detroit and surrounding Wayne County (the 36th District) receive more favorable retirement benefits than state-court judges based elsewhere in the State.

They brought the lawsuit on behalf of themselves and other similarly situated state-court judges; they filed the lawsuit in federal court; and they named several state officials, all with various responsibilities for managing the retirement system, in their official capacities as defendants (“the State” or “state defendants”). Among other forms of relief, plaintiffs asked the state defendants to “make restitution ... by paying ... with interest” the difference between the retirement benefits they received and the amounts they would have received had they been treated like the 36th-District judges.

The primary issue joined by the parties is whether a government retirement system that provides benefits for all state judges (and many other state officials) is an “arm of the State” or a “political subdivision” of the State. If the retirement system is an arm of the State, the parties agree, a federal-law money-damages action (or a state-law action of any sort) against the retirement system or its officials may not proceed in federal court in light of the Tenth and Eleventh Amendments to the United States Constitution.

If the retirement system is a political subdivision of the State, the parties also agree, a money-damages action of this sort may proceed in federal court. As we see it, the retirement system is most naturally characterized as an arm of the State. It is a product of state legislation. It is run by state officials or individuals appointed by state officials. It serves state officials—not just all state-court judges in Michigan but many of the top government officials in the State (e.g., the governor, the lieutenant governor, the secretary of state, the attorney general).

It is funded by the state treasury as well as by contributions from state officials. And if the retirement system faces a monetary shortfall, state legislation requires the state treasurer to make up the difference with state funds. For these reasons and those elaborated below, the district court correctly characterized the retirement system as an arm of the State.

Because plaintiffs have filed only federal claims that seek monetary relief or claims that primarily seek monetary relief and because the state-law claims must be dismissed regardless of the type of relief they seek, the district court correctly dismissed all claims. To the extent the district court meant to dismiss any of plaintiffs’ claims with prejudice, however, that was error, and that portion of the order is reversed. I. In 1992, the Michigan legislature enacted the Judges Retirement Act, Mich. Comp. Laws §§ 38.2101-.2670, which established the judges’ retirement system in its current form.

The retirement system provides defined-benefit and defined-contribution plans for most of Michigan’s state-wide officials: state trial judges (which include probate judges, district court judges and circuit court judges), state intermediate appellate judges, state supreme court justices, the governor, the lieutenant governor, the secretary of state, the attorney general, the legislative auditor general and the constitutional court administrator. Id. § 38.2108.

The retirement system is managed by a board comprised of two state officials (the treasurer and the attorney general) and three appointees named by the governor with the advice and consent of the state senate. Id. § 38.2202(1). The state treasurer serves as the treasurer of the retirement system, id. § 38.2206(1); the state attorney general serves as the legal advis- or to the retirement system, id. § 38.2207; and another state entity (the Michigan Department of Management and Budget) has responsibility “for the budgeting, procurement, and related management functions” of the retirement system, id. § 38.2205.

As amended by legislation enacted in 1996, the retirement system offers all members benefits under one of two pension plans: a defined benefit plan called “Tier 1” and a defined contribution plan called “Tier 2.” Under both tiers, participating officials contribute a portion of their income to their retirement funds. And under both tiers, the State (and in some instances a local government as well) contributes funds to each individual’s plan.

Generally speaking, Tier 1 offers a guaranteed level of fixed benefits during retirement, while Tier 2 does not guarantee fixed benefits but offers potentially higher returns on contributions. All judges who began their service before March 31, 1997, joined Tier 1 because that was the only option available to them before that date. All judges who started after that date were required to join Tier 2. Under the 1996 amendment, Tier 1 participants were authorized to move to Tier 2 if they elected to do so by a certain date in 1998. See D. Ct. Op. at 2.

On September 5, 2001, Judges Ernst, Ervin, Wilson and O’Brien—a probate judge, a district judge, a circuit judge and a retired circuit judge—filed a complaint on behalf of themselves and other similarly situated judges in the Eastern District of Michigan. They alleged that inequities in the retirement system violate (1) the Equal Protection Clause of the United States Constitution, (2) its counterpart in the Michigan Constitution and (3) several state-law fiduciary duties. JA 9-37.

The primary inequity, the complaint alleged, was that judges of the State’s 36th Judicial District, based in Detroit and surrounding Wayne County, pay less in retirement contributions and receive more in contribution benefits than other state-court judges. See JA 17-19. The roots of this alleged pay-less-and-receive-more disparity are part history and part policy. As a matter of history, the State and a local funding unit (usually a city or county) together paid all trial-level judicial salaries before 1980. Harvey v. State, 469 Mich. 1, 664 N.W.2d 767, 769 (2003) (hereinafter “Harvey ”).

Under this dual salary system, trial-level judges belonged to two retirement systems'—a state system and a local system—and the State made retirement contributions to the one system and the relevant local government made contributions to the other. In 1980, through legislation designed to make the State responsible for all state-court operations, the legislature took on responsibility for the state and local components of the salaries (and retirement benefits) of the judges of the 36th District with the goal of eventually doing the same for all other judicial districts in the State. Id.

Yet, “[i]n succeeding years, the goal of full state funding of court operations was not fulfilled. Nevertheless, the state continuefd] to fund one hundred percent of 36th Judicial District judges’ pensions. The retirement systems and pensions of judges outside the 36th Judicial District continue[d] to be funded by both state and local sources.” Id. Under the current system, as a result, 36th-District judges are the only ones who receive retirement benefits from the State based on their total salary level.

Other judges receive state retirement benefits based on their state salary component and local retirement benefits based on their local salary component. And while these other judges may treat up to 40 percent of their local salary component as state salary for purposes of calculating state retirement benefits, judges who choose this 40-percent option must make contributions of 7 percent of the salary they treat as state salary, while 36th-District judges must contribute only 3.5 percent of the salary they treat as state salary.

To the extent certain local retirement benefits are inferi- or to the state retirement benefits, as allegedly is the case in some instances, some state trial judges end up paying more to the state retirement system in order to receive the same (or nearly the same) retirement income as the judges based in the 36th District. As a matter of policy, the State has defended the current system on several grounds. It claims to need a higher compensation package to attract good lawyers to become judges in the Detroit area, and it wishes to ease the fiscal demands on the already-strapped coffers of the City of Detroit.

See id. at 774. The State, at any rate, claims that at some point it still intends to bring all state trial judges within an exclusively state-funded system but for now “the need to reorganize and streamline [is] most urgent in Wayne County and the City of Detroit because they [are] in financial distress.” JA 98. The upshot of plaintiffs’ lawsuit is this: they seek to bring all state-court judges within a retirement system that is exclusively funded and managed by the State.

That, say plaintiffs, will eliminate these disparities—so long as the past funding inequities are alleviated through restitution and so long as plaintiffs’ retirement obligations and payments thereafter are permitted to parallel those of the 36th-District judges.

Relatedly, plaintiffs also claim: (1) that state officials who participate in other state retirement plans receive better benefits than they do because those plans (unlike theirs) provide annual percentage increases in the retirement allowance for Tier 1 participants, JA 20-21; (2) that because of the way the 1996 Retirement Act calculates accrued benefits when transferring those benefits from Tier 1 to Tier 2, “it was possible for gross and unjust disparities in [transfer amount] to come into existence as to Tier 1 Plan members whose ages were but 1 day different and/or whose credited service was but 1 day different,” JA 22-24; and (3) that the State failed to distribute an alleged contribution surplus, amounting to a “wasting trust,” and breached other disclosure and management fiduciary duties, JA 28-32.

Plaintiffs have brought their disparate-treatment allegations under the Equal Protection Clause of the United States Constitution and its counterpart in the Michigan Constitution. They have brought their “wasting trust” and fiduciary-breach allegations under state law. On September 30, 2002, the district court granted the defendants’ “motion to dismiss or, in the alternative, for

summary judgment,” JA 83, on the basis of sovereign immunity. It reasoned that the retirement system was an “arm of the state” based on the structure and management of the system as well as the State’s responsibility for funding it. D. Ct. Op. at 11-12. It then ruled that the judges’ lawsuit was “barred to the extent plaintiffs seek money damages as opposed to purely prospective, injunctive relief.” Id. at 9, 664 N.W.2d 767.

After declining to exercise supplemental jurisdiction over the state-law claims in the case, id. at 12-13, 664 N.W.2d 767, the court dismissed the federal-law claims with prejudice and the state-law claims without prejudice, id. at 14, 664 N.W.2d 767.

Throughout the course of this litigation in the district court, it bears adding, the state courts of Michigan have been considering a similar lawsuit filed by other judges, one also premised on the theory that judges of the 36th District receive better retirement benefits than other state-court judges and also based on the Equal Protection Clause of the Michigan Constitution. A state circuit court judge has twice summarily dismissed the claims, and a state court of appeals has twice reversed the decision. See Harvey v. State, No. 187112, 1997 WL 33354621, 1997 Mich.App. LEXIS 1214 (Mich.Ct.App.

Jan. 3, 1997); Harvey v. State, 251 Mich.App. 323, 650 N.W.2d 392 (2002). In response to the court of appeals’ most recent decision, the Michigan Supreme Court in 2003 reviewed the case and entered judgment in favor of the state defendants. Harvey, 664 N.W.2d at 774 (holding that the legislature’s decision to treat 36th-Distriet judges differently satisfies rational-basis review); id. (“The state, by assuming the entire funding of the pensions of 36th District judges in the financially distressed city of Detroit, made those pensions more secure.

Certainly the Legislature would or could understand that this would induce competent and qualified attorneys to become judges or to remain judges.”). II. A. From birth, the States and the Federal Government have possessed certain immunities from suit in state and federal courts. Alden v. Maine, 527 U.S. 706, 713, 119 S.Ct. 2240, 144 L.Ed.2d 636 (1999); Monaco v. Mississippi, 292 U.S. 313, 322-23, 54 S.Ct. 745, 78 L.Ed. 1282 (1934); Hans v. Louisiana, 134 U.S. 1, 13, 10 S.Ct. 504, 33 L.Ed. 842 (1890).

For the Federal Government, that immunity flows not from any one provision in the Constitution but “is derived by implication” from the nature of sovereignty itself. Keifer & Keifer v. Reconstruction Fin. Corp., 306 U.S. 381, 388, 59 S.Ct. 516, 83 L.Ed. 784 (1939); see also Monaco, 292 U.S. at 321, 54 S.Ct. 745. For the States, that immunity flows from the nature of sovereignty itself as well as the Tenth and Eleventh Amendments to the United States Constitution.

Alden, 527 U.S. at 713, 119 S.Ct. 2240 (“[T]he sovereign immunity of the States neither derives from, nor is limited by, the terms of the Eleventh Amendment. Rather, as the Constitution’s structure, its history, and the authoritative

interpretations by this Court make clear, the States’ immunity from suit is a fundamental aspect of the sovereignty which the States enjoyed before the ratification of the Constitution, and which they retain today.”); id. at 713-14, 119 S.Ct. 2240 (“Any doubt regarding the constitutional role of the States as sovereign entities is removed by the Tenth Amendment.”). The States’ immunity from suits in federal court applies to claims against a State by citizens of the same State as well as to claims against a State by citizens of another State.

See Hans, 134 U.S. at 21, 10 S.Ct. 504; Alden, 527 U.S. at 728, 119 S.Ct. 2240; Barton v. Summers, 293 F.3d 944, 948 (6th Cir.2002). The immunity also applies to actions against state officials sued in their official capacity for money damages. See Lapides v. Bd. of Regents, 535 U.S. 613, 616, 623, 122 S.Ct. 1640, 152 L.Ed.2d 806 (2002); Edelman v. Jordan, 415 U.S. 651, 664-66, 94 S.Ct. 1347, 39 L.Ed.2d 662 (1974). The States’ federal-court immunity comes with a host of exceptions. A State may elect to waive that immunity through legislation, see Port Auth. Trans-Hudson Corp. v.

Feeney, 495 U.S. 299, 305-09, 110 S.Ct. 1868, 109 L.Ed.2d 264 (1990), or through its conduct in litigation, see, e.g., Lapides, 535 U.S. at 616, 122 S.Ct. 1640. The immunity does not attach if the lawsuit is not against the State or an “arm of the State.” Mt. Healthy City Sch. Dist. Bd. of Educ. v. Doyle, 429 U.S. 274, 280, 97 S.Ct. 568, 50 L.Ed.2d 471 (1977); see also Regents of the Univ. of Cal. v. Doe, 519 U.S. 425, 429, 117 S.Ct. 900, 137 L.Ed.2d 55 (1997); Hess v. Port Auth. Trans-Hudson Corp., 513 U.S. 30, 115 S.Ct. 394, 130 L.Ed.2d 245 (1994).

The immunity “does not extend to counties and similar municipal corporations.” Mt. Healthy, 429 U.S. at 280, 97 S.Ct. 568. The immunity does not apply if the lawsuit is filed against a state official for purely injunctive relief enjoining the official from violating federal law. See Ex parte Young, 209 U.S. 123, 155-56, 28 S.Ct. 441, 52 L.Ed. 714 (1908). The immunity may be abrogated by Congress when exercising its enforcement authority under the Fourteenth Amendment, Kimel v. Fla.

Bd. of Regents, 528 U.S. 62, 80, 120 S.Ct. 631, 145 L.Ed.2d 522 (2000), and perhaps other enforcement clauses, such as the Fifteenth Amendment, City of Rome v. United States, 446 U.S. 156, 178-80, 100 S.Ct. 1548, 64 L.Ed.2d 119 (1980). See also U.S. Const, amends. XIII, XIX, XXIV, XXVI. The immunity does not apply when the Federal Government brings the lawsuit. See United States v. Mississippi, 380 U.S. 128, 140-41, 85 S.Ct. 808, 13 L.Ed.2d 717 (1965); EEOC v. Ky. Ret. Sys., 16 Fed.Appx. 443 (6th Cir.2001).

And the immunity does not apply when another State brings the lawsuit on behalf of its own interests rather than those of specific citizens. See Colorado v. New Mexico, 459 U.S. 176, 182 n. 9, 103 S.Ct. 539, 74 L.Ed.2d 348 (1982). Whether immunity exists in a given case is a question of constitutional law that we review de novo. S.J. v. Hamilton County, 374 F.3d 416, 418 (6th Cir.2004).

In deciding whether an entity is an “arm of the State” on the one hand or a “political subdivision” on the other—the principal issue that occupies us today—the Supreme Court has considered several factors: (1) the State’s potential liability for a judgment against the entity, Hess, 513 U.S. at 51, 115 S.Ct. 394; (2) the language by which state statutes, id. at 44, 115 S.Ct. 394, and state courts, id. at 45, 115 S.Ct. 394, refer to the entity and the degree of state control and veto power over the entity’s actions, id. at 44, 115 S.Ct. 394; (3) whether state or local officials appoint the board members of the entity, id.; and (4) whether the entity’s functions fall within the traditional purview of state or local government, id. at 45, 115 S.Ct. 394.

In discussing these factors, the Court has emphasized that the first factor—the liability of the State for a judgment—is the foremost factor, id. at 51, 115 S.Ct. 394, and that it is the state treasury’s potential legal liability for the judgment, not whether the state treasury will pay for the judgment in that case, that controls the inquiry, see Doe, 519 U.S. at 431, 117 S.Ct. 900. Our cases follow a similar approach.

In S.J., we looked at the following factors: “(1) whether the state would be responsible for a judgment against the entity in question; (2) how state law defines the entity; (3) what degree of control the state maintains over the entity; and (4) the source of the entity’s funding.” 374 F.3d at 420. See also Alkire v. Irving, 330 F.3d 802, 813 (6th Cir.2003); Dubuc v. Mich. Bd. of Law Examiners, 342 F.3d 610, 615 (6th Cir.2003); Brotherton v. Cleveland, 173 F.3d 552, 560 (6th Cir.1999). Earlier cases adhere to a similar approach, though they break down some of these inquiries into still other questions.

See, e.g., Hall v. Med. Coll. of Ohio, 742 F.2d 299, 302 (6th Cir.1984) (considering as well “whether the agency is performing a governmental or proprietary function; whether it has been separately incorporated; ... whether it has the power to sue and be sued and to enter into contracts; whether its property is immune from state taxation, and whether the sovereign has immunized itself from responsibility for the agency’s operations” (citation and quotations omitted)). B. As measured by these benchmarks, Michigan’s retirement system for state-court judges and other state officials is an arm of the State.

First, the State would be liable for any judgment against the retirement system that existing funds of the system could not satisfy. If, for example, a federal court ordered the retirement system to pay the proposed class of plaintiff judges sufficient funds to equalize their retirement accounts with those of the 36th-District judges, it is quite possible that the retirement system could not satisfy that judgment and it is clear in that event that the state treasury would have to pay the bill.

As state law indicates, “[t]he legislature shall annually appropriate to the retirement system the amount [of money needed] ... to reconcile the estimated appropriation made in the previous fiscal year with the actual appropriation needed to adequately fund the retirement system for the previous fiscal year.” Mich. Comp. Laws § 38.2302(1). And the Michigan Constitution makes this duty a “contractual obligation” owed by the State to each retiree. See Mich. Const, art. 9, § 24; see also Musselman v.

Governor, 448 Mich. 503, 533 N.W.2d 237, 246 (1995) (“We hold that the state is obligated to prefund health care benefits under art. 9, § 24.”). See generally Mich. Comp. Laws § 38.2208 (“The retirement system shall draw its warrants upon the state treasury, payable out of funds of the retirement system, for the payment of retirement allowances, accumulated contributions, and the payment of salaries and other expenses necessary in the administration of the retirement system.”). Second, the State has extensive and detailed control over the retirement system.

The system is a product of comprehensive state legislation known as the Judges Retirement Act. Id. §§ 38.2101-2670. The board of the retirement system “is created in [Michigan’s Department of Management and Budget],” id. §§ 38.2202(1), 38.2104(5), and the Department is responsible “for the budgeting, procurement, and related management functions of the retirement system,” id. § 38.2205. The state treasurer is the treasurer of the retirement system, id. § 38.2206(1), and the state attorney general is the legal advisor to the system, id. § 38.2207.

State law also imposes extensive requirements with respect to the investment of, and custody over, the retirement system’s funds. The treasurer must invest the funds and keep custody over them in accordance with another comprehensive state statute, id. § 38.2206(1), the Public Employee Retirement System Investment Act, id. §§ 38.1132-38.1140i, and must deposit funds “in the same manner and subject to the laws governing the deposit of state funds by the state treasurer,” id. § 38.2206(2); see also Fitzpatrick v.

Bitzer, 519 F.2d 559, 565 (2d Cir.1975) (“Although the money in [the Connecticut State Employees’ Retirement System] may be used only for a designated purpose, it nonetheless remains public money.” (quotations omitted)), rev’d in part on other grounds, 427 U.S. 445, 96 S.Ct. 2666, 49 L.Ed.2d 614 (1976); Mich. Const., art. IX, § 19 (permitting “[t]he state” to invest “funds accumulated to provide retirement ... benefits”).

The retirement system must present an annual report each fiscal year to the governor and legislature “regarding the financial, actuarial, and other activities of the retirement system.” Mich Comp. Laws § 38.2209. As history proves, the Michigan legislature has the power to amend and revamp the statute as it sees fit. See Harvey, 664 N.W.2d at 769 (detailing the history of amendments to the judges’ retirement systems in Michigan).

Removing any doubt that the State controls this retirement system, the Michigan Supreme Court itself has described the retirement system in related litigation as “maintained by the state.” Id. Third, three of the five members of the board of the retirement system are appointed by Michigan’s governor with the advice and consent of the Michigan Senate. Mich. Comp. Laws § 38.2202(1). The other two members are state officials: the treasurer and the attorney general. Id.

Board members take an oath of office, which is filed with the Michigan Secretary of State, id. § 38.2203(1), and they are compensated for their expenses by the Michigan Legislature, id. § 38.2202(3). Fourth, the retirement system’s operations have far more in common with a traditional state function than a local one. Doubtless, a local government may create and fund a retirement system, and many local governments do just that.

But when, as in this case, the retirement system is funded by annual appropriations from the state legislature, operates in part through the Michigan Treasury and in part through the State’s Department of Management and Budget, operates on a statewide basis and serves the officers of one of three essential branches of state government (the judiciary) as well as several other state-wide officials, it is fair to say that the retirement system performs a traditional state function. In reaching this conclusion, we are not alone.

In a prior unpublished decision of this court, a panel noted that a suit against a state retirement system “brought by a private individual ... would [have been] barred by the Eleventh Amendment” but for the fact that the federal government filed the lawsuit. EEOC v. Ky. Ret. Sys., 16 Fed.Appx. 443, 448 (6th Cir.2001). In addition to this dictum from our court, several other courts have held that state employee retirement systems are arms of the State. See McGinty v.

New York, 251 F.3d 84, 100 (2d Cir.2001) (holding that the New York Retirement System is an arm of the State); Fitzpatrick, 519 F.2d at 561 (holding that the Connecticut State Employees’ Retirement System is an arm of the State); JMB Group Trust IV v. Penn. Mun. Ret. Sys., 986 F.Supp. 534, 538 (N.D.Ill.1997) (holding that the Pennsylvania Municipal Retirement System is an arm of the State where the duties and responsibilities of the Retirement System are “totally defined and limited by the Commonwealth of Pennsylvania under the provisions of the Pennsylvania Code”); Sculthorpe v. Va. Ret.

Sys., 952 F.Supp. 307, 309-10 (E.D.Va.1997) (holding that the Virginia Retirement System is an arm of the State); Hair v. Tenn. Consol. Ret. Sys., 790 F.Supp. 1358, 1364 (M.D.Tenn.1992) (holding that the Tennessee Consolidated Retirement System is an arm of the State); Mello v. Woodhouse, 755 F.Supp. 923, 930 (D.Nev.1991) (holding that the Nevada Public Employees’ Retirement Board is an arm of the State); Reiger v. Kan. Pub. Employees Ret. Sys., 755 F.Supp. 360, 361 (D.Kan.1990) (holding that the Kansas Public Employees Retirement System is an arm of the State); Retired Pub. Employees’ Ass’n of Cal.,

Chapter 22 v. California, 614 F.Supp. 571, 573, 581 (N.D.Cal.1984) (holding “this Court is without jurisdiction to consider plaintiffs’ [ ] claim” against the “Public Employees Retirement System” of the State of California because “the Eleventh Amendment” bars claims “against the state and state officials and agencies”), rev’d on other grounds, 799 F.2d 511 (9th Cir.1986); United States v. South Carolina, 445 F.Supp. 1094, 1099-1100 (D.S.C. 1977) (holding that the South Carolina State Retirement System is an arm of the State); 21 Properties, Inc. v.

Romney, 360 F.Supp. 1322, 1326 (N.D.Tex.1973) (holding that the New York State Teachers’ Retirement System is an arm of the State because the State would be required to increase its contributions to the retirement system to compensate for a judgment against it). C. In attempting to counter this conclusion, the plaintiffs make several arguments, all unconvincing. Contending that the retirement system’s funds are not commingled with general state funds, they initially argue that a judgment paid for by the system’s funds would not be the equivalent of a judgment paid for by general state funds.

Two statutory provisions, they add, support this conclusion'—Mich. Comp. Laws § 38.2604(6) (requiring that retirement system funds “be held in trust” and that they not be “used for or diverted to [any other] purpose”) and § 38.2208 (requiring that retirement payments be “payable out of funds of the retirement system”). The first response to this claim is that a judgment against the retirement system would not be satisfied by member contributions alone that have never been commingled with state funds.

As the district court correctly reasoned and as the plaintiffs must acknowledge, “[p]art of the relief plaintiffs are seeking in this case is a refund of the allegedly overfunded Tier 1 plant,] which [the judges] concede, includes ‘the State’s mandatory contribution to the Tier 1 Plan.’ ” D. Ct. Op. at 12. Whether member contributions are commingled with state funds or not, in other words, the plaintiffs’ complaint by its terms asks for money that the State has contributed to these retirement accounts.

Anticipating this response, plaintiffs argue that they nonetheless are seeking no more than what the retirement system has in surplus and accordingly a judgment in this case will not compel additional monetary allocations from the state treasury. That leads to the second response to this claim: As Regents of the University of California v.

Doe explains, the proper inquiry is not whether the state treasury would be liable in this case, but whether, hypothetically speaking, the state treasury would be subject to “potential legal liability” if the retirement system did not have the money to cover the judgment. 519 U.S. at 431, 117 S.Ct. 900. In a variation on this contention, plaintiffs argue that the pertinent state statutes and Michigan Constitution do not compel the state treasury to pay a judgment obtained against the retirement system but compel it only to fund the system on an annual basis.

But in making this argument, plaintiffs fail to come to grips with the fiscal reality that the State’s funding-requirement assuredly could increase if the retirement system were to use its current and future funding to pay off a judgment against it. Where else would the money come from? Plaintiffs never have asserted that the 36th-District judges should make up the difference-which of course would undo the very nature of the equitable system they purport to wish to establish.

Rather than looking to whether a judgment would be paid directly by the state treasury, Hess frames the pertinent inquiry this way: “If the expenditures of the enterprise exceed receipts, is the State in fact obligated to bear and pay the resulting indebtedness of the enterprise?” 513 U.S. at 51, 115 S.Ct. 394. That, as shown, is precisely what the Michigan statutes and § 24 of

Article 9 of the Michigan Constitution require of the Michigan legislature in this instance.

The plaintiffs next argue that the Michigan Supreme Court’s mandamus decision in Musselman establishes that this provision of the Michigan Constitution is not self-executing and that only the legislature or the governor, as opposed to the courts, may enforce it. “[I]nsofar as the plaintiffs are asking us to require the Legislature to appropriate funds for retirement health care benefits,” Musselman holds, “we understand that the intention of the drafters was that the second sentence of Const. 1963, art. 9, § 24, is not self-executing.

Because the provision does not alter the rule that legislative action is necessary to appropriate funds, it fails to Tay[ ] down rules by means of which [its] principles may be given the force of law.’ ” 533 N.W.2d at 246; see id. (“We hold that the state is obligated to prefund health care benefits under art. 9, § 24. However, because we have no authority to order the Governor or the Legislature to appropriate funds, mandamus is denied.”).

In the face of this language from Musselman, plaintiffs reason, the state treasury in reality would not be liable, potentially or otherwise, for any excess judgment against the retirement system because no State court could force the legislature to comply with the funding obligation. This is a bridge too far. Such a test not only would permit this lawsuit to go forward but it also would come close to eliminating, if not completely eliminate, all state sovereign immunity in federal court—and presumably all federal sovereign immunity in federal court.

Like Michigan, the National Government and each State embrace the bedrock principle of a constitutional separation of powers. See Jim Rossi, Institutional Design and the Lingering Legacy of Antifederalist Separation of Powers Ideals in the States, 52 Vand. L.Rev. 1167, 1190-91 & nn. 104-07 (1999) (addressing each State’s approach in this area); John Devlin, Toward a State Constitutional Analysis of Allocation of Powers: Legislators and Legislative Appointees Performing Administrative Functions, 66 Temp. L.Rev. 1205, 1221 (1993).

And like Michigan, the National Government and virtually every State have an explicit appropriations clause in their constitutions that mandates legislative, rather than judicial, control of the treasury. Richard D. Ro-sen, Funding “Non-Traditional” Military Operations: The Alluring Myth of a Presidential Power of the Purse, 155 Mil.

L.Rev. 1, 137 & nn. 672-74 (1998) (noting that “[tjoday, all but three state constitutions (Mississippi, Rhode Island, and Utah) include some form of appropriations clause” and identifying 47 appropriations clauses); id. at 143 (“[Sjtates have uniformly interpreted their constitutional schemes—particularly their appropriations clauses—to command exclusive legislative supremacy over the power of the state purse.”); id. at 143 n. 688 (citing cases). If plaintiffs were correct, there thus would be few, if any, settings in which States could assert a sovereign immunity defense in federal court.

Even a lawsuit against the State itself would be permitted under this approach. Had the State of Michigan been the defendant in this case, for instance, plaintiffs still could have shown that Musselman prohibits state courts from compelling the legislature to make an appropriation to fund a judgment against “the State.” And if these state separation-of-powers limitations bear on this inquiry, why is it not the case that state sovereign-immunity limitations would bear on this inquiry?

There, too, the ability to collect any judgment against the State or one of its alter egos would be limited by state sovereign immunity. Both inquiries, however, look at the question through the wrong end of the lens. When a State imposes separation-of-powers or sovereign-immunity limitations on lawsuits against the State and when a potential judgment in federal court against an entity would implicate those limitations, that is further proof that the entity is properly characterized as an arm of the State, not that the entity is a political subdivision.

Arms of the State, after all, generally may benefit from these limitations while political subdivisions generally may not. Under an alternative system, quite strangely, the more vigorously a State protected its treasury from judicial encroachment in state court the more vulnerable it would be to money-damages claims in federal court. See Kelley v. Metro. County Bd. of Educ., 836 F.2d 986, 995-97 (6th Cir.1987) (reasoning that the appropriations clause in the Tennessee Constitution provided an additional reason for applying the Eleventh Amendment to bar a federal lawsuit against a State).

Not only has the United States Supreme Court never blessed this unusual theory but its rulings in numerous cases implicitly contradict it. We are not aware of a single sovereign-immunity Supreme Court decision arising from a claim in federal court where the State at issue did not place separation-of-powers or sovereign-immunity limitations on the enforcement of money-damages judgments against the State. And most importantly, this approach cannot be squared with the “potential liability” question that the Court has told us to ask and answer.

If a State’s constitution and statutory law make the State responsible for funding a certain agency’s programs, that reality makes the State potentially responsible for a judgment against that agency—no matter whether the judgment is difficult to collect, whether the State responsibility is not self-executing or whether some other feature of state law imposes hurdles on collecting the “potential liability” flowing from the judgment. Finally, Doe seems directly to contradict plaintiffs’ suggestion.

In Doe, the Ninth Circuit had concluded that a state instrumentality (the Regents of the University of California) was not an arm of the State because the Federal Government had agreed to indemnify it for any liability arising out of the lawsuit. 519 U.S. at 427-28, 117 S.Ct. 900. Writing for a unanimous Court, Justice Stevens wrote that this approach mistakenly “converged] the inquiry into a formalistic question of ultimate financial liability.” Id. at 431, 117 S.Ct. 900.

Instead, he reasoned, “it is the entity’s potential legal liability, rather than its ability or inability to require a third party to reimburse it, or to discharge the liability in the first instance, that is relevant.” Id. (emphasis added). In the end, the Court noted: “Surely, if the sovereign State of California should buy insurance to protect itself against potential tort liability to pedestrians stumbling on the steps of the State Capitol, it would not cease to be ‘one of the United States.’ ” Id.

The same can be said of plaintiffs’ argument here: “Surely, if the sovereign State of [Michigan] should [prevent its judiciary from forcing its legislature to make fiscal appropriations], it would not cease to be ‘one of the United States.’ ” Relying on language from some of our cases, plaintiffs next suggest that the only relevant inquiry in the arm-of-the-State analysis is whether the state treasury may be impacted by a judgment in the case. See Alkire, 330 F.3d at 811-12; Brotherton, 173 F.3d at 561.

While there can be little doubt that the state-treasury inquiry will generally be the most important one, it also seems clear that it is not “the sole criterion for determining whether an agency is a state entity for sovereign immunity purposes.” S.J., 374 F.3d at 421. “[T]he sovereign immunity doctrine is about money and dignity—it not only protects a State’s treasury, but also ‘pervasively ... emphasizes the integrity retained by each State in our federal system.’ [Hess, 513 U.S.] at 39, 115 S.Ct. 394; see id. at 47, 115 S.Ct. 394 (noting that when immunity factors cut in different directions, ‘the Eleventh Amendment’s twin reasons for being remain our prime guide’ in arm-of-the-state inquiry).” Id.; see also Seminole Tribe v.

Florida, 517 U.S. 44, 58, 116 S.Ct. 1114, 134 L.Ed.2d 252 (1996) (stating that sovereign immunity “does not exist solely in order to prevent federal-court judgments that must be paid out of a State’s treasury; it also serves to avoid the indignity of subjecting a State to the coercive process of judicial tribunals at the instance of private parties” (brackets, citations and quotations omitted)). Proving the point: When a State is sued by name in a lawsuit, sovereign immunity bars the lawsuit regardless of whether monetary relief is sought or not, see Pennhurst St. Sch. & Hosp. v.

Halderman, 465 U.S. 89, 102, 104 S.Ct. 900, 79 L.Ed.2d 67 (1984); see also S.J., 374 F.3d at 421; when a State or state official is sued in federal court in a lawsuit filed under state law, sovereign immunity bars the lawsuit regardless of whether monetary relief is sought, see Pennhurst, 465 U.S. at 102, 104 S.Ct. 900; and when state officials are sued solely for prospective injunctive relief, sovereign immunity does not apply even if the injunc-tive relief may affect the state treasury, see Edelman, 415 U.S. at 667, 94 S.Ct. 1347. Important as the monetary liability factor may be, it is not the only factor.

Plaintiffs next argue that two decisions from other courts—Blake v. Kline, 612 F.2d 718, 728 (3d Cir.1979), and Boatmen’s First National Bank of Kansas City v. Kansas Public Employees Retirement System, 915 F.Supp. 131, 135 (W.D.Mo.1996)—undermine our conclusion. The Third Circuit’s decision, however, did not reverse the district court’s conclusion that sovereign immunity barred the claim; it remanded the case for further consideration.

Even in doing that, the court was dealing with Pennsylvania’s Public School Employees’ Retirement Board, which serves employees of local public schools, entities that the Court has already concluded fall on the political subdivision side of the line, see Mt. Healthy, 429 U.S. at 280-81, 97 S.Ct. 568, and whose board was primarily made up of members who were not appointed by state officials, Blake, 612 F.2d at 723. In Boatmen’s, it is true, the court addressed a retirement system that has legitimate parallels to the Michigan retirement system. 915 F.Supp. at 135.

But the court reasoned that the mere “theoretical possibility” that the Kansas treasury might one day be liable for a judgment in the case failed to make the retirement fund an arm of the State, id. at 137, a theory that has since been rejected by the Supreme Court, see Doe, 519 U.S. at 431, 117 S.Ct. 900 (“[I]t is the entity’s potential legal liability ... that is relevant.” (emphasis added)). That leaves a few lingering contentions raised by the plaintiffs, each of which can be addressed briefly.

Plaintiffs point to the fact that the retirement system was created as a “qualified pension plan created in trust” and as an exempt organization under the Internal Revenue Code. But the federal tax treatment of an entity does not prove whether it functions more like a political subdivision or a state agency. We suspect that the Treasury Department of each State is tax exempt, and yet no one would suggest that this fact turns these quintessential state agencies into (or even begins to turn them into) political subdivisions.

Plaintiffs contend that the retirement system is more proprietary than governmental because it operates for the benefit of its members only and not for the benefit of the entire State. But the system still serves a statewide purpose—providing retirement benefits for the judicial officers of the third branch of state government as well as other prominent statewide officials, all of whom indisputably serve the State. Were it otherwise, the Michigan Department of Military and Veterans Affairs would not be a state agency as it directly serves only those individuals who have served in the armed forces.

Plaintiffs finally contend that the retirement system has “full autonomy” over its operations. But the statute that gives them this autonomy, see Mich. Comp. Laws § 38.2204, merely authorizes the board to fulfill the “proper discharge of retirement board duties pursuant to [Michigan’s] executive organization act of 1965”—an act that also organizes, among other state agencies, the Departments of State, the Attorney General, Treasury, Management and Budget and State Police, id. § 16.104.

Not only does § 38.2204 thus link the retirement system with the organizational legislation of other state agencies but it also imposes several requirements on the system that it is the duty of other departments of the State to follow—to promulgate rules under the state administrative procedures act, to hold meetings in compliance with the state open meetings law and to comply with the state freedom of information act. Id. III.

Even if the district court correctly dismissed their complaint on sovereign-immunity grounds, plaintiffs argue that it should not have dismissed their federal claims with prejudice—that it should not, in other words, have prevented them in the future from filing the claims in state court or have prevented them from filing a permissible Ex parte Young claim in federal court. A district court’s decision to dismiss a claim with prejudice or without it receives abuse-of-discretion review. Craighead v. E.F.

Hutton & Co., Inc., 899 F.2d 485, 495 (6th Cir.1990). “[EJrrors of law” invariably establish an abuse of discretion, United States v. McDaniel, 398 F.3d 540, 544 (6th Cir.2005), and we apply de novo review in interpreting an order to determine whether it dismisses claims with prejudice, see United States v. Spallone, 399 F.3d 415, 423 (2d Cir.2005); cf. United States v. Moore, 131 F.3d 595, 598 (6th Cir.1997). The district court’s decision leaves some doubt as to whether it meant to dismiss plaintiffs’ federal claims with prejudice.

The opinion itself suggests only that the plaintiffs’ money-damages claims may not be refiled in federal court. For example: it says that the court lacks jurisdiction over the state defendants, D. Ct. Op. at 8; it says that “[t]his case does not belong in federal court,” id. at 14; and it says that the “[plaintiffs’ suit is barred to the extent plaintiffs seek money damages as opposed to purely prospective, injunc-tive relief,” id. at 9. On the other hand, the final language of the decision contains no such limitation. It simply states that “plaintiffs’ federal claims ... are dismissed with prejudice.” Id. at 14.

Construing the order against the backdrop of the opinion it enforces, we think the better reading of the order is that it prevents the judges only from re-filing their claims against the state defendants for monetary relief in federal court but does not prevent the judges from re-filing their federal claims in state court or from filing any permissible Ex parte Young claims in federal court. This

interpretation of the order not only respects the reasoning of the district court’s decision but also comports with the customary rules for dismissing claims for lack of jurisdiction. In Costello v. United States, 365 U.S. 265, 81 S.Ct. 534, 5 L.Ed.2d 551 (1961), the Court addressed a district court’s dismissal order that failed to specify whether it was made with or without prejudice.

Under the common law, the Court explained, “dismissal on a ground not going to the merits was not ordinarily a bar to a subsequent action on the same claim.” Id. at 285, 81 S.Ct. 534; see also id. at 286, 81 S.Ct. 534 (“If the first suit was dismissed for ... the want of jurisdiction, or was disposed of on any ground which did not go to the merits of the action, the judgment rendered will prove no bar to another suit.”); Fed.R.Civ.P. 41(b) (specifying that “a dismissal for lack of jurisdiction” does not “operate[ ] as an adjudication upon the merits” unless the court “otherwise specifies”).

Our cases, too, recognize that dismissals for lack of jurisdiction should generally be made without prejudice. See Bauer v. RBX Indus., Inc., 368 F.3d 669, 581 (6th Cir.2004) (vacating a district court’s judgment for lack of jurisdiction and concluding (in reliance on Costello) that the “district court should have dismissed the [statutory] claim without prejudice”); Mitan v. Int'l Fid. Ins. Co., 23 Fed.Appx. 292, 297 (6th Cir.2001) (“Dismissals of actions that do not reach the merits of a claim, such as dismissals for lack of jurisdiction, ordinarily are without prejudice.”). See also Freeman v.

Oakland Unified Sch. Dist., 179 F.3d 846, 847 (9th Cir.1999); Voisin’s Oyster House, Inc. v. Guidry, 799 F.2d 183, 188-89 (5th Cir.1986). “ ‘[I]n rare circumstances,’ ” it is true, “ ‘a district court may use its inherent power to dismiss with prejudice (as a sanction for misconduct) even a case over which it lacks jurisdiction.’ ” Mitan, 23 Fed.Appx. at 298 (quoting Caribbean Broad. Sys., Ltd. v. Cable & Wireless PLC, 148 F.3d 1080, 1091 (D.C.Cir.1998)). But there was no basis for applying any such exception here.

In the final analysis, the district court’s dismissal order was premised on a lack of jurisdiction, and the court gave no explanation for turning its back on the heavy presumption that a dismissal for lack of jurisdiction will be without prejudice. To the contrary, the decision appeared to contemplate the filing of these claims in state court or the filing of Ex parte Young claims in federal court. Under these circumstances, the better reading of the order is that the district court meant to dismiss the federal claims without prejudice.

To the extent the district court had something else in mind (e.g., a dismissal ■with prejudice), that was error because the court gave no explanation for abandoning the assumption, based on precedent and Rule 41(b), that a dismissal for lack of jurisdiction will be made without prejudice. IV. Our conclusion that the dismissal ruling is without prejudice diminishes the significance of plaintiffs’ next argument—that their complaint should be construed to contain permissible requests for prospective injunctive relief under Ex parte Young, 209 U.S. 123, 28 S.Ct. 441, 52 L.Ed. 714 (1908).

While it may be that plaintiffs could frame a claim for injunctive relief that satisfies Ex parte Young and while our without-prejudice ruling will give them an opportunity to formulate such a claim (if they so choose), we do not interpret their current complaint to contain any such claims. In Ex parte Young, 209 U.S. 123, 159-60, 28 S.Ct. 441, 52 L.Ed. 714 (1908), the Supreme Court carved out an exception to the States’ constitutional immunity from suit, one that permits federal courts to enjoin state officials from the future enforcement of state legislation that violates federal law.

Under the exception, “a federal court’s remedial power ... is necessarily limited to prospective injunctive relief, and may not include a retroactive award which requires the payment of funds from the state treasury.” Edelman, 415 U.S. at 677, 94 S.Ct. 1347 (citations omitted); see also Garten v. Kent State Univ., 282 F.3d 391, 395 (6th Cir.2002).

In distinguishing between forbidden monetary relief and permissible injunctive relief, the Supreme Court has explained that “[r]elief that in essence serves to compensate a party injured in the past by an action of a state official in his official capacity that was illegal under federal law is barred even when the state official is the named defendant.” Papasan v.

Allain, 478 U.S. 265, 278, 106 S.Ct. 2932, 92 L.Ed.2d 209 (1986), “On the other hand, relief that serves directly to bring an end to a present violation of federal law is not barred by the Eleventh Amendment even though accompanied by a substantial ancillary effect on the state treasury.” Id. The ancillary-effect exception, we have explained, “is a narrow one.” Kelley v. Metro.

County Bd. of Educ., 836 F.2d 986, 992 (6th Cir.1987). “The dividing line” between ancillary relief and essentially compensatory relief, we have also explained, “is whether the money or the non-monetary injunction is the primary thrust of the suit.” Barton v. Summers, 293 F.3d 944, 949 (6th Cir.2002); id. (“If the injunctive relief sought by the plaintiff is truly prospective non-monetary relief, sovereign immunity will not bar the suit simply because the state may be required to make incidental expenditures in complying with the injunction.”).

We consider Eleventh Amendment immunity, as well as any exceptions to it, on a claim-by-claim basis. See Pennhurst, 465 U.S. at 121, 104 S.Ct. 900; Henry v. Metro. Sewer Dist., 922 F.2d 332, 337 (6th Cir.1990). And because the purposes of Ex parte Young do not apply to a lawsuit designed to bring a State into compliance with state law, the States’ constitutional immunity from suit prohibits all state-law claims filed against a State in federal court, whether those claims are monetary or injunctive in nature.

See Pennhurst, 465 U.S. at 106, 104 S.Ct. 900 (explaining that the “entire basis for the doctrine of Young and Edelman disappears” when “a plaintiff alleges that a state official has violated state law”). Many of plaintiffs’ 19 requests for relief in their complaint, it is clear, amount to classic requests for monetary relief.

As they acknowledge in their brief, one request (¶ 12) asks the court to order the defendants “to pay” them the “Excess Contributions” made to the Tier 1 Plan, see Ernst Br. at 14, a claim that plaintiffs estimate has a $109 million value (see Ernst Reply Br. at 1) and that is anything but ancillary.

Three other requests for relief are monetary in nature by their very terms, demanding that the defendants “refund ..., with interest, ... past contributions” (¶ 4), and “make restitution ... by paying ... with interest” the difference between the amounts of money they in fact received and the amounts to which they believe they are entitled (¶¶ 6 & 8).

Two more paragraphs (¶¶ 10 & 11) vary the request for money only slightly by asking first for a recalculation of the value of the plaintiffs’ accounts, then by asking the court to order the defendants to “transfer the difference” between the old value and the recalculated value to the plaintiffs’ accounts. While some of these requests for relief have an equitable ring to them (the request for restitution comes to mind), that fact does not alter the monetary nature of the relief requested.

See Barton, 293 F.3d at 949 (“[Rjelief should not be granted if ‘the relief is tantamount to an award of damages for a past violation of federal law, even though styled as something else.’ ” (quoting Papasan, 478 U.S. at 278, 106 S.Ct. 2932)). Against this backdrop, plaintiffs specifically contend that 10 of their 19 requests for relief amount to permissible requests for injunctive relief. See Ernst Br. at 35-36 (citing ¶¶ 3, 5, 7, 9, 10, 11, 12, 13, 14 & 16). As an initial matter, and as already explained, ¶¶ 10-12 amount to thinly veiled requests for retroactive monetary relief.

Paragraphs 13, 14 & 16 request relief that by its terms is tied to plaintiffs’ state-law claims. The plaintiffs ask the court, for instance, to enjoin the State from transferring Tier 1 Plan funds to the “court fee fund” or to the “court equity fund.” (¶ 13). This request coincides with their state-law breach-of-fiduciary-duties claim (Count 10), where they allege that transfers of Tier 1 Plan funds to the “court fee fund” and the “court equity fund” are impermissible under Mich. Comp. Laws § 38.2604(6). JA 23-24.

The plaintiffs next ask the court to order the State to prepare “an annual report for the current fiscal year and future fiscal years” that accounts for Tier 1 Plan activity, including transfers to the court fee fund and court equity fund. (¶ 14). This request again coincides with Count 10, where they allege a violation of trust duties because the State has “not required ... the preparation of an annual report,” leading “by way of example” to the allegedly impermissible transfers to the court fee fund and court equity fund. JA 22-23.

The plaintiffs finally ask the court to enjoin the State from transferring excess funds in Tier 1 Plan accounts “to the treasury at the time of termination of the Tier 1 Plan,” and to order the State “to pay such funds to ... members, vested former members, retir-ants, and retirement allowance beneficiaries.” (¶ 16). This request also coincides with Count 10, where they allege that Mich. Comp. Laws § 38.2604(6) establishes that “the Tier 1 Plan’s assets may not be used for any purpose except for the exclusive benefit of members, vested former members, retirants, and retirement allowance beneficiaries.” JA 23.

As requests for relief tied to state-law claims, we need not consider whether they are monetary or injunctive in nature, because they may not form the basis for an exception to state sovereign immunity in the federal courts in either event. See Pennhurst, 465 U.S. at 106, 104 S.Ct. 900. The remaining four paragraphs (¶¶ 3, 5, 7 & 9) also amount to direct requests for monetary relief and accordingly do not fall within the Ex parte Young exception.

Two paragraphs explicitly request monetary payments, asking the court to order the defendants to “afford to Plaintiffs ... who ... have not yet retired a retirement allowance upon their retirements equal to that which judges of the 36th District Court ... will be entitled” (¶ 5) and to “afford to Plaintiffs ... an annual percentage increase” in their retirement benefits (¶ 7).

And the other two paragraphs effectively ask for monetary payments, requesting that they be permitted to switch plans (¶ 9) and that the court (¶ 3) “enjoin Defendants from requiring those Plaintiffs ... who have remained as participants in the Tier 1 Plan to contribute a higher percentage of their compensation for a retirement allowance than the judges of the 36th District Court.” In considering these four claims, it is true, “the difference between the type of relief barred by the Eleventh Amendment and that permitted under Ex parte Young will not in many instances be that between day and night.” Edelman, 415 U.S. at 667, 94 S.Ct. 1347.

But these claims fall on the Eleventh Amendment side of the line for three reasons. First, this is not a case in which plaintiffs have asked the court to equalize treatment by diminishing the benefits to the 36th-Distriet judges, and it thus is not a case in which the impact of the relief on the state treasury will be zero.

As the masters of their complaint, plaintiffs asked the court for an order entitling them to a retirement allowance equal to what the 36th-District judges “will be entitled” (¶ 5), “an annual percentage increase” in their retirement benefits (¶ 7), the opportunity to switch to the allegedly more generous state plan (¶ 9) and the luxury of not having to make “higher” contributions for their retirement allowance (¶ 3). Whether out of altruism or self-interest, plaintiffs did not ask the court for an order that diminishes the benefits of their colleagues from the 36th District.

They thus did not ask the court to lower the 36th-District judges’ retirement benefits to what plaintiffs “will be entitled,” an order decreasing the “annual percentage increase” in retirement benefits for 36th-District judges, an order forcing the judges of the 36th District to switch to plaintiffs’ retirement plan or an order forcing the judges of the 36th District to make “higher” contributions for their retirement allowance. Confirming this

interpretation of the complaint are two features of plaintiffs’ appellate briefing in this matter. At no point do they argue that their complaint seeks—or indeed that they would want— an equalization order that will not cost the State any money and that will not monetarily benefit their class of claimants. And in their reply brief, in a

section addressing their claims for injunctive relief, they implicitly acknowledge that their injunction claim will require a reallocation of “dollars from the Tier I Plan’s trust fund.” See Reply Br. at 12 (“Here, the record does not disclose how many dollars from the Tier I Plan’s trust fund (not from Michigan’s general treasury) would have to be spent to afford Plaintiffs the prospective injunctive relief that they request.”).

This case accordingly is not one in which plaintiffs either have requested an equalization order that will not cost the State any money or have simply requested an order of invalidity that leaves it to the State to determine how to comply. Cf. Kelley v. Metro. County Bd. of Educ., 836 F.2d 986, 993 (6th Cir.1987) (noting that the requested order in Papasan “would necessarily entail a corresponding decrease in payments” to entities previously receiving the higher benefit and that “[t]he ancillary effect of the order on the state’s treasury would be absolutely nil”).

Second, as the dissent correctly acknowledges, the Eleventh Amendment does not permit a prospective injunction that amounts to a “direct monetary award.” Infra at 381. See Cory v. White, 467 U.S. 85, 90, 102 S.Ct. 2325, 72 L.Ed.2d 694 (1982); Kelley, 836 F.2d at 995. While an injunction order may have an “ancillary” effect on the state treasury, it may not directly require payments from the state treasury. See Kelley, 836 F.2d 986 (declining to enter prospective injunction that would require the State, as opposed to a local school board, to bear 60% of the costs of a desegregation decree).

Third, in view of the way plaintiffs have litigated this case in general and in view of the way they have crafted these four paragraphs of their complaint in particular, this relief amounts to a request for a “direct monetary award.” These counts do not involve a mere request for equal welfare benefits that leaves it to the State to determine how to equalize treatment on a going-forward basis. See Edelman, 415 U.S. at 667, 94 S.Ct. 1347.

Plaintiffs have insisted that their pension benefits be ratcheted up, a request that knows no other form of implementation than that the State make up the difference between what they would have received and what they wish to receive.

If they want a retirement allowance equal to what the 36th-District judges “will be entitled” (¶ 5), if they want a remedy that “afford[s] ... an annual percentage increase in retirement allowance equivalent to the annual percentage increase afforded” to other retirement plans (¶ 7), and if they want to switch plans (¶ 9), plaintiffs have given us no explanation how such orders amount to anything less than an order directly demanding additional state funding.

In trying to provide such an explanation, the dissent proposes (infra at 380 n. 4) that the other plans’ benefits could be immediately “lowered.” But this approach does not account for the salutary ban on “lowering” vested retirement benefits. See Mich. Const, art. 9 § 24; Seitz v. Probate Judges Ret.

Sys., 189 Mich.App. 445, 474 N.W.2d 125, 128 (1991) (“[A] retirement benefit cannot be reduced.”)- And when plaintiffs say they want an injunction preventing them from having “to contribute a higher percentage of their compensation for a retirement allowance than the judges of the 36th District Court” (¶ 3), they face the same problem. They are not asking to pay a lower contribution in return for a lower “retirement allowance.” They want to pay a lower contribution while receiving at least the same, if not a higher, retirement allowance—a remedy that necessarily demands additional state money.

All of these problems are compounded by the fact that this case does not present a mere going-forward welfare benefit problem. Pension plans by their nature have backward-looking components to them. Because state and individual contributions to the pension system are made on an annual basis, a request that plaintiffs receive a higher pension benefit in the future not only compels greater state contributions in the future but also will compel other transfers of state funds to account for the lack of adequate contributions in the past.

See Papasan, 478 U.S. at 281, 106 S.Ct. 2932 (“We discern no substantive difference between a not-yet-extinguished liability for a past breach of trust and the continuing obligation to meet trust responsibilities asserted by the petitioners. In both cases, the trustee is required, because of the past loss of the trust corpus, to use its own resources to take the place of the corpus or the lost income from the corpus.”) In sum, all of the identified federal requests for relief would “lead inexorably to the payment of state funds,” Quern v.

Jordan, 440 U.S. 332, 347, 99 S.Ct. 1139, 59 L.Ed.2d 358 (1979), and thus can only be regarded as requests for monetary relief. See id. at 347-49, 99 S.Ct. 1139 (holding that the requested relief of providing notice was not barred because it would not necessarily require state funding); see also Green v.

Mansour, 474 U.S. 64, 71, 106 S.Ct. 423, 88 L.Ed.2d 371 (1985) (holding that notice relief was barred by sovereign immunity); id. at 71, 73, 106 S.Ct. 423 (emphasizing that in Quern “the notice would not automatically lead to any particular action” and would not “bind state officials in any way,” but “the issuance of a declaratory judgment in these circumstances would have much the same effect as a full-fledged award of damages”); Barton, 293 F.3d at 948 (holding that plaintiffs cannot avoid the Eleventh Amendment bar “by phrasing their requests for monetary relief as requests for future payments”).

Put another way, these last four requests for relief seek nothing more than future monetary payments. Money is not only the “primary thrust,” id. at 949; it is their only concern. That makes the effect on the state treasury “ancillary only to itself’ and therefore barred by sovereign immunity.

Kelley, 836 F.2d at 992; see also Green, 474 U.S. at 71, 106 S.Ct. 423 (refusing to order declaratory relief because it was not “ancillary to the grant of some other appropriate relief’); Barton, 293 F.3d at 950 (“A court may enter a prospective injunction that costs the state money, but only if the monetary impact is ancillary, i.e., not the primary purpose of the suit.”). At the end of the day, the requested relief targets one of the most essential factors in the sovereign-immunity inquiry: state treasury liability.

When a State submits itself, without reservation, to the jurisdiction of a court in a particular case, that jurisdiction may be used to give full effect to what the State has by its act of submission allowed to be done; and if the law permits coercion of the public officers to enforce any judgment that may be rendered, then such coercion may be employed for that purpose.

But this is very far from authorizing the courts, when a State cannot be sued, to set up its jurisdiction over the officers in charge of the public moneys, so as to control them as against the political power in their administration of the finances of the State. Kelley, 836 F.2d at 991 (quoting Louisiana v. Jumel, 107 U.S. 711, 728, 2 S.Ct. 128, 27 L.Ed. 448 (1883)); see also Pennhurst, 465 U.S. at 101, 104 S.Ct. 900 (citing Jumel).

All of this is not to say that a permissible federal claim under Ex parte Young could not be formulated to challenge the retirement system—a point we do not reach today and a point that plaintiffs remain free to explore in view of our conclusion that the complaint should be dismissed without prejudice. It is only to say that these claims and these prayers for relief do not satisfy this “narrow” exception. The challenged requests for relief are either monetary by their very terms or are ancillary to nothing but monetary relief. V.

We, lastly, reject plaintiffs’ argument that they were prejudiced by the district court’s failure to specify the rule— Rule 12 or Rule 56—-by which dismissal was granted. The district court granted “defendant’s motion to dismiss or, in the alternative, for

summary judgment,” JA 83, in which the defendants moved for dismissal “pursuant to Rule 12(

b) or ... pursuant to Rule 56.” Id. at 84. Plaintiffs argue that because a 12(b)(6) motion with attached evidentiary support must be treated as a motion for

summary judgment, the district court erred in not addressing whether there were genuine issues of material fact and in ruling without affording plaintiffs additional opportunities for discovery. Yet plaintiffs acknowledge that the defendant’s motion fairly could have been characterized as a motion to dismiss for lack of subject matter jurisdiction under Rule 12(b)(1), and that when such a motion is accompanied by evidentia-ry support it is not converted into a motion for

summary judgment. See Rogers v. Stratton Indus., Inc., 798 F.2d 913, 915 (6th Cir.1986) (“[W]here subject matter jurisdiction is challenged under Rule 12(b)(1), as it was here, the plaintiff has the burden of proving jurisdiction in order to survive the motion. Perhaps even more importantly, when a Rule 12(b)(6) motion is converted to a Rule 56 motion for

summary judgment, the court, upon finding genuine issues as to material facts, must deny the motion; whereas on a Rule 12(b)(1) challenge to subject matter jurisdiction, the court is empowered to resolve factual disputes.”). In addition to misconceiving the role of evidence in a motion to dismiss for lack of jurisdiction, plaintiffs have failed to show how they were prejudiced.

They point to just one possible issue of material fact bearing on the jurisdictional issue: that the retirement system was overfunded by approximately $109,000,000—a fact that is “directly relevant to the determinative factor of whether or not any monetary relief afforded to [the plaintiffs] would have to be paid out of Michigan’s treasury.” Ernst Br. at 43. But as explained above, the relevant inquiry is whether the state treasury would be exposed to “potential legal liability,” Doe, 519 U.S. at 431, 117 S.Ct. 900, assuming that the retirement system did not have sufficient funds to satisfy a judgment.

On this record, plaintiffs have not shown how they were prejudiced by the district court’s characterization of the defendants’ motion. VI. For these reasons, we affirm the district court’s judgment in all respects, save to the extent the district court meant to dismiss the federal claims with prejudice, which was error and is reversed.