OPINION

KETHLEDGE, Circuit Judge.

In 2000, several plaintiffs sued Sunrise Children's Services and Kentucky, alleging that Kentucky had violated the Establishment Clause by paying Sunrise — a religiously oriented organization — for services it provides to children in State custody. Thirteen years later, the plaintiffs and Kentucky — but not Sunrise — agreed to a settlement that singled out Sunrise for monitoring by the American Civil Liberties Union and the Americans United for Separation of Church and State. Sunrise objected to the settlement, arguing that after more than a decade of litigation it was entitled to a merits adjudication to clear its name. Over Sunrise's objection, however, the district court dismissed the plaintiffs' Establishment Clause claim, incorporated the settlement into its dismissal order, and retained jurisdiction to enforce that order. In doing so, the court held that its dismissal order was not a consent decree, notwithstanding the order's incorporation of the settlement agreement; and for that reason, the court determined, Sunrise could not object to the order's entry. We respectfully disagree with the court's conclusion that its order was not a consent decree. Thus, we vacate that order and remand for further consideration of whether, among other things, the settlement agreement is fair to Sunrise.

I.

Sunrise operates group homes, places children in foster care, and provides related services for the State of Kentucky, which provides 65% of Sunrise's revenue. Sunrise describes its mission as "to extend the grace and hope of our loving God to the young people in our care by meeting their physical, emotional and spiritual needs." Some of those young people have alleged that Sunrise pressured them to become practicing Christians.

Fifteen years ago, Alicia Pedreira and some other Kentucky taxpayers filed this lawsuit, arguing that Kentucky's payments to Sunrise violated the Establishment Clause. The plaintiffs named Sunrise as a necessary defendant under Federal Rule of Civil Procedure 19. Without Sunrise, the plaintiffs alleged, they could not obtain complete relief and Sunrise itself would be unable to protect its interests. Seven years later, Sunrise and Kentucky moved to dismiss the suit for lack of standing. The district court granted the motion, but on appeal we reversed, holding that the plaintiffs have standing as Kentucky taxpayers. See Pedreira v. Ky. Baptist Homes for Children (Pedreira I), 579 F.3d 722, 731-33 (6th Cir.2009).

On remand, the plaintiffs filed an amended complaint, which again named Sunrise as a necessary defendant. In 2012, Sunrise and Kentucky moved for summary judgment. R. 480. The plaintiffs never responded to the merits of that motion. Instead, citing ongoing settlement negotiations, they moved to extend their deadline for responding to it. Over Sunrise's objection, the district court granted the motion.

A few months later, the plaintiffs and Kentucky — but not Sunrise — agreed to the settlement agreement at issue here, which runs 15 pages single-spaced. Kentucky expressly denies in the agreement that it (or Sunrise) violated the Establishment Clause or otherwise violated the rights of children in Sunrise's care. But the settlement requires Kentucky to change some of the terms in its standard two-year contracts with Sunrise and other providers. The new terms require providers to inform a child and the child's parents of a foster home's religious affiliation, to provide children with opportunities to go to the church of their choice, and to provide non-religious alternatives to religious activities. Providers must also agree not to discriminate against children on the basis of religion, coerce children to engage in religious activity, or attempt to convert children to a new religion. Further, when children leave their care, providers must give them an exit survey that asks, among other things, whether the provider tried to convert the child to a new religion.

The settlement includes monitoring provisions that single out Sunrise in some ways. Specifically, Kentucky must provide the ACLU and Americans United with information about the religious beliefs for all children in Sunrise's care, the completed exit surveys for those children, any reports that the State's caseworkers write about Sunrise, and records of any religious activities at Sunrise's group homes. Kentucky must give the ACLU and Americans United similar information about other providers only if Kentucky investigates a complaint about them, and even then only for the children who were the subject of those investigations.

In return, the plaintiffs agree to dismiss their lawsuit with prejudice and to waive any claims based on conduct occurring before the settlement. The plaintiffs retain the right to bring claims based on future conduct, but must submit to arbitration before doing so.

The settlement provides that the Kentucky district court that entered the agreement shall have exclusive jurisdiction to enforce it. Although the ACLU and Americans United (neither of which is a party to this case) have the same rights as Kentucky and the plaintiffs to seek enforcement of the agreement, Sunrise (which is a party to the case) has no rights to do the same. The settlement also recites that it is "Not [sic] Consent Decree," and purports to divest the district court of its power to hold Kentucky in contempt as a remedy for violations of the agreement (which, the parties contemplated, the district court would incorporate into its order dismissing the case). The settlement expires seven years after its effective date, subject to certain exceptions not relevant here.

After the plaintiffs and Kentucky reached agreement on the settlement, they asked the court to stay the case while they finalized some of the settlement's terms. Again over Sunrise's objection, the district court granted the motion. In September 2013 — nearly a year after Sunrise moved for summary judgment — the plaintiffs and Kentucky filed a motion asking the court to dismiss the suit and retain jurisdiction to enforce the settlement. Sunrise objected and filed a motion to dismiss for lack of jurisdiction. The district court denied Sunrise's motion, granted the plaintiffs' motion to dismiss, entered an order incorporating the settlement, and retained jurisdiction to enforce that order. This appeal followed.

II.

A.

We begin with two issues of standing. First, though none of the parties argues that Sunrise lacks standing to appeal, we have a duty to ensure that it does. See City of Cleveland v. Ohio, 508 F.3d 827, 835 (6th Cir.2007). Discharging that duty requires brief discussion here.

A party has standing to appeal if the party is "aggrieved by the judgment or order from which the appeal is taken." City of Cleveland, 508 F.3d at 836. To be aggrieved in this sense, a party need not be "formally bound or restricted by" the judgment it appeals from. See Vanguards of Cleveland v. City of Cleveland, 753 F.2d 479, 484 (6th Cir.1985). Rather, a party to the case can appeal any final judgment — including a consent decree — that imposes "some detriment" on the party. Id. (emphasis removed).

Here, Sunrise appeals from the district court's dismissal order, which incorporated the settlement between the plaintiffs and Kentucky. That order requires Kentucky to change the terms on which it offers contracts to Sunrise and singles Sunrise out for extra scrutiny by the ACLU and Americans United. Thus, the district court's order imposes some detriment on Sunrise, and Sunrise has standing to appeal it.

Second, Sunrise argues that the plaintiffs lack standing to bring this suit altogether. We have already rejected that argument once in this case: in Pedreira I, we held in a published decision that the plaintiffs have standing as Kentucky taxpayers to bring their Establishment Clause claim. 579 F.3d at 731-33. This panel may not revisit that question "unless an inconsistent decision of the United States Supreme Court requires modification of the decision or this Court sitting en banc overrules" the earlier panel. Ward v. Holder, 733 F.3d 601, 608 (6th Cir.2013) (internal quotation marks omitted).

Sunrise contends we can revisit that question because Pedreira I is inconsistent with the Supreme Court's later decision in Ariz. Christian Sch. Tuition Org. v. Winn, 563 U.S. 125, 131 S.Ct. 1436, 179 L.Ed.2d 523 (2011). The short answer to that contention — and the answer we stand on here — runs as follows. Federal-taxpayer standing has two elements: first, that there is "a logical link between the plaintiff's taxpayer status and the type of legislative enactment attacked[,]" Winn, 131 S.Ct. at 1445 (internal quotation marks omitted); and second, that there is "a nexus between the plaintiff's taxpayer status and the precise nature of the constitutional infringement alleged." Id. (internal quotation marks omitted). In Pedreira I, we held that state-taxpayer standing — which is the type of taxpayer standing the plaintiffs assert here — requires a plaintiff to satisfy a different standard, namely that she has suffered a "good-faith pocketbook injury." 579 F.3d at 731-32 (internal quotation marks omitted). But in Winn the Supreme Court held that state-taxpayer standing requires a plaintiff to establish the same two elements required for federal-taxpayer standing. 131 S.Ct. at 1445-47. That said, we have no occasion to revisit our holding in Pedreira I — because there we held that, required or not, the plaintiffs had established both elements of federal-taxpayer standing. 579 F.3d at 732-33. We therefore adhere to that holding in this case.

C.

Sunrise's remaining arguments go to the merits. Sunrise argues that the district court "erred" in dismissing this case because the court's dismissal "with prejudice" (under Fed.R.Civ.P. 41(a)(2)) will in fact operate as a dismissal without prejudice. However one characterizes the dismissal, we review it for an abuse of discretion. See Bridgeport Music, Inc. v. Universal-MCA Music Pub'g, Inc., 583 F.3d 948, 953 (6th Cir.2009).

We begin (and end) with the premise of Sunrise's argument, i.e., whether the dismissal was with prejudice or without. A dismissal with prejudice "operates as a final adjudication on the merits and has a res judicata effect." Warfield v. AlliedSignal TBS Holdings, Inc., 267 F.3d 538, 542 (6th Cir.2001). Sunrise contends that the dismissal here flunks this test for two reasons: first, different taxpayer-plaintiffs (i.e., persons other than Alicia Pedreira, et al.) could bring a new lawsuit against Kentucky and Sunrise asserting claims identical to the claims dismissed here; and second, even the named plaintiffs in this case could bring a new lawsuit against Kentucky and Sunrise asserting claims based on conduct occurring after the dismissal. But Sunrise overlooks that both of those things would be true of a dismissal with prejudice: an adjudication on the merits normally lacks res-judicata effect against persons not a party to the suit giving rise to it, see Amos v. PPG Indus., 699 F.3d 448, 451 (6th Cir.2012); and a dismissal with prejudice normally does not bar claims based on conduct that occurs after the dismissal is entered, see Cellar Door Prods., Inc. v. Kay, 897 F.2d 1375, 1378 (6th Cir.1990). Sunrise therefore gives us no reason to think the dismissal here was without prejudice — and we otherwise think the dismissal was with prejudice.

What Sunrise appears to want is not merely an order from the district court dismissing this case with prejudice, but a published opinion from this court holding the plaintiffs' claims invalid as a matter of law. That the district court did not posture this case for such an opinion was not an abuse of discretion.

D.

Sunrise's remaining argument rests on two premises: first, that the district court's incorporation of the settlement agreement into its dismissal order converted the order into a consent decree; and second, that the district court did not properly determine that the order-qua-consent decree was fair.

1.

We first consider whether the order is a consent decree. We review de novo the district court's interpretation of its order. Northeast Ohio Coal. for the Homeless v. Sec'y of State of Ohio, 695 F.3d 563, 569 (6th Cir.2012). "A consent decree is essentially a settlement agreement subject to continued judicial policing." Williams v. Vukovich, 720 F.2d 909, 920 (6th Cir.1983). Consent decrees typically have two key attributes that make them different from private settlements. First, when a court enters a consent decree, it retains jurisdiction to enforce the decree. Id. In contrast, the parties to a private settlement typically must bring another suit (for breach of contract) to enforce it. See Kokkonen v. Guardian Life Ins. Co. of Am., 511 U.S. 375, 381-82, 114 S.Ct. 1673, 128 L.Ed.2d 391 (1994). Second, a consent decree puts "the power and prestige of the court behind the compromise struck by the parties." Williams, 720 F.2d at 920. The same is not true of a dismissal order that does not incorporate the parties' terms.

Both of these key attributes are present here: the court expressly retained jurisdiction to enforce compliance with the settlement's terms; and by incorporating the settlement into the court's own dismissal order, the court gave its imprimatur to the settlement's terms.

These attributes notwithstanding, the plaintiffs say the dismissal order is not a consent decree for two reasons. The first is that that the settlement agreement purports to strip the court of its power to hold Kentucky in contempt for violations of the dismissal order (and thus for violations of the settlement's terms). One problem with that argument, however, is that we doubt that the parties or even the court itself can divest a federal district court of this power. Another is that the agreement expressly allows the plaintiffs to seek an injunction against the State requiring specific performance of the agreement's terms. And that in turn leads to a third problem: the plaintiffs themselves concede that the no-contempt provision would merely require them to file two motions rather than one to obtain the same relief. To wit, if the State violates the terms of the dismissal order (i.e. the settlement's terms), the plaintiffs could then move for specific enforcement of the violated terms. If the State then violates the specific-enforcement order, the plaintiffs could move for a second order holding the State in contempt for violating the specific-enforcement order. Suffice it to say that it takes more than this procedural two-step to circumvent this court's precedents regarding what counts as a consent decree and — more to the point — the requirements for entering one.

The plaintiff's remaining argument is of a piece. The plaintiffs say the settlement is not a consent decree because the agreement itself says that it is "Not [sic] Consent Decree[.]" But on this point we think the agreement protests too much. And in any event our precedents, and not the parties' recitations (even as incorporated by the district court), determine whether an order is a consent decree.

In sum, the district court's order has both of the key attributes of a consent decree. Moreover, a governmental entity (the State of Kentucky) is a party to the agreement incorporated into the court's order, and the agreement itself provides for monitoring and prospective injunctive relief. On these facts, we hold that the district court's dismissal order is a consent decree.

2.

Before entering a consent decree, a district court must determine, among other things, that the agreement is "fair, adequate, and reasonable, as well as consistent with the public interest." United States v. Lexington-Fayette Urban Cnty. Gov't., 591 F.3d 484, 489 (6th Cir. 2010) (internal quotation marks omitted). Moreover, the court must allow anyone affected by the decree to "present evidence and have its objections heard[.]" Tenn. Ass'n of Health Maint. Orgs. v. Grier, 262 F.3d 559, 566-67 (6th Cir.2001) (internal quotation marks and alterations omitted).

Here, the district court mistakenly characterized the settlement as a private agreement and thus held that Sunrise had no right to object to it. True, the court did go on briefly to address in dicta whether the agreement was fair to Sunrise. But the very reason we distinguish between dicta and holdings is that judges think about questions in a different way when real consequences turn on their answers. Of course, we could ourselves decide in this appeal whether the consent decree is fair, reasonable, and consistent with the public interest; and given that this case has already been here twice, there is some temptation to do so. But on balance we think it best to have the district court first address these questions in earnest. We will therefore remand this case for that purpose.

We do not, for purposes of the remand, express any opinion as to the matters discussed by the court in its dicta concerning the decree's fairness to Sunrise. The point of the remand is to allow the district court to consider that question anew. But we do flag one concern that the court did not consider. As a practical matter, the complaint's allegations of wrongdoing are directed largely at Sunrise. Sunrise, in turn, has steadfastly denied any wrongdoing on its part, and for more than a decade of litigation, including to this day, has a sought a merits adjudication to clear its name. Meanwhile, over Sunrise's objection, the consent decree singles out Sunrise by name for special monitoring by the ACLU and Americans United; and in doing so, Sunrise argues, the decree subjects Sunrise to unique reputational harm. Thus, the decree denies Sunrise a chance to clear its name — and instead, over Sunrise's objection, imposes the very reputational harm that Sunrise sought to avoid by means of 15 years of litigation. A decree that did not, directly or indirectly, single out Sunrise in this manner would stand on different ground than the decree as it comes to us here. As the decree now stands, however, the matters discussed above should be among those considered by the district court on remand.

* * *

The district court's June 30, 2014 order is vacated, and the case remanded for proceedings consistent with this opinion.

DISSENT

BLACK, District Judge, dissenting.

After fourteen years of contentious litigation, the district court judge helped effectuate settlement of this case. His actions should be entitled to our deference.

In many, many civil actions, the district court retains jurisdiction to enforce a private settlement agreement, typically at the parties' request. See Kokkonen v. Guardian Life Ins. Co. of America, 511 U.S. 375, 381, 114 S.Ct. 1673, 128 L.Ed.2d 391 (1994) (finding that a district court would have ancillary jurisdiction to enforce a settlement agreement where "the parties' obligation to comply with the terms of the settlement agreement had been made part of the order of dismissal — either by separate provision (such as a provision "retaining jurisdiction" over the settlement agreement) or by incorporating the terms of the settlement agreement in the order."). The simple retention of jurisdiction should not ipso facto transform a settlement agreement into a consent decree — if it did, virtually all private settlement agreements would be consent decrees, subject to review for fairness, reasonableness, and consistency with the public interest.1 Here, the settlement agreement provided for monitoring by the state and, with respect to Sunrise, by Plaintiffs' counsel — not by the state nor by the district court. This is not "continued judicial policing" indicative of a consent decree. See Williams v. Vukovich, 720 F.2d 909, 920 (6th Cir.1983).

In any event, the trial court judge did review the settlement agreement for fairness to Sunrise, and he found that the settlement agreement was fair. We review a district court's finding as to the fairness of a consent decree for an abuse of discretion. See United States v. Cty. of Muskegon, 298 F.3d 569, 581 (6th Cir. 2002). Seeing no abuse of discretion, I would affirm.

However, presuming instead that the case should be remanded for a more extensive fairness review, this court ought not to single out any issue for the district court to consider on remand, i.e., Sunrise's concern about reputational harm. The district court is clearly aware of this concern, having already noted that, in the settlement agreement, the state categorically denied that Sunrise's actions violated the religious rights or freedoms of children placed in its care. Upon remand, the district court should not yet be directed to accept Sunrise's position as to fairness.

For the reasons set forth above, I respectfully dissent.