These interlocutory appeals follow the district court’s denial of preliminary injunctive relief. We have jurisdiction under 28 U.S.C. § 1292(a)(1).

The facts are straightforward (although the legal implications are complex). The plaintiff, Stephen P. Laffey, is the mayor of Cranston, Rhode Island. A local radio station, corporately owned, offered Mayor Laffey the opportunity to host a weekly talk show. The mayor declined any remuneration but accepted the free air time and began a string of weekly appearances.

The president of the Cranston City Council — a political rival of the mayor— filed a complaint with the Rhode Island State Board of Elections (the Board). The complaint alleged that Mayor Laffey, who has not yet announced his plans for the 2006 elections, 1 was receiving an in-kind corporate contribution from the radio sta *363 tion in violation of the Rhode Island Campaign Contributions and Expenditures Reporting Act, R.I. Gen. Laws § 17-25-10.1. The Board held a hearing, found the complaint meritorious, and ordered the mayor to cease and desist from hosting the talk show.

The mayor complied, but brought suit against the members of the Board (in their official capacities) in the federal district court. He claimed, inter alia, that the Board’s order abridged rights secured to him by the First Amendment. The district court, ruling from the bench on May 17, 2005, refused to enjoin the operation of the Board’s order. These appeals followed. 2 We consolidated them and granted expedited review.

The briefing revealed that the Board’s decision, and to some extent the embedded constitutional issues, rested on uncertain questions of state law — a matter to which we shall return. At oral argument on June 9, 2005, we suggested that the parties might wish to cooperate in obtaining answers to these state law questions from the Rhode Island Supreme Court and that, in the interim, the Board might wish to suspend the operation of its cease and desist order. Mayor Laffey’s counsel readily agreed to this proposal and the Board’s counsel quite reasonably asked for time to allow the Board to consider it. We are now advised that the Board met on June 13, 2005, and accepted the proposal. It has stayed the operation of the cease and desist order pending resolution of the pertinent state law questions. We applaud the commitment to fair play and the orderly administration of justice that this decision evinces.

The parties’ agreement renders these appeals moot, but does not dissipate the underlying controversy. See 13A Charles Alan Wright, et al., Federal Practice and Procedure § 3533.2 (2d ed. 1984) (“A partial settlement moots the issues involved in the settlement, but not those that the parties did not intend to settle.”) (collecting cases).

The principal issue in this case — whether the state campaign finance law, as applied to these facts, violates the First Amendment — remains unresolved. That issue, in turn, depends to some degree on significant and unsettled state law questions related to the extent of the Board’s enforcement authority and the scope and meaning of Rhode Island’s campaign finance statute (including, but not limited to, the meaning of terms such as “candidate” and “in-kind contribution”). The parties have agreed, and we concur, that these questions should be answered as expeditiously as possible by the state supreme court. See Noviello v. City of Boston, 398 F.3d 76, 91 (1st Cir. 2005) (explaining that “the highest court of a state is ... the final arbiter of state-law questions”). Only then can a federal court rule intelligently on the constitutional claims. 3

To implement the parties’ agreement, we remand this case to the district court. We note that several abstention doctrines appear to have potential relevance to the proceedings. See, e.g., Colo. River Water Conserv. Dist. v. United States, 424 U.S. 800, 96 S.Ct. 1236, 47 L.Ed.2d 483 (1976); R.R. Comm’n v. Pullman Co., 312 U.S. 496, 61 S.Ct. 643, 85 L.Ed. 971 (1941); see also Maymó-Meléndez v. Alvarez-Ramírez, 364 F.3d 27 (1st Cir. 2004) (applying abstention principles of Younger v. Harris, 401 U.S. 37, 91 S.Ct. 746, 27 L.Ed.2d 669 (1971), to coercive administrative proceed *364 ings). If the district court determines that one or more of these doctrines apply, it may abstain from an immediate exercise of jurisdiction, stay the federal proceeding, and allow the parties to resolve the pertinent state law questions in the state court system.

Of course, the district court’s abstention decision may be influenced by the availability vel non of state court review. See Pullman, 312 U.S. at 501, 61 S.Ct. 643 (suggesting that abstention is not appropriate upon a “showing that ... obvious methods for securing a definitive ruling in the state courts cannot be pursued”). The Board has suggested that state court review can be achieved should the mayor file a petition for writ of certiorari to the Rhode Island Supreme Court, asking that tribunal to pass upon the validity of the Board’s cease and desist order. See Van Daam v. DiPrete, 560 A.2d 953, 954 (R.I. 1989) (per curiam). The state law questions embedded in this case are, in the Van Daam court’s phrase, “substantial,” id,., and such review may well be available. In the spirit of the parties’ agreement, the district court may direct the mayor to file such a petition.

If such review is not available and other conventional routes to the state supreme court appear for any reason to be precluded, the district court may certify the appropriate state law questions to the Rhode Island Supreme Court. See R.I. Sup.Ct. R.App. P. 6. Upon its receipt of the state supreme court’s response, the district court may proceed to adjudicate the constitutional issues unless the state supreme court’s resolution of the state law questions or a change in circumstances renders such an adjudication unnecessary.

Let us be perfectly clear. These are merely suggestions. We have complete confidence in the district court and, in the final analysis, it is for the district court to determine how best to proceed. Nothing contained in this opinion is intended to cabin the district court’s discretion.

We need go no further. The parties’ agreement disposes of any live controversy related to these appeals. Consequently, we dismiss the appeals as moot and remand the case for further proceedings consistent with this opinion and with the parties’ agreement (which we deem binding upon them). Each side shall bear its own costs.

It is so ordered.