
592 F.3d 816 (2010)
Sandra BERGQUIST, Plaintiff-Respondent,
v.
MANN BRACKEN, LLP, and FIA Card Services, N.A., Defendants-Petitioners.
Nos. 09-8046, 09-8047.
United States Court of Appeals, Seventh Circuit.
Submitted December 22, 2009.
Decided January 26, 2010.
*817 Cathleen M. Combs (submitted), Edelman, Combs & Latturner, Chicago, IL, for Plaintiff-Respondent.
James Christopher Martin (submitted), Reed Smith LLP, Pittsburgh, PA, for FIA Card Services, N.A.
Martin J. O'Hara (submitted), Much, Shelist, Freed, Denenberg, Ament & Rubenstein, Chicago, IL, for Mann Bracken LLP.
Before EASTERBROOK, Chief Judge, and BAUER and ROVNER, Circuit Judges.
EASTERBROOK, Chief Judge.
Sandra Bergquist borrowed money on a credit card issued by FIA Card Services (formerly known as MBNA American Bank). The bank hired Mann Bracken, a law firm, to collect the debt. Mann Bracken invoked the arbitration clause of the credit-card contract. The National Arbitration Forum rendered an award against Bergquist, and a state court in Illinois entered a judgment enforcing that award.
Bergquist believes that the National Arbitration Forum and Mann Bracken secretly are under common control, which if true could vitiate the award (that would depend on how the arbitrators were chosen and compensated). She asked the state judge to set aside the judgment enforcing the award; without saying why, the judge did so, and the case was dismissed without prejudice. Bergquist also filed an independent suit seeking relief on behalf of a class of all persons whose disputes have been arbitrated by the National Arbitration Forum when Mann Bracken represented the creditor. Before the state court could act, defendants removed it to federal court under the Class Action Fairness Act of 2005, 28 U.S.C. §§ 1332(d), 1453. The proposed class includes more than 100 persons, the defendants include citizens of states other than Illinois (FIA is a national bank with its head-quarters in Delaware, and Mann Bracken has partners in many states), and the notice of removal asserts that the stakes exceed $5 million.
The district court did not find fault with any of these jurisdictional allegations. But it remanded the case nonetheless, concluding that the Rooker-Feldman doctrine prevents federal adjudication of any claim that seeks to invalidate judgments entered *818 by state courts. Mann Bracken and FIA Card Services filed petitions for appellate review under § 1453(c). We grant those petitions and, because the papers already on file cover the essential arguments, we resolve the appeals summarily. The absence of class certification is no obstacle to jurisdiction in either the district court or this court. See Cunningham Charter Corp. v. Learjet Inc., No. 09-8042, ___ F.3d ___, 2010 WL 199627 (7th Cir. Jan. 22, 2010).
The Rooker-Feldman doctrine takes its name from Rooker v. Fidelity Trust Co., 263 U.S. 413, 44 S.Ct. 149, 68 L.Ed. 362 (1923), and District of Columbia Court of Appeals v. Feldman, 460 U.S. 462, 103 S.Ct. 1303, 75 L.Ed.2d 206 (1983). Those decisions hold that only the Supreme Court of the United States may set aside a state court's decision in civil litigation. The lack of any civil analog to 28 U.S.C. § 2241 or § 2254 means that federal district judges may not entertain collateral attacks on state judges' decisions. If a state court fails to rectify an injury that predates the state litigation, then a federal suit about those extrajudicial events is possible  though it may be blocked by doctrines of issue or claim preclusion. See 28 U.S.C. § 1738. But if the state court's decision causes the federal plaintiff's injury, then review is limited to the state's own appellate judiciary, with the possibility of review by the Supreme Court once the state has made its final decision. 28 U.S.C. § 1257(a). See Exxon Mobil Corp. v. Saudi Basic Industries Corp., 544 U.S. 280, 125 S.Ct. 1517, 161 L.Ed.2d 454 (2005); GASH Associates v. Rosemont, 995 F.2d 726 (7th Cir.1993).
The petitions for leave to appeal question whether the Rooker-Feldman doctrine applies to proceedings under the Class Action Fairness Act. It does. The Act expands federal jurisdiction to cover large-stakes class actions with minimal diversity of citizenship. It amends § 1332, which creates jurisdiction in diversity cases, without changing the nature of that jurisdiction to permit collateral review of state-court decisions. Nothing in the 2005 Act so much as hints at allowing federal district judges to review state-court decisions  other than the interlocutory steps taken in the same case before its removal, a power that the federal court enjoys no matter the source of authority for removal. The Rooker-Feldman doctrine was originally stated as a limitation on federal-question jurisdiction under 28 U.S.C. §§ 1331 and 1343; today no one doubts that it is equally applicable to diversity litigation. See Exxon Mobil, 544 U.S. at 291, 125 S.Ct. 1517; Downs v. Westphal, 78 F.3d 1252, 1256 (7th Cir.1996). It therefore applies as well to suits in which federal jurisdiction rests on the 2005 Act's extension of diversity jurisdiction.
The problem with the district court's decision is not that it applies the Rooker-Feldman doctrine to a suit removed under § 1453, but that the doctrine does not apply to Bergquist's claim. She is no longer a state-court loser; the state judiciary itself vacated its decision enforcing the arbitration award. The state court's order dismissing the action without prejudice restores the parties to the position they occupied before FIA Card Services filed suit. Any injury comes from the award itself, and the Rooker-Feldman doctrine does not apply to arbitral awards. Federal as well as state courts are empowered to review and enforce, or set aside, decisions rendered by private arbitrators. See 9 U.S.C. §§ 1-16. And when injuries created by the process of arbitration are redressable in damages, federal courts are competent to act  provided that the diversity and amount-in-controversy requirements are met. See Vaden v. Discover Bank, ___ U.S. ___, 129 S.Ct. 1262, 173 *819 L.Ed.2d 206 (2009) (discussing how the jurisdictional rules work for disputes that entail arbitration).
The district court recognized that the Rooker-Feldman doctrine does not apply to Bergquist's claim. It remanded the suit nonetheless because Bergquist seeks relief on behalf of persons who lost in state court when judges confirmed arbitral awards adverse to their interests. Bergquist wants those decisions vacated, which would indeed be incompatible with the Rooker-Feldman doctrine. The district judge thought that only a state court could resolve the whole dispute, so it remanded the whole case.
Federal law does not permit a district judge to remand the complete litigation just because portions belong in state court. Judges must exercise the jurisdiction they have been given and may not adopt common-law rules that prefer state over federal adjudication of claims that are within the jurisdiction defined by Congress. See Thermtron Products, Inc. v. Hermansdorfer, 423 U.S. 336, 96 S.Ct. 584, 46 L.Ed.2d 542 (1976). If some parts of a single suit are within federal jurisdiction, while others are not, then the federal court must resolve the elements within federal jurisdiction and remand the rest  unless the balance can be handled under the supplemental jurisdiction. See 28 U.S.C. §§ 1367(c)(3), 1441(c). See also Carlsbad Technology, Inc. v. HIF Bio, Inc., ___ U.S. ___, 129 S.Ct. 1862, 173 L.Ed.2d 843 (2009); Carnegie-Mellon University v. Cohill, 484 U.S. 343, 108 S.Ct. 614, 98 L.Ed.2d 720 (1988). Because of the Rooker-Feldman doctrine, the balance of this suit cannot be resolved in federal court, but the need to remand some of it does not entail a power to remand all.
The district judge may have been thinking along the lines of Colorado River abstention. See Colorado River Water Conservation District v. United States, 424 U.S. 800, 96 S.Ct. 1236, 47 L.Ed.2d 483 (1976). The Court held in Colorado River that, when a state is conducting an in rem procedure that the federal tribunal cannot replicate, a district judge should abstain so that all parties and claims will be before the state court. The issue in Colorado River was water rights in an appropriation state. Colorado has a procedure for adjudicating competing claims to the same flows, and, because allocation is a zero-sum game (a court cannot increase the amount of water in a drainage system), only a single forum can avoid the risk of inconsistent decisions about rights in the water. Colorado River abstention is not a good fit for Bergquist's complaint, not only because credit-card-debt arbitration is not an all-or-none proceeding for all borrowers, but also because Illinois does not guarantee that similar claims throughout the state will be assigned to a single judge. The potential for inconsistency in allowing a federal judge to consider one group of borrowers' arguments, while a different group litigates in state court, is no worse than the potential for inconsistency if one group of borrowers sues in Rockford and another in Springfield.
Actually it is not clear that the district judge needs to remand any claims in this suit. True, the federal court lacks jurisdiction to vacate a state court's judgments. But there would be no occasion for such a remedy if the class were suitably defined. There are at least three potential subclasses of persons whose debts were determined by the National Arbitration Forum when Mann Bracken represented the creditor: (1) persons who lost in state court (award confirmed), (2) persons who won in state court (award set aside), and (3) persons who have neither won nor lost (because, for example, the creditor never asked a court to confirm the award, or a suit ended without a conclusive resolution). *820 Bergquist is in the third subclass, while only the first presents a Rooker-Feldman problem. Federal courts do not certify "across-the-board" classes; the named plaintiff's claim must be typical of the claims held by persons being represented. Fed.R.Civ.P. 23(a)(3); General Telephone Co. of the Southwest v. Falcon, 457 U.S. 147, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982). Bergquist does not have a claim typical of state-court losers (subclass 1), so a class definition not only can but also should be limited in a way that avoids any Rooker-Feldman problem, and thus avoids a need for even a partial remand.
The district court needs to determine whether more than 100 persons would be in a properly defined class with Bergquist as the representative, and whether the amount in controversy exceeds $5 million. Valuation may be difficult, because the persons in subclasses 2 and 3 have not (yet) lost anything. Even if a court were to deem awards by the National Arbitration Forum tainted by a conflict of interest, this would not affect the amount that the borrowers owe; it would just complicate the banks' tasks of reducing their claims to judgment. The district court has yet to consider Bergquist's argument that the stakes of this dispute are less than $5 million. The judgment is vacated, and the case is remanded so that the district court can determine whether the jurisdictional requirements of the 2005 Act have been met and, if they have been, for the certification of an appropriate class and decision on the merits.
