EASTERBROOK, Circuit Judge.

Cable TV operators in Chicago have signed contracts promising to pay the City 5% of their gross revenues from any service, including what the parties call “cable modem service,” furnished over the franchised cable. (We put the phrase in quotations because no modem is involved. A modem converts between analog and digital signals, while the service at issue here is digital throughout. But we follow common usage in applying the phrase “cable modem” to a broadband Internet service provided over a cable that also carries television signals.) In 2002 the Federal

*903 Communications Commission concluded that cable-modem service is an information rather than a telecommunication product. See Inquiry Concerning High-Speed, Access to the Internet Over Cable and Other Facilities, 17 F.C.C.R. 4798 ¶¶7, 33-59 (Mar. 15, 2002). Chicago’s cable operators then stopped remitting payments based on cable-modem services. They rely on 47 U.S.C. § 542(b), which provides that “the franchise fees paid by a cable operator with respect to any cable system shall not exceed 5 percent of such cable operator’s gross revenues derived in such period from the operation of the cable system to provide cable services.” If cable-modem service is not a programming service, the reasoning goes, then receipts from the cable operators’ role as Internet service providers cannot be included among “gross revenues derived in such period from the operation of the cable system to provide cable services ” (emphasis added). If the fee on revenues from TV service already is at the statutory cap of 5% (as it is in Chicago), then cities that collect fees based on gross revenue from other services would receive income exceeding 5% of the allowable revenue base.

Chicago accepts the FCC’s understanding of the difference between data and telecom services (but see Brand X Internet Services v. FCC, 345 F.3d 1120 (9th Cir.2003), cert. pending, No. 04-281 (filed Aug. 27, 2004)) but disagrees with the operators’ reading of § 542(b). Although the parties acknowledge that “cable services” in § 542(b) means programming services, see 47 U.S.C. § 522(6), and thus excludes cable-modem service, see AT&T Corp. v. Portland, 216 F.3d 871 (9th Cir.2000), they differ on the consequences of this definition. Chicago contends that other products are outside the statute’s domain, so that governments may impose unlimited fees (under tax statutes, contracts, or both) on all revenue from other uses of the cable. As the cable operators understand the statute, however, once a city requires a franchise fee “with respect to any cable system,” the total payments with respect to that system can’t exceed 5% of its programming revenue, no matter how the city tries to apportion the required payments.

Unable to persuade the cable operators to resume payments, Chicago filed this suit seeking a declaratory judgment that the operators must comply in full with the contracts and ordinances. The suit was filed in the Circuit Court of Cook County. Invoking 28 U.S.C. §§ 1331 and 1441(b), defendants removed the proceeding to federal court. They asserted that the City’s action arises under federal law either because the demand for payment rests on 47 U.S.C. § 542(a) — which reads: “Subject to the limitation of subsection (b), any cable operator may be required under the terms of any franchise to pay a franchise fee” — or because the meaning and effect of § 542(b) will be the only issue contested in the litigation. The district court denied the City’s motion to remand, concluding that federal adjudication is appropriate because the City’s complaint “implicates ... provisions of the Communications Act” and the FCC’s order. Chicago v. AT & T Broadband, Inc., 2003 WL 1888839, (N.D.Ill. Apr. 14, 2003), 2003 U.S. Dist. LEXIS 6268 at *9. A few months later the district judge held that § 542(b) preempts any state and city statutes and excuses the cable operators from making the payments called for in the franchise contracts on account of cable-modem service. Chicago v. AT & T Broadband, Inc., 2003 WL 22057905, (N.D.Ill. Sept. 4, 2003), 2003 U.S. Dist. LEXIS 15453. We need not consider that aspect of the disposition, because the suit does not arise under federal law and therefore belongs in state court.

*904 Under the venerable well-pleaded-complaint doctrine, “whether a case is one arising under the Constitution or a law or treaty of the United States ... must be determined from what necessarily appears in the plaintiffs statement of his own claim in the bill or declaration, unaided by anything alleged in anticipation or avoidance of defenses which it is thought the defendant may interpose.” Taylor v. Anderson, 234 U.S. 74, 75-76, 34 S.Ct. 724, 58 L.Ed. 1218 (1914). See also, e.g., Holmes Group, Inc. v. Vomado Air Circulation Systems, Inc., 535 U.S. 826, 830-32, 122 S.Ct. 1889, 153 L.Ed.2d 13 (2002); Franchise Tax Board v. Construction Laborers Vacation Trust, 463 U.S. 1, 9-12, 103 S.Ct. 2841, 77 L.Ed.2d 420 (1983); Blackburn v. Sundstrand Corp., 115 F.3d 493 (7th Cir.1997); Rice v. Panchal, 65 F.3d 637 (7th Cir.1995). So the federal defense in § 542(b) does not supply jurisdiction if the claim itself rests on state or local law — which it does. Both an ordinance enacted under Chicago’s home-rule power and a series of contracts supply the basis of Chicago’s complaint. The American Law Institute once favored federal-defense removal, see Study of the Division of Jurisdiction Between State and Federal Courts § 1312(a)(2) (1969), but in the face of strong criticism, e.g., Henry J. Friendly, Federal Jurisdiction: A General View 124 (1973), abandoned that position, see Federal Judicial Code Revision Project § 1441 (T.D. 3 1999). Congress never embraced it; both § 1331 and § 1441 have not been materially changed since the Supreme Court first articulated the well-pleaded-complaint doctrine.

That the federal defense will be the only contested issue does not matter. Two decisions illustrate this point. A railroad that had settled a tort claim in exchange for a lifetime pass later refused to honor that pass, contending that a federal statute enacted in the interim forbade the provision of free transportation. The pass holder sued in federal court, contending that the only issue requiring resolution was the interpretation of this statute — for, on the plaintiffs view, the pass was not “free” but had the same value as the tort claim that had been surrendered. That view of what issues controlled the case proved to be correct; the railroad did not contest the pass’s validity as a matter of contract. The Supreme Court never reached the merits, however, holding that a contract claim does not arise under federal law even when the only contested issue is the effect on that obligation of a federal statute. Louisville & Nashville R.R. v. Mottley, 211 U.S. 149, 29 S.Ct. 42, 53 L.Ed. 126 (1908). The Court adhered to that position in Gully v. First National Bank, 299 U.S. 109, 57 S.Ct. 96, 81 L.Ed. 70 (1936), in which a state tax collector sued in state court on a contract by which one bank promised to pay the tax obligations of another as part of an acquisition. The bank removed to federal court, contending that the promise amounted to a tax on shares of the bank, which under federal law states are forbidden to levy. Once again the only contested issue in the litigation was the effect of this federal statute; once again the Court held that the claim arose under the contract (or perhaps under the state tax law), and that a potential federal defense did not convert the suit to one arising under federal law. Just so here: it is scarcely possible to see any gap between these proceedings and either Mottley or Gully.

The contracts between Chicago and the cable operators recognize that the payments are subject to any limits imposed by federal law. This does not mean, however, that the claim is itself based on federal law; stating the obvious (given the Supremacy Clause, what other option do the parties have?) does not affect the source of law under which a claim arises. That’s the point of the language in Taylor from which we quoted above. Mentioning a federal *905 issue in a contract, or for that matter a complaint, does not determine the source of the claim itself. Think of the Federal Arbitration Act, 9 U.S.C. §§ 1-16, which authorizes parties to prescribe arbitration as a means to resolve disputes growing out of interstate transactions, precludes any state interference with these agreements except to the extent the general law of contract would regulate any other agreement, and provides in § 9 and § 10 detailed criteria for confirming or vacating awards. Many arbitration agreements refer to this federal statute, and whether they refer to it or not any dispute about arbitrability or the validity of an award must be resolved under the Arbitration Act’s terms. Yet even this is not enough to create federal jurisdiction, because the claim that the plaintiff seeks to vindicate still arises under the contract, and thus under state law. See Southland Corp. v. Keating, 465 U.S. 1, 15 n. 9, 104 S.Ct. 852, 79 L.Ed.2d 1 (1984); Moses H. Cone Memorial Hospital v. Mercury Construction Corp., 460 U.S. 1, 25 n. 32, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983); Minor v. Prudential Securities, Inc., 94 F.3d 1103 (7th Cir.1996). Like the Federal Arbitration Act, the Federal Communications Act regulates transactions without creating the claim sought to be vindicated. Chicago’s financial demand rests on state law (including the state law of contract); § 542(b) sets a cap on payments without creating a federal floor under them (cities could agree to accept less than 5%); and if one reads § 542(a) as creating federal support for a fee on telecom services, as the Arbitration Act creates federal support for arbitration, the plaintiff as master of its complaint may foreswear reliance on that entitlement and rest on state law, as Chicago has done.

Defendants say that this is not so, because (in their view) federal law so completely dominates this field that it is impossible to frame any claim under state law. This appeal to the misleadingly named complete-preemption doctrine is unavailing. (The name is misleading because the doctrine is unrelated to preemption but deals with occupation of the field, as with labor relations and some aspects of pension law. See Metropolitan Life Insurance Co. v. Taylor, 481 U.S. 58, 107 S.Ct. 1542, 95 L.Ed.2d 55 (1987); Avco Corp. v. Machinists Union, 390 U.S. 557, 88 S.Ct. 1235, 20 L.Ed.2d 126 (1968); Bartholet v. Reishauer A.G. (Zurich), 953 F.2d 1073 (7th Cir.1992).) Section 542(a) does not suggest that only federal law could support a claim. Unlike, say, the National Bank Act, which knocks out all state regulation of national banks’ interest charges, so that any claim must rest on federal law alone, see Beneficial National Bank v. Anderson, 539 U.S. 1, 123 S.Ct. 2058, 156 L.Ed.2d 1 (2003), the Federal Communications Act leaves to state law most questions about the regulation and taxation of cable TV franchises. Section 542(a) does not purport to override state law, let alone to deny states all power in the field. So if, for example, Illinois law capped fees at 3%, Chicago could not rely on § 542(a) to charge 5%. Cf. Nixon v. Missouri Municipal League, 541 U.S. 125, 124 S.Ct. 1555, 158 L.Ed.2d 291 (2004) (holding that another provision of federal telecommunications law does not permit a municipality to disregard state controls on its conduct). All § 542(b) does is limit authority that has some other source. If § 542(b) makes the City’s claim a federal one, then any statute preempting state law would allow removal, and decisions such as Mottley, Gully, and Franchise Tax Board would be overthrown.

The judgment is vacated, and the district court is instructed to remand this litigation to state court.