MEMORANDUM OPINION
BRIAN BARNETT DUFF, District Judge.Plaintiffs S.I. Jacobson Manufacturing Co. and Arthur and Harold Jacobson move under 28 U.S.C. § 1447(c) (1982) to remand this case to the Circuit Court of Cook County, Illinois, claiming that the defendants, Johnathan Bittner and Plastic Film Corporation of America (“PFCA”), improvidently removed this case to this court. The plaintiffs argue further that they are entitled to just costs under § 1447(c) because it is so clear that this case should not have been removed. While this court agrees with the plaintiffs that it does not have subject-matter jurisdiction over this case, the issues raised in the plaintiffs’ motion are complex ones, and for that reason costs will not be awarded.
The following facts are taken from the plaintiffs’ complaint for reasons that will become clear shortly. The Jacobsons are in the business of developing, manufacturing, and selling vinyl and vinyl-laminated products. They allege that they met Bittner about twenty years ago and that they established a business relationship with Bittner’s company, PFCA, in 1978. This relationship continued until things soured between the parties in May 1988.
The dispute that ended the relationship centers on an invention of a process for embossing vinyl. Vinyl manufacturers emboss vinyl sheets in order to enhance the appearance or texture of the vinyl. Prior *508to the invention in dispute here, a company could easily emboss one side of a vinyl sheet, but in order to emboss the other side, a company had to add a costly second step to the process. This second step made the price of double embossed sheets too prohibitive for most customers.
The Jacobsons allege that in late 1984 or early 1985, they began to conceive of a single-step process for obtaining double embossed sheets. They allege that they shared their ideas with Bittner in a series of meetings in early 1985. At one of these meetings, Bittner is said to have agreed to take these ideas to a Taiwanese vinyl manufacturer to have that company test them. Bittner returned from Taiwan with news that these tests were unsuccessful. The parties consulted further, improved their concept, and sent Bittner back to Taiwan for more tests.
The improved process worked. In order to verify the tests and to underwrite the costs in perfecting the invention, S.I. Jacobson submitted a series of test orders of the product commencing in April 1985 and extending through 1986. Sometime after the first test order, the Jacobsons claim that they discussed the patenting and commercial exploitation of the invention with Bittner. The Jacobsons allege that Bittner agreed to seek a patent on behalf of himself and the Jacobsons, and that by late 1985 he had begun applying for the patent. In a meeting in early December 1985, Bittner accepted checks from the Jacobsons as payment of their share of the filing fees for the application, checks that Bittner apparently never cashed.
Soon after the December meeting, the parties took the first steps to reap benefits from the invention. The plaintiffs allege that they agreed with Bittner to purchase double embossed vinyl through Bittner at cost. They also agreed to let Bittner market double embossed vinyl to other manufacturers at prices substantially in excess of those paid by the Jacobsons while the patent was pending.
At that point the plaintiffs thought that things were progressing smoothly. Sometime in January 1986, Bittner sent the Jacobsons a copy of the patent application, which described the invention but did not include the application’s title page — a page that usually names the inventors. S.I. Jacobson purchased large quantities of double embossed sheets throughout 1986 and 1987, and the Jacobsons were eager for further exploitation of their new process. The parties met in the fall of 1987 to discuss the progress of the patent application. The plaintiffs allege that Bittner advised them that the U.S. Patent and Trademark Office (“PTO”) had approved the application and that the patent would issue shortly thereafter. He represented throughout this meeting that the application listed the Jacobsons as co-inventors and joint owners of the patent, and thus the Jacobsons continued to rely on Bittner to pursue the application as well as market double embossed sheets.
Having heard that the patent would be forthcoming, Harold Jacobson suggested to Bittner that they prepare a written agreement setting up a joint venture. Bittner agreed to review such an agreement, and in late 1987 or early 1988 Jacobson delivered a draft. Bittner did not return any comments. The Jacobsons continued to be interested in the venture, however, and in March 1988 they asked Bittner about the progress of the patent. Bittner assured them that the patent would issue in June of 1988. When June 1 arrived, the Jacobsons demanded that Bittner comment on the joint venture agreement and advise them of his efforts to exploit the invention. Bittner’s attorney advised the Jacobsons that they had no rights to the invention and that Bittner was negotiating to sell or merge PFCA, in part to realize the benefits of the invention. Later the plaintiffs learned that the PTO had issued a patent for the double embossing invention on May 17, 1988. The file history of the patent apparently lists Bittner as the inventor and PFCA as the record owner.
The plaintiffs filed suit in the Circuit Court of Cook County on June 15, 1988. The defendants removed the case to this court on July 7, 1988, claiming that the plaintiffs could have filed it pursuant to *509this court’s jurisdiction under 28 U.S.C. § 1338(a). In their present motion the plaintiffs claim that they could not have filed under § 1338(a), and so, they claim, this case must be sent back to the Cook County Circuit Court.
Section 1338(a) provides, in part, that “[t]he district courts shall have original jurisdiction of any civil action arising under any Act of Congress relating to patents ____” As the Supreme Court noted so recently in Christianson v. Colt Industries Operating Corp., — U.S. -, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988), this language is remarkably similar to that used in the general jurisdictional provision for federal question cases, 28 U.S.C. § 1331. The language is so similar that, as Christianson emphasized, the jurisprudence that the Court has developed under § 1331 is fully applicable to § 1338. Thus, a case arises under the federal patent laws, and falls within the jurisdiction of this court under § 1338, only when
a well-pleaded complaint establishes either that federal patent law creates the cause of action or that the plaintiff’s right to relief necessarily depends on resolution of a substantial question of federal patent law, in that patent law is a necessary element of one of the well-pleaded claims.
Christianson, 108 S.Ct. at 2173.
This court thus must resolve the question of jurisdiction raised by the parties by looking at the plaintiffs’ complaint. That complaint contains six counts. Three of them, Counts 2-4, plainly do not arise under the federal patent laws. In Counts 2 and 3, the plaintiffs argue that the defendants breached a contract to share the rights to and arising from the double embossing invention. Neither count states a cause of action under the federal patent laws, and neither necessarily depends on the resolution of a substantial question of federal patent law. The issues in these counts are whether there was a contract, what it contained, and whether the defendants breached it.
If the contract required Bittner to apply for a patent on behalf of himself and the Jacobsons, a court need not immerse itself in federal patent law to decide whether Bittner performed: either he applied for the patent j.ointly, or he did not. See Becher v. Contoure Laboratories, 279 U.S. 388, 49 S.Ct. 356, 73 L.Ed. 752 (1929). Similarly, in Count 4 the plaintiffs argue that Bittner breached a fiduciary duty to the plaintiffs to patent the invention jointly and to share in the proceeds of licensing it. This count too does not state a federal cause of action, and the issues of whether Bittner owed the plaintiffs a duty, what that duty was, and whether Bittner breached it do not involved substantial questions of federal patent law.
Counts 1 and 6 pose trickier issues of jurisdiction. In Count 1, the plaintiffs allege that Bittner and PPCA intentionally and fraudulently misrepresented to the plaintiffs that Bittner was going to file the patent application on behalf of all of the parties, including listing the Jacobsons as co-inventors and joint owners. As a result of relying on these representations, the plaintiffs claim that they have “foregone the opportunity to prosecute a patent application for the double embossing invention, and have refrained from taking other actions with regard to the ... invention.” Complaint at 17-18. They also claim that they “have lost or may lose their right to share in the patent for the ... invention and any royalties or other income which may ensue from [its] exploitation----” Id. at 18.
The problem here is that the plaintiffs pose two theories of damage for one claim of right. On the one hand, the plaintiffs assert that, had they known what Bittner was up to, they could have filed for the patent. They essentially argue that they are co-inventors of the double embossing process, and they suggest that, as one way of remedying the alleged fraud, this court order the defendants to amend the patent application “to include the names of Arthur F. Jacobson and Harold D. Jacobson as co-inventors or assignees.” Id. at 26. This court may have the power to do that, but only under the federal patent laws. See 35 *510U.S.C. § 256 (1982); Donald S. Chisum, 1 Patents § 2.04[7] (1988).
If the plaintiffs contended under Count 1 that there had been fraud only in the patenting of the invention, it could be said that the claim (and thus this case) arises under the federal patent laws. This is because this court would have to decide who invented the embossing process in order to decide if the defendants’ representations damaged the plaintiffs, and whether the plaintiffs are entitled to an amended patent application. But the plaintiffs pose a second theory under the first count, one that puts a different twist on the fraud claim: they assert that as a result of the defendants’ fraud, they may lose their right to share in the proceeds from the invention. This merely rephrases the contract claims examined above.1
In their brief on this motion the plaintiffs trumpet the second theory and downplay the first. The plaintiffs could change their minds, of course, but that does not concern this court at present. See Kennedy v. Wright, 851 F.2d 963, 965 (7th Cir.1988) (jurisdiction is fixed by what the complaint contains, not by how the dispute is ultimately resolved). Where a claim is supported by alternative theories in the complaint, § 1338 jurisdiction is not present unless federal patent law is essential to each theory. Christianson, 108 S.Ct. at 2174. Because the plaintiffs state theories under Counts 1 and 6 that do not raise essential issues of patent law, those counts do not state claims that arise under the patent laws.2 As a result, this court does not have subject-matter jurisdiction under § 1338(a), and so this case must be remanded to the Circuit Court of Cook County.
There remains the matter of costs. Under § 1447(c), a court may order the payment of just costs upon remanding a case that was improvidently removed from state court. Had the complaint in this case consisted only of Counts 2-4, or had the plaintiffs carefully alleged in Counts 1 and 6 that the purported fraud and conversion affected rights stemming solely from the contractual arrangements of the parties, such an order would be appropriate. Such was not the case here — in fact, it is only in the plaintiffs’ motion to remand that the gravamen of Counts 1 and 6 becomes clear. As this court’s analysis of those two counts shows, the plaintiffs’ original grievances were not straightforward. The defendants should not have to pay for the plaintiffs’ original choice to state their case in broad terms.
The plaintiffs’ motion to remand this case to the Circuit Court of Cook County, Illinois, is granted, without costs.
. Similarly, in Count 6 the plaintiffs allege conversion of their rights and interests in the double embossing process. If these rights arose purely because the plaintiffs invented the process, the plaintiffs might be stating a claim under the patent laws. But if these rights arose because of an agreement among the parties, then Count 6 stems from contract law. Patent issues thus would not be a necessary element of the plaintiffs' case.
. Count 5 is one for unjust enrichment. It incorporates the theories presented in Counts 1-4, and since this court believes that none of these claims arises under the federal patent laws, this claim does not either.