Charles W. Howard, Jr. sued Vulcan Materials Company; the district court granted Vulcan’s motion for summary judgment on the grounds that Howard’s exclusive remedy was workman’s compensation. This court affirmed but remanded for a determination of who should pay the cost of Vulcan’s defense.1 AAA Contracting Company had an indemnity agreement with Vulcan but contended that its insurer, Travelers Insurance Company, was ultimately liable for the costs of Vulcan’s defense. The district court agreed and ordered Travelers to pay $7,728.65 in court costs and attorneys’ fees. We reverse.
Travelers’ policy with AAA covered only “designated contracts,” and the indemnity agreement between AAA and Vulcan was not on the list of designated contracts. All parties agree that the indemnity agreement was not covered under the policy schedule. *303But AAA contends that under Louisiana law an insurer has a duty to defend that is broader than its liability. American Home Assurance Co. v. Czarniecki, 255 La. 251, 230 So.2d 253 (1969); Benoit v. Fuselier, 195 So.2d 679 (La.App.1967). This is true, but not in the sense asserted.
Czarniecki requires an insurer to defend “unless the petition unambiguously excludes coverage.” 230 So.2d at 259. The district court interpreted this language to mean that unless a policy has an exclusionary clause an insurance company must defend claims alleged to be covered under that policy. Because Travelers’ policy had no clause excluding AAA’s indemnity agreement with Vulcan, the district court found that Travelers had a duty to defend Vulcan. But Czarniecki requires an insurance company to defend against groundless claims, not to defend against uncovered claims. If there is a factual dispute in the nature of the claim, the allegations must be taken as true. When the allegations, if true, would make the insurer liable under the policy, there is a duty to defend. But when the allegations, even if true, do not create liability there is no duty to defend.2 Travelers need not insert an exclusionary clause in a designated contracts policy to avoid defending a claim under a contract not covered under the terms of the policy.3 Because Travelers had no duty to defend Vulcan under its contract with AAA, the award of attorneys’ fees and costs is
REVERSED.
. Howard v. Vulcan Materials Co., 494 F.2d 1183 (5th Cir. 1974).
. Thus, if, assuming all the allegations of the petition to be true, there would be both (1) coverage under the, policy and (2) liability to the plaintiff, the insurer must defend the insured regardless of the outcome of the suit.
American Home Assurance Co. v. Czarniecki, 255 La. 251, 230 So.2d 253, 259 (1969).
. An exclusionary clause was found to preclude defense by the insurer in Mut v. Newark Ins. Co., 289 So.2d 237 (La.App.1973), and in Spiers v. Lane, 278 So.2d 549 (La.App.1973), but neither of those cases required an exclusionary clause to excuse the duty to defend a suit not covered under the policy. Indeed, Mut found no duty to defend under one policy because of an exclusionary clause and no duty to defend under a second policy because coverage had lapsed, so that the accident was not covered under the terms of the.,policy.