
765 So.2d 87 (2000)
RELLER, INC., Appellant,
v.
HARTFORD INSURANCE COMPANY OF the SOUTHEAST, a foreign insurance company for profit, Appellee.
No. 1D99-1945.
District Court of Appeal of Florida, First District.
May 8, 2000.
Eilon Krugman-Kadi, of Law Offices of Eilon Krugman-Kadi, P.A., Gainesville, for Appellant.
Charles Cook Howell, III, of Howell & O'Neal, Jacksonville, for Appellee.
KAHN, J.
The trial court correctly ruled that appellee, Hartford Insurance Company of the Southeast, had no obligation to prosecute an appeal on behalf of appellant, Reller, Inc. Accordingly, we affirm.
Hartford provided a policy of liability insurance for Reller. A third party brought a trademark infringement suit against Reller and others in the United States District Court in California. This suit sought money damages as well as an injunction against future infringement. Hartford provided Reller a defense through the conclusion of the trial. The district court in California entered judgment against Reller for money damages in the amount of $10,000, together with taxable costs, and permanently enjoined and restrained Reller from manufacturing and selling a particular jewelry design. Hartford then satisfied that portion of the judgment awarding money damages and costs, and obtained a partial satisfaction of the judgment. Hartford refused Reller's request to take an appeal. Reller obtained its own counsel and is currently appealing the order to the Ninth Circuit Court of Appeals. Reller brought this action against Hartford for breach of an insurance contract. The trial court granted summary judgment to Hartford, finding that no coverage under the policy would apply to the claim for injunctive relief.
The parties agree that only the claim for money damages was covered under Hartford's insurance contract. Nevertheless, Hartford recognized and honored its obligation to defend Reller at trial because the *88 "complaint against [Reller] contains allegations which are partially within and partially without the scope of the insured's coverage...." The Garden Sanctuary, Inc. v. Insurance Co. of N. Am., 292 So.2d 75, 78 (Fla. 2d DCA 1974). Having paid the insured claim, however, Hartford had no further obligation because "the claims giving rise to coverage have been eliminated from the suit." Baron Oil Co. v. Nationwide Mut. Fire Ins. Co., 470 So.2d 810, 815 (Fla. 1st DCA 1985).
Reller argues that Hartford had a continuing obligation to prosecute an appeal based upon Aetna Insurance Co. v. Borrell-Bigby Electric Co., Inc., 541 So.2d 139 (Fla. 2d DCA 1989). In Borrell-Bigby, the appellate court stated, "[w]here good faith grounds exist, the insurer is obligated to appeal from an adverse judgment." 541 So.2d at 141. As pointed out by the concurring opinion in that case, the court's suggestion that a primary carrier can never terminate its defense at either the trial or appellate level by interpleading its policy limits to pay a judgment, is overbroad. See id. at 142 (Altenbernd, J., concurring in result). The insurer in Borrell-Bigby simply did not exhaust its policy "by payment of a judgment...." Id. Borrell-Bigby did not involve the question of a covered claim of damages and a distinctly uncovered claim of injunctive relief, as does the present case. Because Hartford obtained full satisfaction of the only covered claim, it had the right to withdraw its defense. See Meadowbrook, Inc. v. Tower Ins. Co., Inc., 559 N.W.2d 411, 416 (Minn. 1997) ("[A]n insurer who undertakes an insured's defense under a reservation of rights can withdraw its defense once all arguably covered claims have been dismissed with finality.").
AFFIRMED.
WOLF and LAWRENCE, JJ., CONCUR.
