Killer Music, Inc., doing business as HLC Partnership; TTBB, Inc., doing business as Killer Tracks; and Ron Hicklin (collectively, “Killer Music”) appeal the district court’s grant of Zurich Insurance Co.’s (“Zurich”) motion for summary judgment on Zurich’s declaratory judgment action and the dismissal of Killer Music’s counterclaims on a motion for summary judgment. The issues are whether Zurich had a duty to defend and indemnify Killer Music in a suit brought by a third party (Pfeifer) and whether Zurich’s denial of coverage was in bad faith. We reverse and remand because we hold that Zurich wrongfully refused to defend Killer Music. We affirm the summary judgment on the bad faith issue.

Killer Music contracted with Pfeifer to sell jingles which Pfeifer produced to radio and television stations and movie studios. Killer *677 Music agreed to pay Pfeifer for each jingle sold. The contract also provided that Pfeifer would perform on certain songs, and that he would be paid for these performances when the Songs were sold. That contract expired in 1988.

After that date, Killer Music compiled and sold a music library which included Pfeifer songs which had not been sold during the contract period. The songs were not attributed to Pfeifer and no compensation was paid. In April 1990, Pfeifer filed a complaint in which he alleged copyright infringement, false designation of origin, unfair competition, palming off, conversion, and unjust enrichment. He sought punitive and compensatory damages, an accounting, the establishment of a constructive trust, and attorneys’ fees.

Killer Music was insured under a Comprehensive General Liability Policy written by Zurich. The policy was sold by DeWitt Stern, an insurance broker. The policy covers “advertising injury,” which includes “those sums that the insured becomes legally obligated to pay as damages because of ‘personal injury’ or ‘advertising injury’ to which this insurance applies.” “Advertising injury” is defined to include injury from infringement of copyright. The policy excludes coverage, however, for advertising injury “arising out of breach of contract.”

Killer Music first learned of the Pfeifer litigation when they were notified that Pfeifer had obtained a temporary injunction against them. At this point, Killer Music contacted DeWitt Stern, advised a clerk there that the Pfeifer suit was going to be filed against them, and asked her to check into the matter. Killer Music did not ask that the insurer defend them. The clerk may or may not have contacted persons at Zurich to confer about the policy coverage; at any rate, she advised Killer Music that they were not covered. Another telephone call was made to another clerk that same week, who also reported that there was no coverage. Killer Music never followed up with any written notice of claim either to Zurich or DeWitt, nor did Killer Music transmit any of the court documents to either company. 1

Killer Music settled with Pfeifer soon after the suit was filed. Under the settlement agreement, Pfeifer transferred his rights to the songs which had been used in the music library, and agreed to drop his suit, in exchange for a $175,000 settlement.

At this point, Killer Music, through counsel, began corresponding with Zurich over the issue of coverage, seeking recovery of defense costs in the suit and indemnification. Zurich responded by filing an action for a declaratory judgment that it had no duty to defend or indemnify. Killer Music counterclaimed and asserted that Zurich breached its duty of good faith. The district court granted Zurich’s motions for summary judgment on both its claim and the counterclaim.

On appeal, a summary judgment motion is reviewed de novo. Kennedy v. Allied Mutual Ins. Co., 952 F.2d 262, 265 (9th Cir.1991). “Viewing the evidence in the light most favorable to the non-moving party, this court must determine whether there are any genuine issues of material fact, and whether the district court correctly applied the relevant substantive law.” Id.

III

Under the contract with Killer Music, Zurich had “the right and duty to defend any ‘suit’ seeking [damages for ‘advertising injury’].” “Advertising injury” was defined to include infringement of copyright. Pfeifer alleged copyright infringement, among other causes of action, in his complaint against Killer Music. The pplicy excludes coverage, however, for advertising injury “arising out of breach of contract.” Zurich, based on a reasonable reading of case law, including *678 Home Indem. Co. v. Avol, 706 F.Supp. 728 (C.D.Cal.1989) (applying California law), aff'd without opinion, 912 F.2d 469 (9th Cir.1990), and Allstate Ins. Co. v. Hansten, 765 F.Supp. 614 (N.D.Cal.1991) (applying California law), determined that Pfeifer’s copyright infringement claim arose out of a breach of contract and was therefore not covered. Other cases suggest, however, that the Pfeifer action should be characterized as sounding in tort. See Fragomeno v. Insurance Co. of the West, 207 Cal.App.3d 822 , 255 Cal.Rptr. 111 (1989); Fireman’s Fund Ins. Co. v. City of Turlock, 170 Cal.App.3d 988 , 216 Cal.Rptr. 796 (1985). Under California law, “the duty to defend is so broad that as long as the complaint contains language creating the potential of liability under an insurance policy, the insurer must defend an action against its insured.” CNA Casualty of California v. Seaboard Sur. Co., 176 Cal.App.3d 598, 606 , 222 Cal. Rptr. 276 (1986); Republic Indem. Co. v. Superior Court, 224 Cal.App.3d 492, 500 , 273 Cal.Rptr. 331 (1990). Based on our reading of the California cases, we conclude that there was at least a “potential of liability” so Zurich had a duty to defend Killer Music in that action.

Zurich contends that the claim was not potentially covered because coverage was excluded by operation of California Insurance Code § 533. Section 533 provides that “[a]n insurer is not liable for a loss caused by the willful act of the insured_” 2 According to Zurich, Pfeifer’s suit against Killer Music was based on intentional misconduct, a “willful act” by Killer Music. Killer Music argues that the use of Pfeifer’s music in the music library was inadvertent and certainly not “willful” as defined in the statute.

A “clear line of authority” in California directs that “even an act which is ‘intentional’ or ‘willful’ within the meaning of traditional tort principles will not exonerate the insurer from liability under [§] 533 unless it is done with a ‘preconceived design to inflict injury.’” Clemmer v. Hartford Ins. Co., 22 Cal.3d 865 , 151 Cal.Rptr. 285, 297 , 587 P.2d 1098, 1110 (1978); California Shoppers, Inc. v. Royal Globe Ins. Co., 175 Cal.App.3d 1, 32 , 221 Cal.Rptr. 171 (1985); Waters v. Bourhis, 40 Cal.3d 424 , 220 Cal.Rptr. 666, 673 , 709 P.2d 469, 476 (1985). The term “willful” is used to describe “an act done with malevolence,” Capachi v. Glens Falls Ins. Co., 215 Cal.App.2d Supp. 843, 849 , 30 Cal. Rptr. 323 (1963), or with “malice in fact.” City Products Corp. v. Globe Indem. Co., 88 Cal.App.3d 31 , 36 n. 3, 151 Cal.Rptr. 494 (1979). A “ ‘willful act’ within the meaning of section 533 means ‘something more than the mere intentional doing of an act constituting [ordinary] negligence’, and appears to be something more than the intentional violation of a statute.” B & E Convalescent Center v. State Compensation Ins. Fund, 8 Cal.App. 4th 78, 94 , 9 Cal.Rptr.2d 894 (1992) (citation omitted) (brackets in original).

Killer Music’s actions were not proven to be “willful” as a matter of law. While Zurich characterizes Killer Music’s infringement as “knowing,” Killer Music’s president Hicklin, by sworn affidavit, indicated that he did not know that any of Pfeifer’s work was being used in the music library and that he “never intended to engage in any unauthorized use of any work owned in whole or in part by Pfeifer.” He also disavowed any intent to injure or harm Pfeifer.

Zurich points out that California courts have been willing to find some activities “willful” as a matter of law “if the harm is inherent in the act itself.” B & E Convalescent Center, 8 Cal.App. 4th at 97 , 9 Cal. Rptr.2d 894 (citation omitted). It is true that a subjective desire to injure or harm need not always be proven and can be assumed by the nature of the act. See Fire Ins. Exchange v. Altieri, 235 Cal.App.3d 1352, 1358 , 1 Cal.Rptr .2d 360 (1991); Aetna Casualty & Sur. Co. v. Sheft, 756 F.Supp. 449, 451 (1990); Fire Ins. Exchange v. Abbott, 204 Cal.App.3d 1012, 1020 , 251 Cal.Rptr. 620 (1988). However, copyright infringement is not one of those activities that is “willful” per se. Zurich admits in its brief that “[c]opyright infringement can be inno *679 cent or intentional.... Innocent infringement may be covered.”

The possibility that § 533 might operate to exclude coverage does not excuse Zurich’s initial decision to deny coverage. “[I]n order to rely upon Section 533 to justify its refusal to defend, [Zurich] must show that information available to it at that time demonstrated that [Pfeifer] was required to establish that [Killer Music] intended him harm, not merely that it intended to act.” Republic Indem., 224 Cal.App.3d at 502 , 273 Cal.Rptr. 331 . Zurich did not demonstrate that Pfeifer was required to prove Killer Music’s intent to harm him to succeed on his claim for copyright infringement; indeed, Zurich itself noted that “[c]opyright infringement can be innocent or intentional.” We hold that the district court erred in granting Zurich’s motion for summary judgment on the basis of § 533.

Zurich argues that it had no duty to cover Killer Music’s claim since no written notice was given, as required by the policy, and Zurich had no actual or constructive notice of the claim. Although the parties dispute whether Zurich ever received actual notice of the claim from an employee of DeWitt Stern, this question is immaterial since under California Civil Code § 2332 notice to an agent is equivalent to notice to the principal. It is clear that DeWitt Stern must be considered Zurich’s agent. The only address on the policy for the insured to contact was DeWitt Stern’s. See California Civil Code §§ 2300, 2317 (1992). The lack of written notice alone does not excuse Zurich’s refusal to defend. Fidelity Sav. & Loan Ass’n v. Aetna Life & Casualty Co., 647 F.2d 933, 938 (9th Cir.1981); Moe v. Transamerica Title Ins. Co., 21 Cal.App.3d 289, 302 , 98 Cal.Rptr. 547 (1971). Here Zurich’s agent had actual notice and, without requesting a copy of the complaint, the agent decided not to defend on the basis of lack of coverage, not inadequate notice. See, e.g., Clemmer v. Hartford Ins. Co., 22 Cal.3d 865 , 151 Cal.Rptr. 285 , 587 P.2d 1098 (1978) (insurer made no showing that it would have defended if it had had timely tender of defense). See also California Shoppers, Inc. v. Royal Globe Ins. Co., 175 Cal.App.3d 1, 38 , 221 Cal.Rptr. 171 (1985); Samson v. Transamerica Ins. Co., 30 Cal.3d 220 , 178 Cal. Rptr. 343, 353-54 , 636 P.2d 32, 43 (1981).

We now address the consequences of Zurich’s breach. As to the settlement, the mere fact that Zurich failed to defend does not mean that Zurich is liable for the amount of the settlement. See, e.g., Ceresina v. Fire Ins. Exchange, 215 Cal. App.3d 814 , 264 Cal.Rptr. 30 (1989); Hogan v. Midland Nat’l Ins. Co., 3 Cal.3d 553 , 91 Cal.Rptr. 153, 160 , 476 P.2d 825, 832 (1970). Zurich is liable only for the amount of a “reasonable settlement of the claim in good faith.” Isaacson v. California Ins. Guarantee Ass’n, 44 Cal.3d 775 , 244 Cal.Rptr. 655, 666 , 750 P.2d 297, 308 (1988). “A reasonable settlement made by the insured to terminate the underlying claim against him may be used as presumptive evidence of the insured’s liability on the underlying claim, and the amount of such liability.” Id. This presumption “may be overcome by proof’ that the settlement agreement is unreasonable in amount. Culley & Assoc. v. Superior Court, 10 Cal.App.4th 1484 , 13 Cal.Rptr.2d 624 , modified, 11 Cal.App.4th 1206e, 13 Cal. Rptr .2d 624 (1992).

We recognize that the settlement agreement represents, in part, an exchange of cash consideration for the rights to Pfeifer’s songs, not simply compensation for damages from copyright infringement. Cf. Bank of the West v. Superior Court, 2 Cal.4th 1254 , 10 Cal.Rptr.2d 538 , 833 P.2d 545 (1992) (holding that term “damages” does not include restitution, just compensation); AIU Ins. Co. v. Superior Court, 51 Cal.3d 807 , 274 Cal. Rptr. 820 , 799 P.2d 1253 (1990) (same); State Farm Fire and Casualty Co. v. Superior Court, 191 Cal.App.3d 74 , 236 Cal.Rptr. 216 (1987) (same). We also note that Zurich had no control over the terms of the settlement agreement, which was structured so that Killer Music received the rights to the songs. When the issue of the amount of a reasonable settlement in good faith is addressed on remand, Zurich will have the opportunity to *680 demonstrate that some portion, if not all, of the settlement amount is allocable to the value of the songs which Killer received in the settlement agreement.

By breaching its duty to defend, Zurich is also liable for attorneys’ fees as provided in the policy or as “incurred in good faith, and in the exercise of a reasonable discretion” in defending the action. California Civil Code § 2778. Zurich’s liability extends to fees arguably allocable to defense of noncovered claims. Hogan v. Midland Nat’l Ins. Co., 3 Cal.3d 553 , 91 Cal.Rptr. 153, 159 , 476 P.2d 825, 831 (1970). Zurich is not liable for fees incurred by Killer Music in bringing this action in the district court, since Killer Music “is not entitled to an award of attorney’s fees incurred in a separate action in which [it] seeks to enforce [its] right to be defended or to be reimbursed for attorney’s fees previously incurred in an action which should have been defended by the insurer.” Carroll v. Hanover Ins. Co., 266 Cal.App.2d 47, 50 , 71 Cal.Rptr. 868 (1968).

VII

As to Killer Music’s counterclaim alleging bad faith on Zurich’s part, there is no evidence of bad faith in this record. Although Zurich breached its duty to defend, “breach of the implied covenant of good faith and fair dealing involves something beyond breach of the contractual duty itself.” California Shoppers, Inc. v. Royal Globe Ins. Co., 175 Cal.App.3d 1, 54 , 221 Cal.Rptr. 171 (1985). Zurich did not reasonably investigate the claim to determine coverage, but “without actual presentation of a claim by the insured in compliance with claims procedures contained in the policy, there is no duty imposed on the insurer to investigate the claim.” Id. at 57 , 221 Cal.Rptr. 171 . Here it is undisputed that Killer Music failed to follow explicit policy conditions requiring written notice, conditions that were incorporated into the contract to avoid just the sort of out-of-channel coverage decision that took place in this case. The fact that Zurich brought a declaratory judgment action to determine its liability for coverage is not bad faith. Atlas Assurance Co. v. McCombs Corp., 146 Cal. App.3d 135, 150 , 194 Cal.Rptr. 66 (1983). The district court did not err in granting Zurich’s motion for summary judgment on the bad faith counterclaim.

VIII

We reverse the summary judgment on Zurich’s claim and remand for a determination of the damages attributable to a reasonable settlement in good faith and for a determination of attorneys’ fees incurred in the defense of the Pfeifer suit. We affirm the grant of Zurich’s motion for summary judgment on the bad faith counterclaim. Neither party shall recover costs on appeal.

AFFIRMED IN PART, REVERSED AND REMANDED IN PART.

. The policy provides in relevant part:

. This statutory exclusion is read into every insurance contract as an implicit term. Allstate Ins. Co. v. Overton, 160 Cal.App.3d 843 , 206 Cal.Rptr. 823 (1984).