
909 So.2d 475 (2005)
Terrell G. LEE, Petitioner,
v.
PROGRESSIVE EXPRESS INSURANCE COMPANY, a Florida corporation, Respondent.
No. 4D05-342.
District Court of Appeal of Florida, Fourth District.
August 24, 2005.
*476 Michael B. Davis and Clark W. Smith of Paxton & Smith, P.A., and L. Martin Flanagan, West Palm Beach, for petitioner.
Hinda Klein of Conroy, Simberg, Ganon, Krevans & Abel, P.A., Hollywood, for respondent.
PER CURIAM.
Terrell Lee, the plaintiff below in a bad faith action against Progressive Express Insurance Company, petitions this court for a writ of certiorari to quash an order that allows discovery of attorney-client communications. We grant the petition.
Lee was injured in an auto accident when his car was hit from behind on the interstate. Progressive insures the driver who struck Lee's car. After filing suit, Lee served a settlement demand letter and a Proposal for Settlement pursuant to Florida Rule of Civil Procedure 1.442 and section 768.79, Florida Statutes, offering to settle his claim and all costs and attorney's fees for Progressive's policy limits. More than 30 days later, Progressive requested an extension of time to respond. Lee's attorney rejected the requested extension and treated this as a rejection of the settlement offer. A few months later, Progressive offered to settle the case for the policy limits. Progressive's offer was rejected and the case proceeded to trial. The jury returned a verdict for Lee and awarded damages that substantially exceeded the policy limits. On appeal, this court affirmed. Matalon v. Lee, 847 So.2d 1077 (Fla. 4th DCA 2003).
Lee subsequently filed a complaint against Progressive for bad faith in failing to settle.
Progressive requested discovery of communication between Lee and his attorney regarding fee arrangements in the bad faith action and counsel's authority to settle the initial suit against the insured. Progressive believes that Lee's attorney orchestrated the rejection of Progressive's policy limits tender solely to set Progressive up for a bad faith action. Lee filed a privilege log and moved for a protective order maintaining that the requested documents are protected by the attorney-client and work product privileges.
In response, Progressive argued that by initiating the bad faith action, Lee injected *477 specific communications with his attorney into this litigation and any privilege was waived. Progressive claims that it needs this information to show that it might not have been able to settle the claim. Progressive also argued that the privilege was waived during Lee's deposition when he testified about counsel's authority to settle the case. Lee indicated that the timing of his demand, the amount of his demand, and rejection of Progressive's settlement offer were decided by his attorney and Lee indicated that he followed counsel's advice.
Following a hearing, the court ordered production of the fee agreements and documents related to counsel's authority to settle. The trial court concluded that any privilege was waived because Lee testified about the matter during his deposition. Lee challenges the portion of the order that allows discovery related to counsel's authority to settle.
We disagree with Progressive and the trial court. The attorney-client privilege was not waived by the filing of this suit or by Lee's deposition testimony.
Generally, the attorney-client privilege is not waived by bringing or defending a lawsuit. Home Ins. Co. v. Advance Mach. Co., 443 So.2d 165, 168 (Fla. 1st DCA 1983). But, if proof of the claim would require evidence of the privileged matter, the privileged matter is discoverable. Id.
Lee has testified that counsel had authority to settle the case for the policy limit. The motives of Lee and his attorney regarding the timing of the settlement offer and rejection of Progressive's subsequent settlement offer are not elements that Lee has to prove to establish a bad faith claim against Progressive. See Berges v. Infinity Ins. Co., 896 So.2d 665 (Fla. 2004) (observing that the focus in a bad faith action is on the insurer's conduct in fulfilling its obligations to the insured, not on the actions of the claimant).
Progressive suggests that because Lee could not remember many details about the settlement offer, he may not have authorized his attorney to settle the case. Contrary to Progressive's argument, Lee is not the one injecting this issue into the litigation. If the insurer raises this as a defense, it has the burden of proving that the claimant was unwilling to settle. Powell v. Prudential Prop. & Cas. Ins. Co., 584 So.2d 12, 14 (Fla. 3d DCA 1991) (recognizing that in a bad faith action the insurer has the burden of showing that there was no realistic possibility of settlement within the policy limits); see also Snowden ex rel. Estate of Snowden v. Lumbermens Mut. Cas. Co., 358 F.Supp.2d 1125, 1128-29 (N.D.Fla.2003) (observing that the claimant's "unwillingness to settle will become a factor only in the unlikely case where the insurer is able to conclusively prove the unwillingness to settle for the policy limits.").
Furthermore, Lee did not waive the attorney-client privilege during his deposition. Although Progressive asked Lee numerous questions about the settlement demand and rejection of Progressive's offer, Lee gave limited responses and did not disclose any specific discussions or the substance of any communications he had with his attorney. Reviewing the deposition testimony, we find that Lee has not waived the attorney-client privilege.
The petition for writ of certiorari is granted and the portion of the order allowing discovery of documents related to counsel's authority to settle the case is quashed.
GUNTHER, TAYLOR and MAY, JJ., concur.
