
581 So.2d 230 (1991)
GOVERNMENT EMPLOYEES INSURANCE COMPANY, a Foreign Corporation, Appellant,
v.
Maria ROBINSON and Adrian A. Robinson, Her Husband, Appellees.
Nos. 90-1969, 91-42.
District Court of Appeal of Florida, Third District.
June 11, 1991.
Rehearing Denied July 18, 1991.
Barnett, Clark and Barnard and James K. Clark, Miami, for appellant.
Maguire and Friend and Michael P. Maguire, Coral Gables, for appellees.
Before NESBITT, FERGUSON and LEVY, JJ.
PER CURIAM.
Three issues are presented in this appeal: (1) Whether a judgment may be entered against an uninsured motorist carrier in an amount which exceeds the known policy limits in the absence of a finding of bad faith, (2) whether attorney's fees may be awarded under the sanctions provision of the offer of judgment rule in the absence of evidence or findings that the defendant-insurer *231 acted unreasonably, and (3) whether a multiplier may be applied to enhance an attorney fee award above the amount fixed by an unqualified forty-percent contingency fee agreement between the plaintiffs and their attorney.
We reverse the order denying GEICO's motion to reduce the judgment in accordance with policy limits, and reverse the attorney's fee award to the extent it exceeds the forty percent of recovery that was contractually agreed upon between the plaintiffs and their attorney.
Maria and Adrian Robinson brought this action against GEICO, their automobile insurance carrier, seeking benefits under the uninsured motorist provisions of their policy. They alleged that they had been involved in an automobile accident with an underinsured motorist, and were entitled to damages for personal injuries. GEICO answered, interposing defenses to both liability and the claimed amount of damages. Plaintiffs' $15,000 offer of judgment was rejected. After discovery and an unsuccessful attempt to settle the case through mediation, the case proceeded to trial before a jury. It had been established in the record that the amount of uninsured motorist coverage available under the plaintiffs' policy was limited to $20,000.
At the conclusion of the trial, the jury returned an $88,000 verdict for the plaintiffs  an amount which exceeded the policy limits by $68,000. The trial court denied GEICO's motion to limit the judgment to the policy limit, and entered a judgment for the full amount of the jury verdict. An appeal was taken from that judgment.
A second appeal was taken from an order awarding attorney's fees. Subsequent to the entry of the $88,000 judgment, the plaintiffs moved for fees pursuant to sections 45.061 and 768.79, Florida Statutes (1989), and Florida Rule of Civil Procedure 1.442, the "offer of judgment" statutes and rule. On a finding that the jury verdict exceeded plaintiffs' offer of judgment by 125 percent, the court awarded fees in the amount of $26,000. No evidence was presented showing that rejection of the offer of judgment by GEICO was otherwise unreasonable so as to justify a sanction, or that the fee agreed upon by plaintiffs and their attorney should be enhanced due to particular circumstances.
First, in the absence of a finding of "bad faith", an automobile insurance carrier's liability is restricted to the amount of its coverage limits. Quinn v. Millard, 358 So.2d 1378 (Fla. 3d DCA 1978); Dixie Ins. Co. v. Lewis, 484 So.2d 89 (Fla. 2d DCA 1986). Thus, the judgment against GEICO could not exceed $20,000, in the absence of a finding of bad faith. Second, a fee award as a sanction is not warranted under rule 1.442, in that there is no evidence which supports any of the ten relevant factors the court is permitted to consider in determining the reasonableness of a defendant's conduct. Third, there is no evidence which justifies the utilization of a multipler to enhance a fee, such as (1) that the relevant market requires a contingency fee multiplier to obtain competent counsel, (2) that there was a risk of nonpayment which the attorney was unable to mitigate, or (3) that the private litigation was a benefit to society. Standard Guar. Ins. Co. v. Quanstrom, 555 So.2d 828 (Fla. 1990). Finally, in no case should the court-awarded fee exceed the fee agreement reached by an attorney and his client, except as a punitive measure. Florida Patient's Compensation Fund v. Rowe, 472 So.2d 1145 (Fla. 1985).
Based on a recovery of $20,000, which accords with the policy limits, the proper fee is $8,000. Our determinations, based on the evidence presented at the attorney's fees hearings, do not preclude a separate bad faith action.
Reversed and remanded for further consistent proceedings.
