
622 So.2d 570 (1993)
Patricia THORNBER, John Franklin and al Grant, Appellants/Cross-Appellees,
v.
The CITY OF FORT WALTON BEACH, Appellee/Cross-Appellant.
No. 92-1405.
District Court of Appeal of Florida, First District.
August 4, 1993.
*571 George E. Day and Timothy I. Meade, Day and Meade, P.A., Fort Walton Beach, for appellants, cross-appellees.
James E. Moore, Bert Moore, Bret A. Moore and Alice H. Murray, Moore, Kessler & Moore, Niceville, for appellee, cross-appellant.
PER CURIAM.
Before us is an appeal and cross-appeal from a post-judgment order on remand from this court awarding attorney's fees to be paid by the City of Fort Walton Beach (City) to the appellants, for services rendered by their attorney, George Day, in defending legal actions brought against them as elected council members of the City. Upon review of the record, and consideration of the briefs and arguments of counsel, we affirm as to all issues.
In Thornber v. City of Fort Walton Beach, 568 So.2d 914 (Fla. 1990), the Florida Supreme Court approved, in part, the decision of this court in City of Fort Walton Beach v. Grant, 544 So.2d 230 (Fla. 1st DCA 1989), by holding that this court correctly found the council members entitled to recovery of attorney's fees for their defense of a federal civil rights action against them. The supreme court also ruled, however, that this court was incorrect in denying attorney's fees incurred in defending a recall petition. Pursuant to the mandate of this court, adopting the opinion and decision of the supreme court, this case was remanded to the trial court for determination of amount and entry of judgment awarding reimbursement for attorney's fees incurred in defense of both the recall and the federal civil rights case. The trial court's order awarding attorney's fees pursuant to proceedings on remand is the subject of this appeal.
Although numerous issues are raised by both sides, we feel it necessary to comment briefly on two points only. The first is the council members' contention that the trial court erred in limiting to only 2.0 the contingency fee multiplier to be applied to the lodestar fee determined under Florida Patients Compensation Fund v. Rowe, 472 So.2d 1145 (Fla. 1985). Appellants' position is that a multiplier of 2.5 is mandated, given the circumstances presented by this protracted litigation, particularly in view of the trial court's finding in the order appealed that the likelihood of success was "unlikely," at the outset of the litigation. We are of the view that appellants misread the requirements of Rowe as modified in Standard Guaranty Insurance v. Quanstrom, 555 So.2d 828 (Fla. 1990). We first note that under Quanstrom, the range of the multiplier of cases where success was unlikely is 2.0 to 2.5. Since the trial court's ruling falls within the allowable range, we find that it has not been shown that the trial court reversibly erred by failing to award the top multiplier. It appears that appellants have also overlooked the holding in Quanstrom, supra, that application of the multiplier is not automatically required in contingent fee cases. 555 So.2d at 831; see also, Department of Administration v. Ganson, 566 So.2d 791 (Fla. 1990).
We are also of the view that although, as appellants' urge, the trial court may have concluded that the 2.0 multiplier was appropriate before considering of all the evidence and argument of both sides, nevertheless, the trial court was fully cognizant of all matters bearing on the proper multiplier prior to a final ruling, and we see no useful purpose in remanding to the trial court for reconsideration of the award.
The second issue we find need to mention is appellants' contention that the trial court erred in failing to award attorney's fees for legal services rendered by their attorney in establishing entitlement to fees for defense of the underlying recall and civil rights litigation. Without elaboration on the many pros and cons of this issue as presented by the briefs and arguments of the respective parties, we affirm the trial court's denial of fees for work in establishment of entitlement to attorney's fees given the posture of the case as it appears before us. As noted by the supreme court in Thornber, appellants in that appeal were seeking recovery of legal fees *572 for litigating the entitlement to such fees based upon section 57.105, Florida Statutes, 568 So.2d at 919. The supreme court ruled that appellants were not entitled to attorney's fees in their efforts to collect those fees. Whether the court intended to preclude the recovery of such fees in this case under any circumstances is a matter of sharp disagreement between the parties in this appeal. The fact remains, however, that the court's ruling dealt only with appellants' claims under section 57.105, and the court clearly did not concern itself with a possible basis for recovery of such fees on other grounds. We see no reason to speculate further on what the court intended. As a practical matter, the supreme court had before it no other possible basis for award of fees except under section 57.105. This is so because Count VI of appellants' complaint, which specifically sought recovery of fees for the legal work in establishing entitlement to those fees from the City,[1] was dismissed by the trial court, and this order of dismissal was not appealed by the council members. City of Fort Walton Beach v. Grant, 544 So.2d at 232-233. Harsh as this result may seem, particularly in view of the considerable efforts of appellants' counsel in this litigation, we find disposition of this issue to be governed by the "law of the case" doctrine, and so further consideration by the trial court on remand, and at this juncture on appeal, was and is foreclosed. Brunner Enterprises v. Department of Revenue, 452 So.2d 550 (Fla. 1984) (supreme court is only court that has power to change law of the case established by that court); Valsecchi v. Proprietors Insurance Co., 502 So.2d 1310 (Fla. 3d DCA 1987) ("law of the case" doctrine applies to any question that could have been raised in prior appeal of same case, as well as question decided by implication); Salta Investment v. Silva, 584 So.2d 172 (Fla. 3d DCA 1991) (award of attorney's fees on remand was error, where award of fees was denied on prior appeal).
Further, the reversal and remand pursuant to Thornber, supra, was for the limited purpose of awarding fees incurred in defense of the recall petition and the civil rights action. The mandate of an appellate court is said to constitute "a final judgment in the cause, and compliance is a ministerial act to be performed by the trial court." Nicholson v. Ariko, 565 So.2d 843, 844 (Fla. 5th DCA 1990), and cases cited therein. "It is the duty of the trial court to enforce the mandate and not to stray from it." Id. We therefore are not called upon to decide whether attorney's fees, under appropriate pleadings and proof, would have been awardable for services rendered in establishing appellants' entitlement to attorney fees.[2]
Accordingly, the judgment appealed is in all respects, AFFIRMED.
BOOTH, SMITH and MINER, JJ., concur.
NOTES
[1]  Paragraph 11, Count VI, of appellants' First Amended Complaint specifically claimed reasonable attorney's fees "for bringing this action to enforce their rights under F.S. 111.07."
[2]  Case law approving an award of attorney's fees and costs for establishing entitlement to fees under a particular statute makes such an award dependent upon a showing, in one way or another, that under the attorney's agreement with the client the award of such additional fees would be beneficial to the client. See, B & L Motors, Inc. v. Bignotti, 427 So.2d 1070 (Fla. 2d DCA 1983) (section 501.2105, Florida Statutes (1979), the "Little FTC Act"), disapproved on other grounds, Travieso v. Travieso, 474 So.2d 1184 (Fla. 1985); Bill Rivers Trailers, Inc. v. Miller, 489 So.2d 1139 (Fla. 1st DCA 1986) (section 448.08, Florida Statutes (1981), actions for unpaid wages); Inacio v. State Farm Fire & Casualty Company, 550 So.2d 92 (Fla. 1st DCA 1989) (sections 624.155(3) and 627.428, Florida Statutes (1987), actions by insureds against insurer). Here, given the absence of testimony establishing the attorney's right to recovery of fees from the appellants for the action to enforce fees under section 111.07, it is doubtful that such recovery could have been obtained even had the issue not been waived by failure to appeal the dismissal of Count VI seeking such fees.
