
909 P.2d 925 (1995)
Susan SLATTERY, Plaintiff and Appellee,
v.
COVEY & CO., INC., and Almon Covey, Defendants and Appellant.
No. 940061-CA.
Court of Appeals of Utah.
December 29, 1995.
David R. King, Salt Lake City, for Appellant.
Ralph C. Petty and Richard Leedy, Salt Lake City, for Appellee.
Before DAVIS, BENCH and GREENWOOD, JJ.
*926 GREENWOOD, Judge:
Appellant, Covey & Co., Inc. (Covey), appeals the trial court's entry of judgment on remand from this court's opinion in Slattery v. Covey & Co., Inc., 857 P.2d 243 (Utah App.1993) (Slattery I). We reverse.

BACKGROUND
The facts are set forth at length in our prior opinion, Slattery I, 857 P.2d at 244-45, but we will briefly address those pertinent to this appeal. The factual basis for this case began in the summer of 1987 when appellee Susan Slattery went to work for Covey. Covey employed Slattery as an assistant to Ray Spilsbury, a stockbroker, and as an independent-contractor stockbroker. Under the terms of her employment contract, Slattery was to receive a salary for services rendered to Spilsbury, but would pay Covey for certain office expenses incurred by her in her capacity as an independent stockbroker.
Problems arose when Slattery began assisting Spilsbury, at his request, in stock "floating" transactions. The floats occurred when Spilsbury's customers ordered stock but did not pay for it and Spilsbury then transferred stock among his clients' accounts to cover the payment deficiency, taking advantage of the seven-day grace period for payment. The floats were intended to forestall Covey's "sell-out" to cover the payment delinquencies.[1] Some of the affected accounts were those of Slattery's own customers.
As might be expected, this house-of-cards soon collapsed, leaving Slattery with substantial debits in her "error account," an account maintained by Covey for all its brokers in which it registered credits and debits between the company and its brokers. Shortly thereafter, Covey determined that Spilsbury was not doing enough business to warrant paying for an assistant, and terminated Slattery.
Slattery then sued Covey, alleging slander, libel and defamation. Covey counterclaimed, seeking the outstanding balance due on Slattery's error account. During trial, Slattery was allowed to amend her complaint to request an offset against the error account balance for the value of her personal stocks retained by Covey.
The trial court entered a no-cause judgment for Covey on Slattery's claims, but found that Slattery was entitled to payment of $10,801.35 after applying various credits and offsets to her error account balance. Specifically, the trial court found that Slattery was entitled to $6,847.50 for the stocks in her personal account and that each party was responsible for their own attorney fees and costs. See Slattery I, 857 P.2d at 245-46.
Covey appealed, claiming, among other things, that the trial court erred in "disallowing certain office expense debits as part of the error account balance" and in "assigning a value to Slattery's securities based on insufficient evidence." Id. at 246. Slattery also appealed, seeking attorney fees incurred on appeal. Id. at 249 n. 4.
In Slattery I, this court reviewed the trial court's entry of judgment against Covey and affirmed in part and reversed in part, making two findings of error. Id. at 250. First, we determined that certain errors had been made in calculating credits for Slattery's office expenses. Id. at 248. On this issue, we gave the trial court the following specific instructions:
The total credit to which Slattery appears to be entitled is the following:


$102.78 for November health insurance
$102.78 for December health insurance
$  6.68 for December AT & T charges and
$194.00 for 1988 state registration fees
-------------------------------------------
$406.24  =  Total credits to error account

We remand this particular issue to the trial court for entry of findings consistent with this opinion.
Id. (emphasis added).
Our second finding of error concerned the award to Slattery of the value of her personal securities. We determined that "the valuation assigned to Slattery's personal accounts does not have a reasonable basis in the evidence *927 and, therefore, is clearly erroneous. Slattery, therefore, is not entitled to judgment for the $6,847.50 offset against Covey & Co." Id. at 249. Notably absent was any further instruction to the trial court on this point.
This court also refused to award Slattery attorney fees, stating:
Slattery also seeks attorney fees on appeal, based on the employment contract. However, she was not awarded attorney fees at trial and did not appeal from that determination. Because Slattery does not present any argument to support her request for fees on appeal, we decline to address the issue.
Id. at 249 n. 4.
On August 6, 1993, we issued a remittitur to the trial court. Following our remand, counsel for Slattery requested a hearing on the issue of the value of securities in Slattery's personal account. Slattery also moved, on September 1, 1993, to amend the pleadings to allow an award of attorney fees and costs. The district court convened a hearing on September 2, 1993, on the value of the securities and the issue of Slattery's attorney fees and costs. The trial court, over Covey's objections, received further evidence on the value of Slattery's personal stock and the amount of her appellate attorney fees.
Subsequently, the trial court entered findings of fact and conclusions law in which it found the value of Slattery's personal securities to be $8,567.50. The trial court also issued a minute entry awarding Slattery attorney fees and costs in the amounts of $13,552.55 for the appeal in Slattery I and $1,937.50 for the hearing on remand. Accordingly, on November 8, 1993, the trial court entered judgment in favor of Slattery in the total amount of $27,771.26.[2] Covey filed a notice of appeal on December 8, 1993. The propriety of the trial court's supplemental evidentiary hearings on, and subsequent award of, the value of Slattery's personal securities and attorney fees forms the basis of this appeal.

STANDARD OF REVIEW
Whether the trial court properly complied, on remand, with our decision in Slattery I is a question of law which we review for correctness. See Amax Magnesium Corp. v. Utah State Tax Comm'n, 874 P.2d 840, 842 (Utah 1994).

ANALYSIS

Valuation of Slattery's Securities
Covey asserts that the trial court acted beyond the limited scope of the authority granted to it on remand when it held an evidentiary hearing to determine the valuation of Slattery's securities. We agree. Both parties cite Rule 30(a) of the Utah Rules of Appellate Procedure, and the case of Street v. Fourth Judicial District Court, 113 Utah 60, 191 P.2d 153 (1948), as authority on the scope of a trial court's powers on remand. These authorities serve to define the problem, but neither provides a definitive answer since the outcome is, by necessity, case specific.
Rule 30(a) provides that an appellate court can dispose of a case in myriad different fashions:
The court may reverse, affirm, modify, or otherwise dispose of any order or judgment appealed from. If the findings of fact in a case are incomplete, the court may order the trial court or agency to supplement, modify, or complete the findings to make them conform to the issues presented and the facts as found from the evidence and may direct the trial court or agency to enter judgment in accordance with the findings as revised. The court may also order a new trial or further proceedings to be conducted. If a new trial is granted, the court may pass upon and determine all questions of law involved in the case presented upon the appeal and necessary to the final determination of the case.
Utah R.App.P. 30(a). Because the real question in this appeal concerns the exact posture *928 in which this case was remanded, Rule 30(a) provides us with little guidance in resolving this matter.
Street, on the other hand, is more instructional. The basic rule of Street is that any definitive ruling by an appellate court becomes the "law of the case, and the trial court is bound to follow it, even though it considers the ruling erroneous." Street, 191 P.2d at 158. The Utah Supreme Court has recently reaffirmed this principle. In Thurston v. Box Elder County, 892 P.2d 1034 (Utah 1995), the court stated that "pronouncements of an appellate court on legal issues ... become the law of the case and must be followed in subsequent proceedings... the lower court must implement both the letter and the spirit of the mandate, taking into account the appellate court's opinion and the circumstances it embraces." Id. at 1037-38 (citations omitted); see also In re Adoption of BBC, 849 P.2d 769, 772 (Wyo.1993) (holding trial court, on remand, has jurisdiction only to the extent conferred by appellate court's opinion and mandate); Bryfogle v. Arizona Dep't of Corrections, 153 Ariz. 598, 739 P.2d 819, 821 (App.1987) (same). The Utah Supreme Court also observed that the law of the case doctrine serves the dual purposes of avoiding reargument of settled issues and ensuring compliance with decisions of courts with appellate jurisdiction. Thurston, 892 P.2d at 1038.
Thus, it is only when issues are left open by an appellate decision that the trial court has discretion to deal with those issues as it sees fit, including allowing supplemental filings or proceedings. Street, 191 P.2d at 158; accord Call v. City of West Jordan, 727 P.2d 180, 181 (Utah 1986) ("Pleadings may be amended after remand ... so long as they do not cover issues specifically foreclosed by the appellate court." (emphasis added)). Consequently, the remaining question in this case is to what extent Slattery I fully decided the issues now before us.
With respect to the valuation of Slattery's securities, we determined that the evidence presented by Slattery at trial was not competent to "provide an objective basis or foundation" for the valuation which the trial court found. Slattery I, 857 P.2d at 249. We stated that this finding was "clearly erroneous" and that Slattery was "not entitled" to judgment on this amount. Id. Therefore, the law of the case on remand, was that while Slattery was entitled to an offset, because she had failed to present sufficient evidence of the stock's value, it had no value as an offset. Id. The trial court's sole duty on this issue was to enter judgment accordingly. Nowhere did we indicate that the trial court should act to supplement the record in any regard.[3]
Generally speaking, appellate review is not intended to grant litigants a second chance to present their case when they have had a full and fair opportunity to do so at an earlier trial. In Slattery I, we determined that the evidence which Slattery presented at trial was insufficient, as a matter of law, to support her claimed offset. Id. She is not entitled to try to present a stronger case the second time around.
As the Utah Supreme Court commented in reference to the law of the case doctrine, "[t]his rule is not only reasonable, but necessary, if litigation is ever to come to an end." Street, 191 P.2d at 158. Enforcement of the doctrine promotes judicial efficiency and fairness. Thus, we conclude that the trial court acted beyond the scope of its authority on remand by accepting evidence anew on the value of Slattery's securities. Accordingly, we reverse the award to Slattery of the value of her personal securities.[4]


*929 Slattery's Attorney Fees and Costs
Covey also argues that the trial court exceeded its authority on remand by awarding Slattery judgment for attorney fees incurred by her in Slattery I. We agree. Our decision in Slattery I specifically declined to consider Slattery's application for attorney fees incurred on appeal. Slattery I, 857 P.2d at 249 n. 4. Our refusal to consider Slattery's request for attorney fees is tantamount to a denial of that request, thus resolving that issue against Slattery. A trial court cannot consider the issue of entitlement to appellate attorney fees on its own initiative because this decision is the sole prerogative of the appellate court. TS 1 Partnership v. Allred, 877 P.2d 156, 160 n. 2 (Utah App. 1994); Yorke Management v. Castro, 406 Mass. 17, 546 N.E.2d 342, 344 (1989); Vinton Eppsco, Inc. of Albuquerque v. Showe Homes, Inc., 97 N.M. 225, 226, 638 P.2d 1070, 1071 (1981); Schere v. Z.F., Inc., 578 So.2d 739, 740 (Fla.3d Dist.Ct.App.1991). The only time a trial court has any discretion in the matter of appellate attorney fees is when an appellate court determines that appellate attorney fees are warranted, but remands the issue to the trial court for a determination of the amount to be awarded. Vinton Eppsco, 638 P.2d at 1071. Therefore, we reverse the trial court's award of appellate attorney fees to Slattery.
Furthermore, because we have determined that the trial court committed error when it conducted the supplemental evidentiary hearings on remand, the award of attorney fees to Slattery for expenses incurred in those hearings was also erroneous. Accordingly, Slattery is not entitled to any attorney fees or costs incurred in pursuing any stage of this matter.[5]

CONCLUSION
The trial court acted outside the scope of the remand when it conducted evidentiary hearings to determine, and subsequently awarded, the value of Slattery's personal stock and her attorney fees and costs. We therefore reverse the trial court's award to Slattery of the value of her personal stock and of her attorney fees and costs.
We reverse and remand to the trial court for entry of a final judgment consistent with this opinion.
DAVIS, Associate P.J., and BENCH, J., concur.
NOTES
[1]  "Sell-out" refers to Covey's practice of selling, on the open market, the unpaid-for securities in the delinquent accounts. These sales could either net a loss or a profit, depending on the prevailing rate for the securities, which would then be entered in the broker's error account.
[2]  This total included a credit to Slattery's error account in the amount of $3,713.71. The trial court made the specific corrections to this credit which we indicated in Slattery I. 857 P.2d at 248. Apparently these corrections were satisfactory, because neither side has contested them.
[3]  The conspicuous lack of instruction on this point should be contrasted with the issue of credits for Slattery's office expenses. On this previous point, where we desired that the trial court should act, we gave very specific and unambiguous directions. Slattery I, 857 P.2d at 248.
[4]  Counsel for Slattery argues that our binding the hands of the trial court creates an anomalous situation in that Covey receives a windfall and retains Slattery's securities. We find no indication in the record of any windfall to Covey. Furthermore, Slattery may well be entitled to the actual securities. However, as counsel so candidly admitted, the securities themselves are essentially worthless, so possession of them is not a hotly contested issue.
[5]  Slattery also requested attorney fees and costs incurred in this appeal. Due to our disposition of this appeal in favor of Covey, there is no basis for such an award.
