
818 P.2d 475 (1991)
ROBERT L. WHEELER, INC., d/b/a Robert Leyton Wheeler, Inc., Appellant.
v.
Robert L. SCOTT, Appellee.
No. 74284.
Supreme Court of Oklahoma.
October 1, 1991.
Robert L. Wheeler, pro se.
Donald K. Blackwell and Joseph A. Fox, Moricoli, Wilson, Harris, Cottingham & Hurst, Oklahoma City, for appellee.
*477 ALMA WILSON, Justice:
The present appeal is from a judgment of the trial court which heard the cause upon remand from a prior appeal, Robert L. Wheeler, Inc. v. Scott, 777 P.2d 394 (Okla. 1989). The appellant, Robert L. Wheeler, Inc., filed an action against the appellee, Robert L. Scott, to collect unpaid attorney fees. Wheeler billed Scott $140,116.87, which the trial court reduced to $125,723.00. The Court of Appeals affirmed the trial court. This Court vacated the opinion of the Court of Appeals, and reversed and remanded the judgment of the trial court finding that the fee was still excessive. We directed the trial court to determine a reasonable attorney's fee in accordance with the standards enunciated in State ex rel. Burk v. Oklahoma City, 598 P.2d 659 (Okla. 1979), and Oliver's Sports Center v. National Standard Ins., 615 P.2d 291 (Okla. 1982).
Upon remand, the trial court issued a letter opinion, signed and filed by the trial judge, reducing the attorney's fee from $125,723.00 to $75,500.00. The trial court added $1,349.00 for expenses, and subtracted $52,606.00 as the amount previously paid by Scott. This resulted in a judgment for $24,243.00. The trial court subsequently awarded attorney's fees and costs to the appellant in the amounts of $14,059.75 and $1,349.00, respectively. Both parties appealed.

I. MOTION TO DISMISS WHEELER'S APPEAL
On July 19, 1990, Scott filed a motion to stay the execution of the judgment, or alternatively, to dismiss the appeal of Wheeler. In his brief supporting the motion, Scott alleged that Wheeler had taken inconsistent positions by filing an appeal of his judgment while simultaneously executing on the judgment. Attached as an exhibit to Scott's brief is a copy of a garnishment affidavit filed May 3, 1990, and a garnishment summons issued the same date.[1] The affidavit states that Scott is indebted to Wheeler in the sum of $24,243.00 and for an attorney fee of $14,059.75 and $1,349.00 for the costs of the action. In his brief objecting to Scott's motion, Wheeler does not deny that he had sought to collect the judgment amount.
The rule is well established that any act by an appellant that recognizes the validity of a judgment either expressly or by implication, operates as a waiver of the appellant's right to appeal from the judgment. Mosier v. Mosier, 121 Okl. 4, 246 P. 1099 (1926). Litigants who voluntarily accepted the fruits of a judgment cannot bring an appeal to reverse it because accepting the benefits of the judgment waives the right to appeal the portion detrimental to that litigant. Adams v. Unterkircher, 714 P.2d 193, 196 (Okla. 1985). Although *478 Wheeler admits he has attempted to collect on the judgment, there is nothing in the record to reveal that he has succeeded in receiving any part of the awarded judgment. Additionally, there is no record of a supersedeas bond having been posted to stay the execution on the judgment against Scott.[2]
The issue is whether an attempt by an appellant to execute on the judgment from which he appealed results in a waiver of the appeal under the "acceptance of benefits" doctrine, even though the appellant received nothing from the attempted execution. The issue before us is one of first impression. The authority on this issue is meager.
The authority which exists supports a rule that benefits must actually be received by an appellant in order to waive his right to an appeal.[3] Oklahoma case law recognizes similar principles. In Bras v. Gibson, 529 P.2d 982, 983-984 (Okla. 1974), this Court held that a party who accepts the benefits of the part of the judgment favorable to him waives the right to appeal the portion that is unfavorable. The Court explained:
Bras needed only to appeal the trial court's actions to protect his interest. His act in cashing the voucher was voluntary and for his benefit. That act was not done in defense of an to protect his rights. As to the trial court's orders, Bras could do nothing more than object and appeal. As to the voucher, Bras could accept or refuse. This was his choice. [Emphasis added.]
The implication of the emphasized sentence in Bras is that acts done in defense of or to protect one's rights may not constitute a waiver of a party's right to appeal under the acceptance-of-benefits doctrine. Such a case is now before this Court. In order to constitute a waiver, a party must intend to relinquish a known right, either expressly or by such conduct as warrants an inference of such a relinquishment. Atlas Life Ins. Co. v. Schrimsher, 179 Okl. 643, 66 P.2d 944, 948 (1937).[4] A mere attempt to collect a judgment does not relinquish the right to appeal because no fruits of the judgment have been accepted. Wheeler's attempt to collect his judgment may have been motivated by a desire on Wheeler's part to force Scott to post a supersedeas bond.[5] Use of such a tactic is not improper and is not inconsistent with *479 an appeal. Because there is nothing in the record to show that Wheeler accepted any of the benefits of his judgment, the motion to dismiss his appeal is denied.
Scott also moves this Court to stay execution of the judgment citing Rule 1.31(b) of the Rules of Appellate Procedure in Civil Cases, 12 O.S.Supp. 1990, ch. 15, app. 2.[6] Scott alleges the trial court denied his motion to stay, and he attaches merely a copy of a pre-trial conference order, not a document of record, of the garnishment proceeding. The copy notes: "Motion to stay overruled" and appears to be signed by the trial judge, no order appears in the record. Because the order is not a part of the record, it cannot be reviewed. Chamberlin v. Chamberlin, 720 P.2d 721, 723-724 (Okla. 1986). The motion to stay is dismissed.

II. WHEELER'S APPEAL
Wheeler argues that the trial court erred by utilizing only certain facts emphasized in this Court's opinion in Wheeler's first appeal. Wheeler challenged several facts as stated in the opinion alleging that these facts were contrary to testimony during the first hearing before the trial court. In the second hearing, following the remand to the trial court, Wheeler addressed his concerns to the trial court that testimony and documents were cited by this Court that were not a part of the record. He argued that the trial court was not bound by the factual determinations that were addressed in this Court's opinion. Wheeler admitted to the trial judge that he had not petitioned for rehearing. The trial judge answered that he did not have the authority to find that the Supreme Court had gone outside the record or erred in its opinion.
In this appeal, Wheeler sets out the facts listed in this Court's opinion he considered to be erroneous and not supported by the record. One purpose of permitting a rehearing is to allow a party to assert what he perceives to be errors in factual statements cited in an opinion of this Court. By failing to petition for rehearing, Wheeler waived his right to challenge any of those statements. This does not prevent this Court from reviewing the trial court judgment to determine if the trial court followed this Court's directions. Where a case is remanded, the trial court is bound by the settled law of the case. The settled law of the case bars relitigation of only those issues that have been settled by an appellate opinion. Mobbs v. City of Lehigh, 655 P.2d 547, 549, 31 A.L.R. 4th 1 (Okla. 1982).
The trial court had set the attorney fee in the remanded case at $125,723.00. The opinion analyzed the fee pursuant to the twelve guidelines listed on pages 395 and 396 of the opinion. Our opinion concluded that the fee allowed by the trial court was excessive. Robert L. Wheeler, Inc., 777 P.2d at 398-399. But we added that making an initial determination of question of fact was not the function of this Court. Robert L. Wheeler, Inc. 777 P.2d at 399. The opinion determined that the attorney fee awarded was too high, and articulated the legal method to be used in setting the fee. This left the trial court free to make initial determinations of fact. Upon remand the trial court made new findings of fact, which the trial court had the authority to do.
Wheeler complains that our opinion should have been guided by the rules of contract instead of principles of equity. Whether this Court considers this case as one of contract, and therefore an action at law, or one in equity determines the extent of review, that is, how this Court views the facts found by the trial court. In cases of purely equitable cognizance, the entire record will be examined and the evidence weighed, but a the judgment of the trial court will not be reversed unless it appears to be clearly against the weight of the *480 evidence. Oklahoma Company v. O'Neil, 440 P.2d 978, 990 (Okla. 1968). Judgment of the appellate court should not lightly displace the judgment of the trial court, which had the advantage of observing the witnesses on the stand. Renegar v. Staples, 388 P.2d 867, 873 (Okla. 1964). In a case involving the breach of a contract, the credibility of witnesses and the effect and weight to be given to testimony are questions of fact to be determined by the trier of the facts, whether court or jury, and are not questions of law for the Supreme Court on appeal. M-A-C Finance Co. of Tulsa v. Parker, 408 P.2d 552, 556 (Okla. 1965). In an action at law, the findings of fact by the trial court have the same force and effect as the verdict of a jury, and those findings will not be disturbed upon appeal where there is any evidence reasonably tending to support the findings. Bounds v. Gooch, 92 Okl. 260, 219 P. 105, 106 (1923).
Neither the Burk case nor the Oliver's Sports Center case involved a contract for attorney fees between a lawyer and his client. Burk involved the fixing of attorney fees from a "common, equitable fund created for the City through the efforts of attorneys." The Oliver's Sports Center case involved the awarding of attorney fees based upon 36 O.S.Supp. 1977 § 3629(B), which is a prevailing party statute. This Court has allowed attorney fees that were fixed by contract to be enforced even though the fees were greater than a court of equity may have allowed on a quantum meruit basis. Bishop v. Franks, 188 Okl. 196, 107 P.2d 358, 359-360 (1940). Nevertheless, even where there is a contract between the lawyer and his client for a certain fee, the contract will not be upheld or enforced where the compensation is so excessive as to evidence a purpose on the part of the attorney to obtain an improper or undue advantage over the client. Renegar v. Staples, 388 P.2d 867, 872 (Okl. 1964). Although this case remains an action at law because it is one of contract, under Renegar the trier of fact may still determine that the compensation was so excessive as to be overreaching, and the Robert L. Wheeler, Inc. case and the reasoning therein is proper authority for making such a determination.
We agree with Wheeler that a simple, basic comparison of the billable hours of the advocates does not determine what is a reasonable "cap" on those billable hours. There are at least two parties to every lawsuit, and each party is faced with different research, modes of strategy and levels of preparation and paperwork. Likewise, the levels of proficiency, experience, and ability may not be equal. If one side of a lawsuit is considered to be "simple" then the opposing counsel may have a more complex and difficult task making a case to overcome that simplicity and prevail. The billable hours will likely reflect those differences. Unfortunately, the trial court read our opinion as placing an outer limit upon attorney's fees based on the billable hours of the prevailing party. Because there is some evidence that the number of billable hours should have been reduced, we do not reverse those factual findings of the trial court.
Nevertheless, there is a mixed question of law and fact concerning whether Wheeler's hourly rate should have been reduced. The parties agreed that the fee would be based on an hourly rate. Robert L. Wheeler, Inc., 777 P.2d at 397. The transcript of the first hearing, which was relied upon in the hearing after remand reveals that Scott admitted Wheeler had told him what the hourly fees would be. Scott: "He [Wheeler] told us that the hourly rates for his associates would be ninety dollars an hour and that his rate would be a hundred and thirty-five dollars an hour." That Scott agreed to the hourly rate is uncontradicted. That Scott had prior dealings with lawyers is uncontradicted. Although the trial court may have found that he did not agree to an unreasonable number of hours, there is no evidence to show that he was overreached by agreeing to an hourly fee of ninety dollars for associates and one hundred and thirty-five dollars for Wheeler's fees. Therefore, as a matter of law, we find that the contract should be enforced at the rate agreed upon. The *481 trial court found that Wheeler expended a total of 390.7 hours, and that the hours expended by the associates which the court considered reasonable were 459.3.[7] This would result in a fee of $41,337.00 for the associates and $52,744.50 for Wheeler for a total attorney's fee of $94,081.50.[8] This amount is less than the $125,723.00 this Court found unreasonable in its prior opinion, but more than the $75,500.00 awarded by the trial court.

III. SCOTT'S CROSS-APPEAL
In his cross appeal, Scott claims that the fee awarded by the trial court was excessive. He argues that because Wheeler presented no new evidence on remand from the first appeal, no evidence exists to support the conclusion that Wheeler is entitled to any fee in excess of the amount that Scott had already paid Wheeler for the services, $54,275.37. The instructions given to the trial court in the "Conclusion" of the original appeal did not require the trial court to hear new evidence concerning the setting of attorney fees. Wheeler, 777 P.2d at 399-400. This Court ordered, "A reasonable attorney's fee should be determined on remand is accordance with an appropriate balancing of the Burk and Oliver's factors discussed herein." Wheeler, 777 P.2d at 400. Scott does not show how the trial court failed to follow this Court's instructions upon remand. Scott's own expert testified in the first hearing the $75,500.00 was a reasonable compensation. Wheeler, 777 P.2d at 397. This Court has now determined that there was not error in the trial court's redetermination of the number of hours for Wheeler and his associates and has set a fee based upon the hourly rate to which Scott contractually agreed.
Finally, Scott appeals the amount awarded for attorney's fees and costs for Wheeler, as prevailing party in the remand hearing, in the amount of $14,059.75 for attorney's fees and $1,349.00 for expenses. Scott argues that because Wheeler failed to receive the full amount for which Wheeler prayed, Wheeler is not entitled to attorney's fees pursuant to 12 O.S. 1981, § 936 as the prevailing party.[9] He also argues that if Wheeler is awarded attorney's fees Wheeler is not entitled to fees that are nearly sixty percent of the amount awarded.[10]
Scott bases his argument that Wheeler is not entitled to attorney's fees as the prevailing *482 party upon policy. He states that § 936 suggests a policy designed to discourage the wrongful refusal to repay a debt owed by allowing the creditor to recover the costs incurred in judicially enforcing the creditor's rights. But Scott asserts that this policy is only served where litigation establishes that the creditor is entitled to the full amount or nearly the full amount claimed. Scott concludes that if the debtor were justified in withholding payment of a substantial portion of the amount claimed, the objective of discouraging the wrongful refusal to pay is not realized. Scott cites no case to support his argument. There is case law to the contrary.
In Hicks v. Lloyd's General Ins. Agency, 763 P.2d 85 (Okla. 1988), the plaintiff/appellant, Hicks, sued for $186,000.00 for breach of an employment contract. The defendant/appellee, Lloyd's General Insurance Agency filed two formal offers to allow judgment to be taken in the amounts of $6,863.00 and $15,000.00. After a trial, the jury awarded the plaintiff $6,750.00. Both parties sought attorney's fees. The trial court awarded the plaintiff attorney's fees of $5,400.00, which fees were assessed up to the time the defendant made his first offer, and awarded the defendant attorney's fees of $12,760.00, which were assessed from the first offer until judgment. The Court of Appeals reversed the award of attorney's fees to the defendant, but this Court granted certiorari, vacated the opinion of the Court of Appeals and affirmed the judgment of the trial court.
The Court cited the "American Rule" and the policy behind it[11] as the rationale for the holding that the defendant was the prevailing party where it had offered more in settlement prior to trial than the plaintiff had been awarded in judgment. The policy behind allowing the award of attorney's fees was to encourage settlement and to discourage the bringing of frivolous claims. Scott maintains in his "Brief of Appellee and Cross-Appellant" that Wheeler is not entitled to an amount over the $54,275.37[12] previously paid to Wheeler by Scott. Scott's own expert witness testified that $75,500.00 was reasonable compensation. Robert L. Wheeler, Inc., 777 P.2d at 397. Wheeler is the prevailing party as the trial court awarded a $24,243.00 judgment to him. In part II of this opinion, we have increased the amount awarded by the trial court. Wheeler is entitled to that attorney's fee as the prevailing party. We find that the trial court did not abuse its discretion in the amount of the prevailing party fee awarded.

CONCLUSION
The judgment of the trial court is MODIFIED in order to set Wheeler's attorney fee at $94,081.50, for the reasons set forth in part II of this opinion. In the first appeal, this Court found that Scott had already paid Wheeler $54,275.37. Robert L. Wheeler, Inc., 777 P.2d at 396. The settled law of the case doctrine operates to bar relitigation of issues that have been settled by an earlier appellate opinion in the case. Muncrief v. Memorial Hosp. of Southern Oklahoma, 767 P.2d 400 (Okl. 1988). Accordingly, Wheeler is awarded a judgment in the amount of $39,806.13 for his attorney's fees on his contract with Scott.
*483 The judgment of the trial court in the setting of prevailing party fees in the amount of $14,059.75 for attorney's fees and $1,349.00 for costs is AFFIRMED. Wheeler has moved this Court to also allow prevailing party attorney fees upon the decision of this second appeal. We have already determined that Wheeler is entitled, pursuant 12 O.S. 1981, § 936, to a prevailing party attorney fee. "Whenever there is statutory authority to award attorney fees in the trial of a matter, additional fees may be allowed (to the prevailing party) for legal services rendered in the appellate court." Sisney v. Smalley, 690 P.2d 1048, 1051 (Okl. 1984). Wheeler's motion for prevailing party attorney fees for this appeal is granted. Consequently, the cause is REMANDED to the trial court to determine and set prevailing party fees in favor of Wheeler in addition to those amounts awarded and affirmed by this Court.
OPALA, C.J., and LAVENDER, DOOLIN and KAUGER, JJ., concur.
HODGES, V.C.J., concurs in part, dissents in part.
SIMMS and HARGRAVE, JJ., dissent.
SUMMERS, J., dissents: I would affirm the trial court.
SIMMS, Justice, dissenting:
I dissent for the reason expressed by me in my dissent in Wheeler I, 777 P.2d 394 (Okla. 1989).
I am authorized to state that Justice HARGRAVE joins me in this dissent.
NOTES
[1]  An instrument which is not incorporated into the assembled record by a certificate of the clerk of the trial court is not considered a part of the appellate record, nor can a deficient record be supplemented by material physically attached to a party's appellate brief. Chamberlin v. Chamberlin, 720 P.2d 721, 723-724 (Okl. 1986). A narrow exception is recognized for uncontroverted extra-judicial facts which stand admitted in the briefs, and these may be regarded as supplementing the appellate record. Chamberlin, 720 P.2d at 724 n. 6.
[2]  Posting a supersedeas bond stays execution of judgment, but is neither a prerequisite nor a jurisdictional requirement to an appeal. Adams v. Unterkircher, 714 P.2d 193, 196 (Okl. 1985).
[3]  The Supreme Court of Iowa held that a plaintiff who appealed the judgment granted to him had not waived his right to prosecute the appeal, even though he had attempted to execute on the judgment but received nothing. Hornish v. Peck, 53 Iowa 157, 1 N.W. 641, 644 (1879), aff'd. on reh. 53 Iowa 157, 4 N.W. 898 (1880).

In McDaniel Gift Shop, Inc. v. Balfe, 179 So.2d 588 (Fla.App. 1965), the court held that the acceptance-of-benefits doctrine does not apply where the appealing party does not actually receive any of the benefits of the judgment. The court reasoned that a purpose of a judgment creditor in securing and delivering a writ of execution to the sheriff is frequently to cause the judgment debtor to post a supersedeas bond to protect the judgment creditor pending the appeal. The court stated that there was nothing irregular in such a tactic.
With similar reasoning, courts in three other states have held that recording a judgment was not "acceptance of benefits." Menges v. Robinson, 132 Cal. App. 647, 23 P.2d 526, 528 (Cal.Dist.Ct.App. 1933); Kittredge v. Graw, 158 La. 154, 103 So. 723, 724 (1925); Ellis v. Scarborough, 279 S.W. 857, 858 (Tx.Civ.App. 1926). The California and Texas cases gave as a rationale that the judgment creditor records his judgment simply as a precaution to provide some security for the satisfaction of the judgment should it be affirmed on appeal.
[4]  "Waiver by acceptance of benefits" may be distinguished from" estoppel by acceptance of benefits" in that estoppel requires that the party against whom the estoppel is claimed should have acted with knowledge of his rights, and the party claiming the estoppel was without knowledge of the facts on which he bases his claim of estoppel, that he was influenced by and relied on the conduct of the person sought to be estopped, and that he changed his position in reliance thereon to his injury. Harjo v. Johnston, 187 Okl. 561, 104 P.2d 985, 998 (1940). "Waiver by acceptance of benefits" does not depend upon the reliance of another party, but is unilateral.
[5]  If so, the attempt was apparently unsuccessful. Although Scott filed a cross-appeal, we have no record nor any allegation that a supersedeas bond was posted.
[6]  That rule provides: "Except as provided in Subdivision (a)(3), review of the trial court's ruling upon any of the matters set forth in this Rule shall be by motion filed in the Supreme Court which shall be entertained in the principal appeal. Armstrong v. Veiser, 54 OBJ 573 [Sup.Ct. No. 57,878, February 22, 1983]." Armstrong v. Trustees of Hamilton Inv. Trust, 667 P.2d 985, 987 (Okl. 1983).
[7]  The findings of the trial court concerning hours and rates for attorneys are as follows:



    ATTORNEY      HOURS          RATE            TOTAL
  Wheeler         390.7          90.00          35,163.00
  Brown           420.6          60.00          25,236.00
  Gaidaroff        .6            80.00             48.00
  Titterington     37.5          80.00           3,000.00
  Harrington        .6           80.00             48.00
                                               $63,495.00

[8]  The trial court set this fee at $63,495.00 and then added $12.005.00 to bring the total fee to $75,500.00, the amount which Scott's expert agreed would be a reasonable fee. There is no support in the evidence for the $12,005.00 addition except to bring the total fee up to the $75,500.00 amount. Therefore, we do not add that amount to the increased award.
[9]  Scott does not argue that 12 O.S. 1981, § 936 is inapplicable. We held in Kay v. Venezuelan Sun Oil Co., 806 P.2d 648 (Okl. 1991) that § 936 must be strictly applied and that an award of prevailing party attorney's fees shall be allowed in actions to collect money promised, whether evidenced by a promissory note, a negotiable instrument, an account whether for sale of tangible property or labor and services and a bill or a contract for goods sold and delivered. Kay, 806 P.2d at 651 n. 11. In the case at bar the trial court correctly granted § 936 prevailing party attorney's fees for successfully pursuing collection on an account for services.
[10]  This Court's redetermination of the attorney's fee based upon the number of hours found by the trial court and the amount Scott agreed to pay for those hours alters the ratio cited by Scott.
[11]  "According to the `American Rule' each party is to pay its own attorney's fees but in some situations attorney's fees are assessed against the losing party. The policy reasons supporting the recovery of attorney's fees and costs are to encourage settlement and to discourage the bringing of frivolous claims. These considerations recognized the limited availability of judicial resources and seek to penalize those which unnecessarily waste them." Hicks v. Lloyd's General Ins. Agency, 763 P.2d 85, 86 (Okl. 1988).
[12]  The letter decision of the trial court credits Scott with $52,606.00 as the amount which had been previously paid. The record of the original trial, and the opinion of this Court, Robert L. Wheeler, Inc. v. Scott, 777 P.2d 394, 396 (Okl. 1989), both support the amount previously paid as $54,275.37. "Where the facts on a second appeal of the case are practically the same as on the first appeal, the decision of the first appeal is the law of the case in all subsequent stages, and will not be reviewed on second appeal." Smith v. Owens, 397 P.2d 673, 678 (Okl. 1963).
