
2 S.W.3d 393 (1999)
MID-CONTINENT CASUALTY COMPANY, Appellant,
v.
SAFE TIRE DISPOSAL CORPORTION, Safe Tire Disposal Corporation of Texas, and Scott Holden, Appellees.
No. 04-98-01048-CV.
Court of Appeals of Texas, San Antonio.
June 23, 1999.
*394 Kevin J. Cook, James Clyde Allums, Payne & Blanchard, L.L.P., Dallas, for appellant.
Lyndon F. Bittle, Frank Michael Prince, Cathy L. Altaian, Carrington, Coleman, Sloman & Blumenthal, Dallas, for appellee.
Before: TOM RICKHOFF, Justice SARAH B. DUNCAN, Justice KAREN ANGELINI, Justice.

OPINION
Opinion by: SARAH B. DUNCAN, Justice.
Mid-Continent Casualty Co. appeals the trial court's judgment (1) declaring it must defend Safe Tire Disposal Corp., Safe Tire Disposal Corp. of Texas, and Scott Holden in a suit brought against them by Cecil Booth and Deborah Markwardt; (2) denying Mid-Continent's request for attorney's fees; and (3) ordering Mid-Continent to pay Safe Tire $5,000 in attorney's fees. *395 Because the settlement of Booth's and Markwardt's suit moots Mid-Continent's appeal of the duty to defend issue, we vacate this aspect of the trial court's judgment and dismiss this aspect of Mid-Continent's appeal. In all other respects, we affirm the trial court's judgment. We also hold Mid-Continent's appeal is frivolous and injures the appellees. As a result, we assess $5000 in damages against Mid-Continent pursuant to Rule 45 of the Texas Rules of Appellate Procedure.

Factual and Procedural Background
Mid-Continent filed this declaratory judgment action seeking a determination it did not owe a duty to defend Safe Tire Disposal Corporation, Safe Tire Disposal Corporation of Texas, and Scott Holden, the president of Safe Tire Disposal Corporation of Texas (collectively "Safe Tire"), against a suit filed in April 1988 in Ellis County by Cecil Booth and Deborah Markwardt for bodily injury and property damage they allegedly suffered as a result of a December 1995 fire at Safe Tire's plant in Midlothian, Texas and Safe Tire's dumping of wastewater. Safe Tire timely answered and, shortly thereafter, moved for summary judgment, contending Mid-Continent was collaterally estopped from relitigating the duty to defend issue by the July 8, 1998 judgment in Cause No. 54,913, styled Safe Tire Disposal Corp., et al. v. Mid-Continent Cas. Co., in the 40th Judicial District Court in Ellis County, Texas. See Mid-Continent Cas. Co. v. Safe Tire Disposal Corp., No. 10-98-00294-CV (Tex. App.-Waco) (submitted May 19, 1999). Mid-Continent filed a cross-motion arguing the claims in Booth are excluded from coverage and thus it has no duty to defend the suit. Both Safe Tire and Mid-Continent also sought attorneys' fees. The trial court declared Mid-Continent must defend Safe Tire in Booth and thus denied Mid-Continent's motion and granted Safe Tire's. The trial court also ordered Mid-Continent to pay Safe Tire $5,000 for attorney's fees. Mid-Continent appealed.

Duty to Defend
Although not mentioned in Mid-Continent's opening brief, Booth was settled and the cause was dismissed with prejudice before Mid-Continent filed its opening brief in this court. Safe Tire thus argued in its opening brief that the duty to defend issue is moot. In its reply brief, Mid-Continent admits Booth has settled, and the only live controversy remaining before this court is the dispute over attorney's fees.
"`[I]t is axiomatic that appellate courts do not decide cases in which no controversy exists between the parties.' Accordingly, if no controversy continues to exist between [the parties], the appeal is moot and this court must dismiss the cause." General Land Office v. OXY U.S.A., Inc., 789 S.W.2d 569, 570 (Tex. 1990) (quoting Caniarena v. Texas Employment Comm'n, 754 S.W.2d 149, 151 (Tex.1988)). Similarly, when an appellate court's jurisdiction is incomplete, it must dismiss that part of the appeal over which it has no jurisdiction. Metzger v. Sebek, 892 S.W.2d 20, 55 ((Tex.App.-Houston [1st Dist.] 1994, writ denied), cert, denied, 516 U.S. 868, 116 S.Ct. 186, 133 L.Ed.2d 124 (1995).
Because Booth has settled and the cause has been dismissed with prejudice, we vacate the trial court's judgment to the extent it declares "Mid-Continent is obligated to provide Safe Tire a defense of the lawsuit pending in the 40th Judicial District, Ellis County, Texas, styled, Cecil Booth and Debra Markwardt v. Safe Tire Disposal Corp., No. 57141, which arose in part out of the December 1995 fire at Safe Tire's Facility in Midlothian, Texas" and, to this extent, dismiss Mid-Continent's appeal. We retain jurisdiction over Mid-Continent's appeal of the attorney's fee award. See Camarena, 754 S.W.2d at 151 (Tex.1988).

Attorney's Fees
Mid-Continent contends the trial court erred in ordering it to pay Safe Tire $5000 *396 tor attorney's tees because it was not obligated to defend Safe Tire in Booth. We disagree.
A trial court may award reasonable and necessary attorney's fees in a declaratory judgment action if it concludes an award is equitable and just. Bocquet v. Herring, 972 S.W.2d 19, 20 (Tex.1998). On appeal, an award is reviewed for an abuse of discretion. Id. at 21. "It is an abuse of discretion for a trial court to rule arbitrarily, unreasonably, or without regard to guiding legal principles, or to rule without supporting evidence." Id. (citations omitted).
The doctrine of collateral estoppel or issue preclusion "precludes the relitigation of identical issues of facts or law that were actually litigated and essential to the judgment in a prior suit. Once an actually litigated and essential issue is determined, that issue is conclusive in a subsequent action between the same parties." Van Dyke v. Boswell, O'Toole, Davis & Pickering, 697 S.W.2d 381, 384 (Tex.1985). Mutuality of parties is required only with respect to the party against whom collateral estoppel is asserted. Sysco Food Servs., Inc. v. Trapnell, 890 S.W.2d 796, 802 (Tex. 1994). Because the doctrine "is designed to promote judicial efficiency, protect parties from multiple lawsuits, and prevent inconsistent judgments by precluding the relitigation of issues," id. at 801, a judgment is final for purposes of collateral estoppel even if an appeal is pending. Scurlock Oil Co. v. Smithivick, 724 S.W.2d 1, 6 (Tex.1986).
The summary judgment evidence establishes, and Mid-Continent concedes, it actually litigated its duty to defend Safe Tire from claims arising out of the December 1995 fire in the Ellis County declaratory judgment action. But, Mid-Continent contends, the court in the Ellis County case did not decide Mid-Continent's duty to defend the Booth suit and thus that judgment does not have any collateral estoppel effect. We disagree. The Ellis County judgment expressly declares and adjudges, "based on the Court's construction of the `pollution exclusion' and other provisions contained in the policy Mid-Continent issued to Safe Tire, that the claims asserted against Safe Tire arising out of the December 1995 fire at Safe Tire's facility in Midlothian, Texas are not excluded from coverage under the pollution exclusion." The issues litigated and decided in the Ellis County declaratory judgment action are identical to those Mid-Continent sought to litigate in this case.
Because the summary judgment evidence conclusively establishes Mid-Continent actually litigated the duty to defend issue in the Ellis County declaratory judgment suit and the resolution of this issue was essential to the court's judgment, Mid-Continent is collaterally estopped from relitigating the issue of its duty to defend Safe Tire from claims arising out of the December 1995 fire. Consequently, the trial court did not err in granting a summary judgment against Mid-Continent to preclude its relitigation of the duty to defend issue in this suit. Nor did it abuse its discretion in requiring Mid-Continent to pay Safe Tire $5000 in attorney's fees.

Sanctions
In a cross-point, Safe Tire argues frivolous appeal damages should be assessed against Mid-Continent. We agree.
Before the most recent amendments to the Texas Rules of Appellate Procedure, this court was authorized to award limited "damages for delay" only if it found "that an appellant ha[d] taken an appeal for delay and without sufficient cause." Tex.R.App. P. 84 (repealed). However, effective September 1, 1997, this court is authorized to award "just damages" if it "determines that an appeal is frivolous" from consideration of "the record, briefs, or other papers filed in the court of appeals." Tex.R.App. P. 45. This rule revision arose in part at the urging of *397 a scholarly critique of the narrowing effect of the 1986 amendment of the appellate sanctions rule. See David Lopez, Why Texas Courts are Defenseless Against Frivolous Appeals: A Historical Analysis With Proposals for Reform, 48 Baylor L. Rev. 51 (1996) (advocating amendment). Under the current rule, "just damages" are permitted if an appeal is objectively frivolous and injures the appellee. See id. at 147 (noting that an appeal was frivolous under Texas law before the 1986 amendments if it was without merit and either injured an appellee or was filed in bad faith). Bad faith is thus no longer dispositive or necessarily even material. See id; see also Diana Rivera & Assocs. v. Calvillo, 986 S.W.2d 795, 799 ((Tex.App.-Corpus Christi 1999, pet. filed) ("In determining whether sanctions are appropriate, we must decide whether Rivera had a reasonable expectation of reversal or whether she pursued the appeal in bad faith.") (citing Tate v. E.I. DuPont de Nemours & Co., 954 S.W.2d 872, 875 ((Tex.App.-Houston [14th Dist.] 1997, no pet.)) (emphasis added).
We have no hesitancy in concluding Mid-Continent's appeal is objectively frivolous. No reasonable attorney could fail to conclude this court would uphold the trial court's summary judgment and its attorney's fees award. Nor is there any doubt Mid-Continent's appeal has injured Safe Tire, at least to the extent of the $5,000 in reasonable and necessary attorney's fees it proved it would incur if an appeal were filed. See Swate v. Crook, 991 S.W.2d 450, 456 ((Tex.App.-Houston [1st Dist.] 1999, no pet. h.) (awarding appellate attorney's fees as damages under Rule 45); Calvillo, 986 S.W.2d at 799 (same). Therefore, having given Mid-Continent notice and an opportunity to respond to Safe Tire's request for damages, we assess $5000 in damages against Mid-Continent pursuant to Rule 45 of the Texas Rules of Appellate Procedure.

Conclusion
Because the underlying suit has been settled and the cause dismissed with prejudice, we vacate the trial court's judgment to the extent it declares "Mid-Continent is obligated to provide Safe Tire a defense of the lawsuit pending in the 40th Judicial District, Ellis County, Texas, styled, Cecil Booth and Debra Markwardt v. Safe Tire Disposal Corp., No. 57141, which arose in part out of the December 1995 fire at Safe Tire's Facility in Midlothian, Texas" and, to this extent, dismiss Mid-Continent's appeal. In all other respects, the trial court's judgment is affirmed. In addition, we order Mid-Continent Casualty Company to pay Safe Tire Disposal Corporation, Safe Tire Disposal Corporation of Texas, and Scott Holden $5000 as frivolous appeal damages no later than fifteen days after the date the mandate issues. All costs are likewise assessed against Mid-Continent Casualty Company.
