
113 Cal.App.3d 243 (1980)
169 Cal. Rptr. 685
CALIFORNIA UNION INSURANCE COMPANY, Plaintiff and Respondent,
v.
CLUB AQUARIUS, INC., et al., Defendants and Appellants.
Docket No. 57856.
Court of Appeals of California, Second District, Division Four.
December 12, 1980.
*245 COUNSEL
Brown & Martin and Carl R. Brown for Defendants and Appellants.
Wise & Nelson, Anthony F. Wiezorek and Michael J. Pearce for Plaintiff and Respondent.
OPINION
KINGSLEY, Acting P.J.
Defendants appeal from a judgment in favor of an insurer in an action for declaratory relief. We affirm the judgment.
*246 Defendants procured from plaintiff insurance company a policy which, by indorsement, insured them against liability in connection with two named publications  "Aquarius" and "Diving Dealer and Professional Instructor." In 1974, defendants were sued in federal court for copyright infringement and unfair competition. The complaint in that action named as offending publications only a book referred to as the "Red Book." Defendants, having retained counsel[1] tendered defense of that action to plaintiff. Plaintiff responded by a letter reading as follows:
"We acknowledge receipt of a copy of a Complaint alleging copyright infringement and unfair competition, Civil Action No. C-74-2168 filed in the U.S. District Court for the Northern District of California on October 10, 1974.
"As you are aware, Publisher's Libel Insurance was added to your coverage by endorsement effective January 19, 1974 and much, if not all, of the issues involved in this litigation pre-date this added coverage. Additionally it is our understanding that this present litigation is essentially a continuation of a similar law suit instituted prior to January 19, 1974 and of which we had no knowledge when adding this additional coverage effective January 19, 1974.
"After a careful review of the allegations set forth in the Complaint together with attendant correspondence, all of which must be considered subject to the terms, conditions and limitations of our policy of insurance, we offer the following:
"(1) We will assume cost of defense for the entire action.
"(2) We do not cover punitive damages, and should there be any award rendered based on count (4) of the prayer for damages seeking exemplary damages, our policy will not respond.
"(3) We do not afford coverage for injunctive relief.
"(4) As applicable Publisher's Libel Insurance coverage did not incept until January 19, 1974, should an award be rendered based on compensatory sustained, our policy will not respond for that portion of the award charged to any time period prior to January 19, 1974 and *247 September 1974, it is expressly stipulated that we reserve all our rights under the policy to disclaim coverage; and the aforesaid action is not to be construed as a waiver on our part of any of our rights under said policy nor to estop us from asserting any of said rights in the future.
"Please acknowledge receipt of this letter and we would ask that defense counsel keep us advised as the matter develops." Defendants' privately retained counsel agreed to the terms of that letter and the trial of the action therein referred to proceeded. The private counsel reported to counsel designated by plaintiff and their fees were paid by plaintiff. The trial was bifurcated and the liability issues were first tried. That portion of the trial resulted in findings of fact imposing liability on defendants for the publication of the "Red Book" (and, as incident thereto, the repetition of offending parts of that book in another book known as the "Black Book"). No finding was made that either of the two publications expressly mentioned in the insurance policy had infringed the rights of the plaintiff in that action. Plaintiff thereupon proposed to withdraw from supporting the defense in the damage portion of the case and filed the present action for declaratory relief, praying for a declaration that its obligation to defend had come to an end.

I
(1a) We think it clear that, except as the letter above quoted may have imposed on plaintiff an obligation broader than its policy created, plaintiff had a right to withdraw from the defense once the federal court, by its findings, had made it clear that the case, in fact, did not involve the limited risk set forth in that policy. (Firco, Inc. v. Fireman's Fund Ins. Co. (1959) 173 Cal. App.2d 524, 528 [343 P.2d 311].) (2) That is a reasonable rule since, under the holding of Firco and of Gray v. Zurich Ins. Co. (1966) 65 Cal.2d 263 [54 Cal. Rptr. 104, 419 P.2d 168], there exists a duty on the insurer to defend an action if potential liability to pay exists, even though that potential liability to pay is remote.

II
(1b) The chief contention of defendants here is that, by the letter above quoted, plaintiff had assumed an obligation to defend broader than the policy required. That claim is based on the use, in the letter above quoted, of the provision: "We will assume the cost of the defense *248 for the entire action." As did the trial court, we reject that contention. An insurer, bound to defend an action against its insured, must defend against all of the claims involved in that action, even though some (or as in this case all) of them ultimately result in recovery for damages not covered by the policy. In Hogan v. Midland National Ins. Co. (1970) 3 Cal.3d 553, at page 564 [91 Cal. Rptr. 153, 476 P.2d 825], the Supreme Court so held, citing cases from other jurisdictions and pointing out the practical impossibility of an allocation in the typical case. The reference in the letter to the "entire action" was but a recognition of that obligation.
However, Hogan expressly recognized an exception to that general obligation in cases where the insurer could "produce undeniable evidence of the allocability of special expenses." That is the case before us. The insurer stands in the position of having shown that the expenses of defending its insured against damages expressly found to be beyond its coverage, is allocable. It has furnished, in the amount of $175,000, a defense on the "entire" liability issue; it need not defend against the remaining portion of the action, as to which it has no obligation to pay.
(3) Defendants argue that the trial court improperly excluded extrinsic evidence that would have shown that the insurer had, by its conduct, shown that it had waived the right above considered. We can see in the proffered evidence no more than that, during the liability phase of the federal trial, the insurer had indicated a willingness to settle the claims therein made. But a willingness to avoid further litigation costs, and to avoid a then potential findings of damages covered by the policy does not show that the insurer, settlement not having been achieved, had waived its right to stand on its rights once it became clear that it could not be subject to pay anything in settlement of a judgment.

III
(1c) Defendants also contend that plaintiff is estopped now to withdraw from paying for the defense because they and their private counsel "relied" on the assumption that plaintiff's subsidy would continue through the damage phase of the trial. The contention is without merit. The private counsel were retained and assumed the duty to try the case to its finish before plaintiff entered the picture. Those counsel are not asked to step into a case in midstream; they are in the same position of any defense counsel in a bifurcated trial. The insurer's withdrawal imposes on them, and on the defendants, no burden that they should not *249 have anticipated once they received the letter reserving the rights of the insurer.
(4) (See fn. 2.) The judgment is affirmed.[2]
McClosky, J., and Laidig, J.,[*] concurred.
NOTES
[1]  The same counsel as represent them on this appeal.
[2]  We have before us a request by the defendants to receive new evidence on appeal. We deny the request. It is well settled that such a request will not be granted, except in rare cases, unless the evidence proffered would result in an affirmance and, thus, necessarily avoid further litigation in the trial court. The only exception is where the proffered evidence will compel both a reversal and a direction to a trial court to enter judgment for the moving party without further proceedings. (See 6 Witkin, Cal. Procedure (2d ed. 1971) Appeal, § 569, pp. 4505-4506.) The evidence here proffered does not fall within that limited exception. At best, it would afford a trial court, on a retrial, an opportunity to consider additional matters on the estoppel issue; it would not compel a finding, after a retrial, in favor of defendant.
[*]   Assigned by the Chairperson of the Judicial Council.
