McDermott Will & Emery thought it had given its client Eastman Kodak Co. a picture-perfect ending to a long-running tax case. After more than 10 years of work, McDermott scored a $581 million tax refund for Kodak related to an unsuccessful business venture the company had made.

But when it came time to collect a $24 million contingency fee, the firm says, Kodak balked.