As Billy Wilder prepared to make "Some Like It Hot," his classic comedy about two jazz musicians forced to go on the run as women after they witness a gangland massacre, he found himself in a bit of a casting quandary. His first choices for the roles of the casanova saxophone player Joe and nervy bassist Jerry were, respectively, Tony Curtis and Jack Lemmon. Though he eventually cast the stars he wanted, getting United Artists to accede to his demands was a circuitous process.

The primary stumbling block was Lemmon. The then 34-year-old actor was very much in demand after winning Best Supporting Actor for his portrayal of Ensign Pulver in John Ford and Mervyn LeRoy's blockbuster "Mister Roberts," but he was under contract to Columbia Pictures at the time, and considered unbankable as a leading man. Though Lemmon had given Wilder a verbal commitment to star alongside the already signed Tony Curtis,...