Robert Mitchum was good in just about any film. He personified cool with a sleepy, fed-up expression and a deliberate walk. What I love most about Two for the Seesaw (1962) is New York City from my earliest memories and André Previn's score. The wandering trumpet belongs to Uan Rasey, a warm-up of sorts for his humid, wandering solo throughout Chinatown (1974), set in Los Angeles of the 1930s. Among the other soloists on the Seesaw score are Ronnie Lang (as), Dick Nash (tb) and Jackie Cain singing on the film's soundtrack album.
Here's Robert Mitchum and Shirley MacLaine in Two for the Seesaw (above), directed by Robert Wise...
Bonus: Here's Jackie Cain singing the theme...