In 1964 Tate made a screen test for Sam Peckinpah opposite Steve McQueen for the film "The Cincinnati Kid". Ransohoff and Peckinpah agreed that Tate's timidity and lack of experience would cause her to flounder in such a large part, and she was rejected in favor of Tuesday Weld. She continued to gain experience with minor television appearances, and after she auditioned unsuccessfully for the role of Liesl in the film version of "The Sound of Music", Ransohoff gave Tate walk-on roles in two motion pictures in which he was the producer: "The Americanization of Emily" and "The Sandpiper". In late 1965, Ransohoff finally gave Tate her first major role in a motion picture in the film "Eye of the Devil", costarring David Niven, Deborah Kerr, Donald Pleasence, and David Hemmings.