Olivor also eased her way into the burgeoning New York City cabaret scene of the early 1970s. She appeared at the Reno Sweeney cabaret, owned and operated by Lewis Friedman and Eliot Hubbard, which Vito Russo described as "the center of the universe during the now-legendary cabaret revival of the early 1970s". Working steadily in the New York City cabaret scene, Olivor became noticeable enough for the Columbia Records label and the William Morris Agency to sign her. Her debut album, "First Night", released in 1976, was named "Stereo Review"s Album of the Year.