Instrumental by Lonnie Lee’s backing band. In the film it had lyrics written and sung by Peggy Lee.
Red Herring Department: In 1959 a record on the Planet label, Melbourne, My Baby Dolly, was
released by "Johnny Guitar with the Henri Bource All Stars and the Moontones" (listed at The First Wave [.pdf]). The identity of "Johnny Guitar" is unknown but
Henri Bource, saxophonist and flautist, was one of Australia’s earliest rock’n’rollers, and he was later a member of The Thunderbirds. In 1964 he was the victim of a shark attack, an incident he made a documentary about in 1969
(see listing at Australian Soundtracks).
But I digress…
Suggestion from Terry Stacey.
With the Victor Young Orchestra.
The title song of Nicholas Ray’s 1954 film starring Joan Crawford and Sterling Hayden. Lyrics by Peggy Lee. See IMDb entry.