I've always thought it was the other way round... :-(
After a little research, I'm not so sure anymore about my earlier statement that John Williams was responsible for the title theme only.
According to soundtrackcollector.com:
Killers, the (1964)
Composer(s): John Williams, Henry Mancini
Theme only (but by whom? Williams? Mancini?)
Released in: 1964
Genre: Crime, Drama, Mystery, Neo-noir
according to imdb.com:
Music by
John Williams ... (as Johnny Williams)
Fred Steiner ... (uncredited)
[no mention about Henry Mancini at all!]
Then I found the opening credits on youtube:
The Killers (1964) Opening Credits (John Williams) - YouTube (
http://www.youtube.com/watch?v=T3adsdiDfJs)
This is what the credit card in the clip is stating:
Music score: Johnny Williams (in later movies, he changed his credited name to John Williams)
Song: "Too Little Time"
Henry Mancini and Don Raye
This seems to indicate that John Williams most probably wrote the complete score, after all, and Henry Mancini (together with Don Raye) was responsible for the song "Too Little Time".