NOBODY ELSE BUT ELSIE was used in the musical film "I Surrender Dear" in 1948. I don't think it was necessarily written for the film, though. TV Guide attributes the song to Allie Wrubel—incorrectly, I suspect, because it isn't mentioned on other Allie Wrubel websites.

NOBODY ELSE BUT ELSIE appears on the album Underneath the Arches by Henry Hall. That page is supposed to have sound samples, but I couldn't get them to play.

The Sheetmusic Warehouse lists it, and attributes it to Archie Gottler, Irving Kahal, and James V Monaco.