"Play Melancholy Baby"

It's clear that even as early as the 40's "My Melancholy Baby" was considered to be some kind of ultimate Tin Pan Alley warhorse -- Judy Garland belts it out vaudeville-style in A Star Is Born, and it's what old-timer Edward G. Robinson hears in his head when he encounters the femme fatale in Scarlet Street. So the definitive, "hit" version of the song must go way, way back -- any ideas as to what that might be?

Like a lot of standards, it's easy to hear a lot of versions of it without trying too hard -- Crosby, Sinatra, Benny Goodman, Ray Charles, Dave Brubeck, ad infinitum. Monk does a nice version, and my favorite swing-style version is by Sonny Stitt. Derek Bailey deconstructs it, and there's a campy Mamas & Papas-style take with fuzz guitar by the Sapphire Thinkers. Any other recommendations?