Lest you think Sam Phillips was all Sun Records, country, blues and rockabilly, dig this one by Barbara Pittman. Though she's much better known for her big rockabilly side, "I Need A Man" (incidentally the only song I could think of off the top of my head), she veered. This one, "Handsome Man" is credited to "Barbara Pittman with Gene Lowery Singers", which should tell you something right there. It is not rockabilly, but some mix of torch singing, jazz and r&b. Still completely dig-able.
~ NOTE: ALL MEDIA IS HOSTED BY THE BLOGS & SITES NAMED BELOW ~Listen:
Barbara Pittman with Gene Lowery Singers - Handsome Man mp3 at Office Naps
Barbara Pittman - I Need A Man (streaming) at YouTube