Okay jaimeeduardo, you left out the possibility that I never expected that info to be there. I tracked it down anyway, and I've ordered this single: http://www.45cat.com/record/930059
An obscure but valuable release, which apparently was not on any album at the time.
I had checked for a rerecording on Bewitching-Lee, but not.
According to information shown in the images, the recording dates from Jan. 1956. Available on CD: Black Coffee and Other Delights (MCA/Decca MCAD2-11122). The images should be legible unless your connection is poor, or if you are unable to view images for some reason.
This recording of Peggy Lee - I Don't Know Enough About You - which year was it recorded, and where found? It's not the early original and I can't find another.
Sounds like ~1960, much better production.