Kiss Them For Me - Jayne tribute by Siouxie and the Banshees
I can't believe I never heard of this song until the last month - and it was actually a modest hit!! http://en.wikipedia.org/wiki/Kiss_Them_for_Me_(song)
Somebody made a video of it with Jayne footage http://vimeo.com/76886030 - there's also a few other Jayne videos at vimeo including a 1950's interview in France and footage of her singing "I Enjoy Being a Girl" with Milton Berle and Martha Raye.