'Fly Me to the Moon' and 'Tell Him' - Alma Cogan
If you never heard of Alma Cogan, especially if you like the swinging pop of the 1950s and '60s, you should definitely seek her out. It's amazing that she was almost unknown in the US, but in my opinion she could out-sing Petula Clark, Dusty Springfield, and all those other fondly remembered 'songstresses.'
Sadly, she checked out in 1966 from cancer, at age 34. Had she lived, I'm sure ten years later, she'd have put out an unbelievable disco album