This is as backless a bra as could be found in the 1950s! I've only ever come across one other of these - very special and sexy!, The measurements are
Sexy Backless Black Wraparound Soft Cup Bullet Bra, Modern-Aire of Hollywood Satin/Lace Mesh Cups, Long Elastic Straps and Metal Hardware
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Jockey® Modern Micro Stretch Seamfree® Bralette
Vintage satin bullet bra - Gem