Not sure about "jazz," not sure Norah does jazz, for that matter, but if you want singers, two that I don't think have been mentioned are Julie London, and currently, Kari Bremnes, from Norway.
You can find Ms. Bremnes, and a great catalog of female singer-songwriters at Harmony Ridge Music, http://www.hrmusic.com/index.html. (I have no affiliation, just offer it as a source of interesting stuff.)
You can find Ms. Bremnes, and a great catalog of female singer-songwriters at Harmony Ridge Music, http://www.hrmusic.com/index.html. (I have no affiliation, just offer it as a source of interesting stuff.)