How about “Why don’t you do right?”. (That’s the solo Jessica Rabbit performed in Who Framed Roger Rabbit.)
Adding: There’s a version of “Why Don’t you Do Right?” by Peggy Lee, and I found an audio sample (not nearly as good as Jessica Rabbit’s rendition) on a compilation too.
How about Sooner or Later? It was written by Stephen Sondheim for Madonna to perform in Dick Tracy. Sultry stuff if done right.
Oooo and *Nowadays * from Chicago!
You might like “Me and My Chauffeur Blues,” originally recorded by Memphis Minnie. My favorite version is by the Geyer Street Sheiks, with vocalist Alice Spencer. Check out some of her other songs on the album, like “Oh, Daddy,” “I’ve Got a Feelin’ I’m Fallin’,” “What Have You Done,” and “World of Trouble.” That woman can vamp up a song! You mentioned you liked to do songs recorded by men; listen to her “Sixteen Tons.”
One for my Baby?
Update:
I was reading this thread and I kept thinking - I have to quote that one and tell them how great it is - but there are so many good ones and I don’t know how to put more than one quote in the post so please forgive me and THANK YOU, all of you! (this goes to all the wonderful people who made it possible tears) 
I’ve done some Chicargo but havn’t done ‘Nowadays’, I already do a lot of Peggy Lee but havn’t done ‘Why don’t you do right’. I’ve done Nora Jones stuff but never found anything interesting enough - I like the music but it’s more background music (for wine and cheeseing and candle lit dinners) it’s hard to take a song like that and keep people’s attention for 4.32 minutes.
Again thank you!!! (and keep it comming! 
)
;j
There are some great torchy, jazzy, sexy songs on Nellie McKay’s debut album “Get Away From Me” (which is a subtle jab at Norah Jones’ blander “Come Away With Me” album). “David,” the first track, is a real lounge-act number, and “Why Can’t You Be Nice” is a lot of fun–a Cole Porter-inspired number with really cute, witty lyrics. Nellie McKay is a young singer-songwriter who runs the gamut stylistically from smoky ballads to quirky, irreverent story songs to angry rap (yeah, you heard me right). I highly recommend her, and you can probably hear samples of her songs on Amazon.com or her own website.
Nope, different songs.
A few more:
“Witchcraft” by Sinatra.
“A Nightengale Sang in Berkeley Square”
“Ain’t Misbehavin’”
“Smoke Gets in Your Eyes”
Run out and get the great CD A Broadway Christmas. Listen to Vicky Lewis’s world premiere rendition of Irving Berlin’s “Happy New Year Blues.” Fantastic.
Yes, the same Vicky Lewis that was on Home Improvement and News Radio. She can really belt out a tune.