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Catch Kat in The House Bunny in theaters nationwide NOW! fandango.com
I don't know if it's Broadway or not, but I heard this song on the "Jazz Brunch" show on a local radio station last weekend, and immediately thought that it would be perfect for Katharine:
http://www.song-teksten.com/song_lyrics/diana_krall/the_look_of_love/maybe_you_ll_be_there/
I just loved "Maybe You'll Be There" immediately, and thought it had the perfect jazzy/bluesy melody and rhythm for Katharine's style!