On The Waterfront OST (Missing Track)

Does anyone know the title of the background music in this clip from the movie "on the waterfront"? Thanks in advance!

I Coulda Been a Contender – On the Waterfront (6/8) Movie CLIP (1954) HD – YouTube (http://www.youtube.com/watch?v=uBiewQrpBBA)

I believe it’s music for the film composed by Leonard Bernstein. There’s a lovely recording of it on the LP. If you track down a copy, let me know!

I believe it’s music for the film composed by Leonard Bernstein. There’s a lovely recording of it on the LP. If you track down a copy, let me know!

No, that cue was never included on the Suite that Lenny made from the score. Btw, the Suite was released afew times on CD, so no need for LP.
The cue was recorded separately awhile back and released on the cassette/CD "Leonard Bernstein’s New York." The cue is "Cab and Bedroom." The listing at Amazon:
Amazon.com: Leonard Bernstein, Eric Stern, Orchestra Of St. Luke’s, Dawn Upshaw, Judy Blazer, Mandy Patinkin, Audra McDonald, Donna Murphy, Richard Muenz: Leonard Bernstein’s New York: Music (http://www.amazon.com/Leonard-Bernsteins-New-York-Bernstein/dp/B000005J40)

You can hear the entire cue here: https://www.youtube.com/watch?v=UtKAqsWdAO0

The actual soundtrack was just released by Intrada.