Marilyn Monroe Dances to Barrel Piano Music - What Is The Song?

In the film, "The Prince and the Showgirl," Marilyn Monroe hears
a barrel piano playing outside her hotel room and starts dancing
to the music.  Marilyn's dancing is fun to watch, but what is the
name of the tune?

    http://www.youtube.com/watch?v=ZOkv4jV1-Bo 

The scene was recreated in the 2011 film, "My Week With Marilyn,"
starring Michelle Williams.  Here's Marilyn and Michelle dancing
side by side:

   http://www.youtube.com/watch?v=f4jupm0kFTY 

If you're not too distracted by the dancing, can you please name
the tune?

Thank you!

Joyce Brite - Player Piano and Mechanical Music Exchange
http://www.mmdigest.com/Exchange/ 

 [ I hear a duet by two live studio pianists playing a hard-hammer
 [ piano (i.e., the barrel piano is a mute prop).  The song might
 [ be unique to the film.  -- Robbie