Ballad of Sweeney Todd?

I know that the Ballad did not make it to the final version of the Tim Burton/Sweeney Todd film, but i was told that the ballad was filmed or recorded(one of the two) and later cut, if that is the case, the recording must be floating around somewhere. My question is, does anyone know where? is it on the special edition of the DVD or can I find it online?