I got it one piece at a time, and it didn't cost me
a dime. (With "piece" referring to conjugal encounters).

The story:

Not really misheard, but misinterpreted. My elderly
neighbor lady told me that she didn't like that song
because it was all about a man getting free sex, one
piece at a time. When I finally stopped laughing, I
remembered that also there is a line in the song
that says: "I always wanted one that was long and
black". That sent me into convulsions of laughter
again.