There's a singing group where I work who are working on a jazzy sort of round/catch/canon thing with those words.
One group of singers start:
Baby just, baby just, baby just cares for,
Baby just, baby just, baby just cares for,
Baby just, baby just, baby just cares for,
Baby cares for only me

The deep voices sing:
My baby cares for,
My baby cares for,
My baby cares for,
My baby cares for only me.

The middle range has:
My babe I sigh for,
My pretty baby I'd die for,
Cos my baby loves nobody but me,
I'm so lucky.

I can't remember the 4th part but it ends with:
me-e oo-aa

Is that the one?
It just goes round and round until you're screaming to get off!
Robyn