Ha Ha! I love the songs my parents sang to me when I was little. Though I don't think they make you think "Huh?" like Rock-a-bye Baby. My Dad used to sing just the chorus of Bushel & Peck as heard here... http://www.ziplo.com/BushelAndAPeck.html

Then here is a song my Mom sang the chorus of to me. http://redbirdjan.freeyellow.com/gerber.html

I can't find the other song Mom sang me. But here are the words...

I had a little parasol long, long ago.
A pretty little parasol tied with a bow.
It was made of paper though, just for pretend.
I took it in the rain one day...
and that was the end.