Help me find the name of this song

First of all, it’s an old song. The first five notes are the same as the first five notes of “Betty Coed” and it has a lot in common with that song, but that’s not quite it, the rhythm is different and the melody diverges. But that was my starting point.

If I ever heard the real words to this song I don’t remember. It is probably somebody’s school song. What sticks in my memory is girls from Stephens College singing this in the late '60s: “I was a virgin through my freshman year, I was a virgin with my conscience clear…” Another one I half remember went: “Oh when a [some, thing, something] walks down the street, she’s got a smile on her that’s hard to beat…”

I’m sure I’m going to be appropriately abashed when I find out the real name of this song. Because I really ought to know it. Repeat, it is NOT “Betty Coed” although there are similarities.

Even more information. The words to “Betty Coed” in the song of that name would go like this: Betty co-ED has lips of red for Cornell, Betty co-ED has eyes of nay-vee bloooo.

If you tried to apply those words to the song I’m looking for it would go: Be-tee co-ed, has lips, of re-eh-ed, Be-tee co-ed, has eyes of blue… (Not enough room for all the words.)

Sorry, I was just getting as close as I could. It’s like I’m trying to sing a few bars, on paper. (Wait: pixels.) Okay, it sounds silly, but it might help.

I found this

http://collections.mun.ca/cdm/ref/collection/munfla_list/id/2088

Moderator Action

Since this is about a song, let’s move it to Cafe Society (from GQ).

Well that’s the ditty all right but I’m thinking surely it started with a real song. A real tune. It wasn’t just chanted.