I.D. Song Fragment, "Just Between You and Me"

There’s just a bit of melody and a few words floating in my head, and 10 minutes of googling didn’t tell me what the song is.

I wouldn’t stake my life on any of the following clues being totally accurate, but…
–The song dates from 1964-1975.
–The lyrics begin with a one syllable girl’s name (Jill?), and then, “just between you and me”
–The lyrics then might go, “I hear your voice”
–The song was probably a minor Top 40 hit.
–The opening of the song is very soft, with an ambiance similar to the beginning of “One is the Loneliest Number…”

Just Between You And Me - April Wine

Thanks you Mr. blondebear, but it turned out to be Gary Lewis and the Playboys. It reached number 55 in 1967.

I was watching a Netflix documentary on Harry Nilsson, and heard him singing “One” which reminded me of the other song. I’ll tell you, Nilsson could sing better than Gary Lewis.

A song with that line was also sung by Charley Pride, late 60s, early 70s.