Music Box mystery

Someone suggested that I should transcribe the melody:

I asked on Facebook and YouTube, and in reference to this page, I wrote: "I put a transcription of the music on a page on my site, of just the melody. A couple of people have said it's probably "My Reverie" by Debussy, which had a jazz revival later. The first two phrases do sound like it, but the end of mine doesn't come back. I guess they added the last line to make it loop back around.

Mystery art (for fun)

Music for goofin' around with

Some other things I've had a long time