While roaming around YouTube videos of jazz bands in New Orleans, I chanced upon one put up by Thomas Balzac. It showed Sarah Peterson singing My Sweet Lovin' Man with the famous Smoking Time Jazz Club Band at The Spotted Cat Music Club in Frenchmen Street:
I remembered that I have the tune on one of my King Oliver CDs. It turned out that it was written by Lil Hardin in 1923.
I also noticed that - after its 12-bar Verse - it has a Chorus based on The Hot Nuts Chord Progression - popular in the 1920s. This is basically a 16-bar progression, with breaks possible on Bars 9 to 12 inclusive. The final two bars of the sixteen are in many songs repeated as a tag. That is what happens in My Sweet Lovin' Man, making 18 bars in all.
I like it; so I decided to add this tune to my mini-filofax collection. I wrote it out, and it sounds quite good on my keyboard.