This is one of my more popular poems. i don't know anyone who doesn't like it, in fact. Whether it is "about jazz" is questionable:

A DOG NAMED ILLINOIS

If I had a dog I would name him Illinois
We would go to the park and meet pretty girls
And other pleasant, down-to-earth people
I would not be allergic to him; life would be good
We would listen to NPR and the BBC World Service
And to Illinois Jacquet at Jazz at the Philharmonic
A real cool cat
A dog more cat than wolf