Rabbit has wet cough with no mucus?

by AL
(Lilburn, Georgia, US)

Hi
I have a mini rex, about six years old.

The last year or so, any time he's just finished eating hay, he has this random hacking wet cough. Like a comical old man coughing when he wakes up. He's not lethargic, poops are normal, no sound of fluid in lungs and no mucus at all.

Any ideas or help anyone?

Thanks