What can I do for my cat’s asthma?

Dear Most Esteemed and Knowledgeable Kitties:
My kitty has been diagnosed with asthma. I’ve been giving him prednisone for a short time but he is still wheezing. Is there something else I can do for him?
~Kelly
Siouxsie: Asthma is a frightening illness, both for the cat and for the cat’s human caretaker.
Thomas: As you’ve probably been told, [...]