Ogden Nash poem on hiccups

Question

I have a vivid memory of reading a poem by Ogden Nash about hiccups that included the word "epiglottis" to help explain why they happen. I think it also had, as a poem, his quote about how "the trouble with a kitten is that it grows into a cat", with a corresponding image of a cat stretching while scratching something (the carpet?) with its claws.

It tickled me as a kid (I probably read it in the early 1980s, but the book was likely from my parents and older than that), but now I can't seem to find it. The book also included "The Tale Of Custard The Dragon", "The Jellyfish", "Adventures of Isabel", "Wombat", "The Pizza", and "The Boy Who Laughed At Santa Claus". I remember it was a paperback, maybe a hundred pages at most, and had sketchy pen-and-ink illustrations of each of those poems that reminded me of those in Roald Dahl books.

Answer 1

My guess: "Can I Get You a Glass of Water? or, Please Close the Glottis after You" by Ogden Nash. which I found on pp. 34-35 of an old hardcover Ogden Nash collection titled You Can't Get There From Here. It's probably the wrong answer, because it's about coughing rather than hiccups and features the word glottis rather than epiglottis. I'm posting this answer anyway because it's the best match I've been able to find, and because identification requests sometimes have misremembered details. Here is the full text of the poem (emphasis added):

One trouble with a cough,
It never quite comes off.
Just when you think you're through coughing
There's another cough in the offing.
Like the steps of a moving stair
There is always another cough there.
When you think you are through with the spasm
And will plunge into sleep like a chasm,
All of a sudden, quickly,
Your throat gets tickly.
What is this thing called a cough
That never quite comes off?
Well, the dictionary says it's an expulsion of air from the lungs with violent effort and noise produced by abrupt opening of the glottis,
To which I can only reply, Glottis — schmottis!
Not that I reject the glottis theory, indeed I pride myself on the artistry
Of my glottistry.
But there is a simple definition with which I freely present you:
A cough is something that you yourself can't help, but everybody else does on purpose just to torment you.