My sister found a scrap of paper in a book with a poem starting, "One bright day in the middle of the night." Does anyone know the author of this nonsense poem?

The full poem goes (from memory):

"One bright day in the middle of the night,
Two dead boys came out to fight.
Back to back, they faced each other--
Drew their swords and shot each other.
The deaf policeman heard the noise;
And came and shot the two dead boys.
If you don't believe this lie is true,
Ask the blind man, he saw it too!"

I didn't want to put the whole poem in the question! Is this a published work?

According to
[From enter.net 2004 article, no longer online]
the music and "new lyrics" are written by Josh Wachtel and Alexei Panshin.

According to all the sites I've looked at, the author of this childrens rhyme is that well known writer A.Non

http://www.scrapbook.com/poems/doc/2945.html

I know the poem, although slightly differently:

One fine day in the middle of the night
Two dead men got up to fight.
Back to back they faced each other,
Drew their swords and shot each other.
A blind policeman saw the sight
And ran away on his motorbike.

The one I know goes:

One fine day in the middle of the night
Two dead men got up to fight.
A blind man came to see fair play,
A dumb man came to shout hurray.

Who knows who wrote it!

The version I learned as a child is very different, but along similar lines...

One fine day in the middle of the night
The Atlantic Ocean caught alight
The blind man saw
The deaf man heard it
The man with no legs ran to get the fire brigade
The fire brigade was pulled by two dead horses

I can't remember the remainder