Do Not Read This Title

While I was looking through my joke collection, I found one that was a collection of absurdities and it included the verse:

One bright day in the middle of the night
Two dead boys got up to fight.
Back to back, they faced each other
Drew their swords and shot each other.

Which I remembered saying as a kid, except the last bit in our version didn't scan properly (or "sounded like it didn't fit" in kid terms) so I always assumed it was a recent addition. Coming across it now, I thought I might be able to find the original version and where it came from.

Not that easy.

It was interesting to see that, like any good folk poetry, the version I knew is a mixture of other variations with a updated twist. That is:

One bright 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 shoot each other.
The blind man saw it.
The deaf man heard it.
The dumb man rang up the fire brigade.
The fire brigade came screeching round the corner at ten kilometres an hour
Ran over dead dog, and half killed it!

Anyone else have a version?