Found the reference to "The Trooper Cut Down." Masato gave a website, with midi, to a version with "handfuls of laurel," and copied a remark from three websites that the song was "collected from Dorset, England," the words dating to the late 18th century.
Thread 47060, 30 Apr 02: Trooper
These sites suggest it is the ancestor of all the others. One said it is Irish, although it was "collected in Dorset."
I looked through the Mudcat references and couldn't find any discussion.
Who collected it?
Who put the late 18th century date to it?
It doesn't seem to be in the DT (only a later version with British India references).
Its similarity to "The Unfortunate Lad" is marked.

THE TROOPER CUT DOWN

As I was walking down by the Lock Hospital.
Dark was the morning and cold was the day
Who should I spy but one of my comrades
Draped in a blanket and cold as the clay.

Then beat the drums slowly and play the pipes lowly
Sound the dead march as we carry him along
And over his coffin throw handfuls of laurel
For he's a young trooper cut down in his prime.

O mother, o mother come sit you down by me
Sit you down by me and pity my plight
My body is injured and sadly disordered
All by a young woman my own heart's delight.

Had she but told me when she did disorder me
Had she but told me about it in time
I might have got salts and pills of white mercury
But now I'm cut down in the height of my prime.

Get six of my comrades to carry my coffin
Six of my comrades to carry me on high
And each of them carry a bunch of white roses
So no-one may smell me as we pass them by.

At the street corner there's two girls a-standing
One to the other she whispered and said,
"Here comes that young squaddy whose money we squandered,
Here comes a young trooper cut down in his prime."

On top of his tombstone these words they are written,
"All you young fellows take warning by me,
Keep away from them flash girls who walk in the city,
The girls of the city was the ruin of me."

A briefer version by Christie Moore is in the DT with the name "Locke (sic) Hospital."