Another American song to a variant of "Derry, Derry Down" is "Red Iron Ore," popularized by Carl Sandburg.

Now almost unknown, however, is "Bucking and Gagging Him," from the Mexican War (1846-48) ("United Service Magazine," Sept., 1852, p. 101):

Come all Yankee soldiers, give car to my song,
It is a short ditty, 'twill not keep you long;
It's of no use to fret on account of our luck,
We can laugh, drink, and sing yet in spite of the buck.
Derry down, &c.

Sergeant, buck him, and gag him, our officers cry,
For each trifling offence which they happen to spy;
Till with bucking and gagging of Dick, Tom and Bill,
Faith, the Mexican ranks they have helped to fill.
Derry down, &c.

The treatment they gave us, as all of us know,
Is bucking and gagging for whipping the foe;
They buck us and gag us for malice or spite,
But they're glad to release us when going to fight.
Derry down, &c.

A poor soldier's tied up in the sun or the rain,
With a gag in his mouth till he's tortured with pain;
Why I'm bless'd, if the eagle we wear on our flag
In its claws shouldn't carry a buck and a gag.

(The singer is described as a "north of Ireland man.")

Though flogging had been abolished in the navy in 1850 and the army in 1861, "bucking and gagging" survived as a form of punishment in the U.S. military until almost 1890.