Which piece? Or it just the main piece? For example The good, the bad, and the ugly could mean any of the listed.

My favorite has to be "The ecstacy of gold". Pure class by Leone-Morricone, especially coz the musical motif (sound of human coyote(s)) for Tuco is blended to the chords, run over the length of Tuco's search in the cemetry. The human Voice(s) is a tinge of bawl (And sadness) as Leone circles the tombstones, and crosses over the buried dead bodies. Tuco's search isn't fasttracked for the audience, while the Morricone piece accentuates. The trademark Leone style is long extinct in ages of jump cuts, and shortened "hollywoodian" scenes.

Another film that just couldn't be without Ennio's haunting character/motif piece happens to be a Leone as well ("Once upon a time in the west")