It's interesting that, in the various recommended links I've browsed through - particularly those of recorded music, the greater part of the recording is, as far as I can tell, of traditional tunes. The rondo that I've been looking at is written in a pleasant, if slightly predictable, two-part harmony, with overlapping, fugue-like lines.

My knowledge of the Uilleann/Union pipes is very sketchy, but I had always assumed that the keyed drones were capable of chordal accompaniment, and were not suitable for a true, two-part harmony piece.