Bill Malley’s Barndance is one of those tunes that is simple but beautiful. It is not quite as easy as Lucy Farr’s but shares something of it’s elegance. It really helps if you sing it (in your head) while you play it.
Apparently written by Bill Malley, a fiddler from County Clare, Martin Hayes has popularised it, recording it on his album, Under the Moon. I haven’t found a video of Hayes playing it but you can hear the album version on YouTube.
There are also several other good recordings:
Brittany and Natalie Haas and their friends
Slightly different guitar version but nice playing
Fiddle and cello together
Mandolin and guitar
Whistle (but no video)