This tune is different than the one usually associated with this name. I learned it from the concertina playing of Nial Vallely on Tim O’Brien’s CD "Two Journeys". It’s my all time favorite concertina tune and works great on and mandolin fiddle too.
Here’s this tune played by Mairead Ni Mhaonaigh & Dermot Byrne
Slight variation idea.
Try the first measure of the B part this way:
A one-note difference with an interesting impact.
Should have changed that measure to: