This is one of the reels occasionally played in Leeds. It’s especially popular among the musicians playing at Irish Centre. I always forget to ask how they call it, but Paul McGrattan and Paul O’Shaunessy recorded it as Micho Russell’s on their "Within a Mile of Dublin." In JC’s it’s listed as Sean Reid’s Fancy.
You can listen to McGrattan and O’Shaughnessy playing this tune: http://www.claddaghrecords.com/www/product.asp?pID=74&cID=17&c=232948 (track14)
This reel is also on Mike Rafferty’s latest recording "Speed 78," where it’s mistakenly called "Peg McGrath’s."
This reel is titled Peg McGrath’s in Martin Mulvihill’s book p12 no.47.
Michael Cooney calls this tune Miss Galvins on the Happy to Meet, Sorry to Part recording with Joe Burke and Terry Corcoran. He plays it as a single reel and make a great pipe tune of it. On the recording it appears to be credited to Sean Ryan, composer, though its not really clear if Belles of Tipperary or Miss Galvins is being referred to. On the album link on this site, there is a link to the wrong tune, Miss Galvins and this one are nothing alike.