Found it!
Definitely only 32 bar tune.
Played straight first two times through, then another instrument (guitar/mandolin/bouzouki) takes the tune and Tony plays a high harmony in the A music, then Tony goes back to the tune but on the repeat of the A music he adds the long high notes (played with RH little finger while still playing the tune underneath - a trademark feature of his style.) So you are probably remembering those harmonies and variations on the A music.
The album includes amongst others Nic Jones on fiddle and guitar and Johnny Moynihan on mandolin, bouzouki and whistle and they are prominent on that track. I'd forgotten what a fine fiddle player Nic Jones was. The CD is still available from
Free Reed for only £6.