These just spring to mind because I am presently learning to play them on the fiddle:

Mi'm shuidh' an deireadha bata (Sitting in the Stern of a Boat)
Flitter Dance
Peter O'Tavy
Old Molly Oxford

The first one is an air, but I tend to play them all slowly as I'm not that good!
But it does have the advantage of bringing out the beauty of the melody.