Originals: No Regrets by Tom Rush (covered by Luna)
No Regrets was written by folk singer Tom Rush and was the closing track on his 1968 album The Circle Game
It was more famous for folk of a certain age for a cover in 1976 by The Walker Brothers
... or for us slightly younger folk, for a cover by Midge Ure in 1982
Luna's cover appeared in 1995 as one of the tracks on the Hedgehog/23 Minutes in Brussels single, and later on the No6 Records EP (and more recently on the Lunafied download only compilation).
Audio: Luna - No Regrets
And as a bonus here's Lee Hazlewood's version from The Cowboy and The Lady from 1969