Scott Miller's 1990 M-WH? list hits on lots of great tunes, including this one from the La's. Here's a performance from the days when Letterman was on NBC and CDs came in longboxes.
Like Scott, I also saw the La's touring behind this album (opening for Elvis Costello), and they were great live.
Anyone who remembers "Timeless Melody" knows that the La's were at the very least two hit wonders, but their entire self-titled debut is great from start to finish.