Dexys Midnight Runners were so much than Come On Eileen . . . (please bear in mind that I originally posted this song choice on an American person's timeline on Facebook.)
Dexys Midnight Runners - Let's Make This Precious (Live Shaftesbury Theatre 1982)
I guess (technically) this qualifies as a one hit wonder, though I know so much of their other work that I could never think of them as a one single band. And there was so much greatdancemusic back in the day that could fall into the category of OHW, but when I think of 'one hit and they were gone', for some reason, I think of The Lotus Eaters and their number 15 hit from 1983, 'The First Picture of You':
Despite the fact that I've always loved this song, I was always a bit hard on them for some reason. Something about them really irritated me. I think it was the guitarist's haircut. I guess I wasn't the only one, and despite possessing a clutch of good songs, they'll always be remembered for just the one.