1. Only had one Top 40 hit
2. Did not have other songs chart in genre specific charts
3. Were/are not successful and influential within their genre, ie, have a cult following.
4. Were not an American act with success overseas
5. Were not a non American act with success overseas
6. Were not a supergroup.
It was much more difficult than expected, and the best I came up with is....
Drum roll please....
"Der Kommissar" by After the Fire! The 80's had the best one hit wonders.
What's your favorite?