I think this was very late 80's (maybe early 90's?) -- not so much new wave (otherwise I'm sure I'd have it in my collection).
The artist is African-American, I think she was a former member of a successful band. I can see the video in my mind's eye -- it features her singing, standing with a (bass) guitar?
Anyway, it's a guitar chord-driven song. I wish I could remember *any* lyrics. It's some sort of "relationship" song. All I remember is the style of song reminds me of the Barenaked Ladies' "It's all been done".