Although they were major stars in their native Australia, Hoodoo Gurus were seen as more of an indy or college band by American audiences. That is not totally unfair, as their music has a college radio vibe, and is eclectic enough to be hard to categorize.
"Bittersweet" is a great, atmospheric song about a failed love affair, from the Gurus awesomely named 1985 album, Mars Needs Guitars. The album barely broke the top 200 in the U.S., but was the second of four consecutive Gurus albums to top the U.S. college charts. The video received some airplay on MTV, but it did not go into heavy rotation. (To be fair to MTV, I do not think the video is as strong as the song.)
By the way, is it me, or is the intro strongly reminiscent of the intro to Robert Plant's 1983 hit "In the Mood?"