One of these songs was the 2nd single off their 1992 album - which I think is their absolute high water maker - Welcome To Wherever You Are. It peaked at #28 on the US charts, and was also featured on the official 1992 Summer Olympics CD. It's also a densely layered, clever pop-rock power ballad. Instant, underappreciated classic.
That's not to say that some of their hits weren't really fun songs. Take this one, one of their last big hits, from their album X - it was meant to designate a ten year anniversary. This song, which peaked at #9 in the US - it would be their penultimate top 10 hit here - is a great, jangly, fun song. The title was reported coined by fellow Wicked Guilty Pleasure Kylie Minogue (who Michael Hutchence dated for awhile) who had to bleach her hair for a movie role.
I don't care that Suicide Blonde was a big hit. I still love the song.