This is one of my all time favorite songs. I have it on a B-Side Collection, although I can't find any mention of what it was B-Side of, just that it came out in 1988.
The words are quite haunting, as is the melody. But, I can hear you say, this is not at all a standard D2 song. Well, no, but what is a standard song by any band? How do you average that? Thomas Dolby's singles were always abnormal compared to the rest of their respective albums. Same with Barenaked Ladies. I think the B-Sides are often truer to what the band wants to be without the pressure of the labels for commercial success.
This is probably more like Duran Duran you're thinking of, right? It's from Pop Trash, released 2000. The words are based on the true story of a boy who was building a nuclear bomb in his garage--because it's that easy.
From Big Thing, also 1988. I listened to this over and over as I worked on my college essays and read "Atlas Shrugged" to enter an essay contest a teacher wanted me to enter. The two seemed to echo each other in strange ways (I've never read of any connection--other than the fact that Simon was once a fan of Ayn Rand's work--but like every sane person, he got over it). Even now, certain passages in the music can evoke the images of the book--empty streets, America collapsing. I bet you never knew D2 could be serious.
Careless Memory, from their very first album--very raw, not overproduced. Simon's early lyrics were not always known for their coherence, but I've always thought "Fear Hangs a Plane of Gunsmoke," an amazing piece of poetry.
[Sidenote: continuing the L'Arc/D2 connection, I have a copy of Simon singing Linger with The Cranberries. It's not a very good recording since it was live, which is why I'm not putting it here.]
Edit: In searching DuranDuran.com and Wikipedia for dates, etc., I have discovered the rather frightening fact that Justin Timberlake has produced/mixed a new D2 single supposedly coming out soon. I listened to it. I am saddened (as were many of the commentors). Is this a bid to become "popular." I think it makes them bland. Crap.