Yeah, the genre issue always comes up when talking about The Stranglers, I like to think you can get away with putting their first album in the punk mix though, although the synth does seem to scare people away..My ex girlfriend's Dad goes to see Cornwell constantly and I've been to see The Stranglers 3/4 times, the impression I get from the "hardcore" fans is that they regarded themselves as punks at the time so I just tend to go along with that.
Still, forget all that, go purely on the music
