I think a case can be made to include some of the New Wave bands into the category as well. Not all New wave bands were synth dominated and more like pop than rock. There were bands that were considered new Wave that were more guitar driven and had a harder edge to them.

The Alarm is a good example of that, so is the Psychedelic Furs, Oingo Boingo, The Fixx, and there's others. The Car's are pretty well accepted as Classic Rock and they were also considered New Wave Pioneers.