I think you need a specularity map… a black and white image that shows the areas that you want specularity and areas that you don’t. I can’t tell you exactly how to use it though as I haven’t ever done one myself! If I find out I will post back.
Have a material with two textures. The first texture is your spec map. The area I wanted spec was white and the area I didn’t black but either way works as long as you toggle the spec button right. Your second texture is your colour/alpha one (I used a PNG with transparency).
To get this to work right I had to drop the material spec to 0 and then control it with the var slider.