Well, you can easily map that "bad" tyre as well. Just select sidewall polygons and apply planar UV map, then select tread polygons and apply cylindrical UV map. You'd also likely will need to apply different materials and/or textures to sidewal and to tread. C4D terminology might be slightly different, but it shouldn't be hard to figure out this.
P.S. don't throw away the tyre if it's still good - that's bad for enviroment :]