It is pretty amazing what you can do with a foam cutting pad mounted to a porter-cable orbital buffer. I use Meguiar's Diamond Cut Compound 2.0 (available at most Autozones) and the orbital/cutting pad combination to remove anything short of an actual chip in the paint.
Just to chime in on this suggestion, while this may work for you, Meguiar's doesn't recommend using our W-7006 foam cutting or any of our compounds with the Porter Cable Dual Action Polisher. This combination may dull or haze your car's finish to the point that it will require a rotary buffer to remove the haze and restore the gloss and clarity. About as aggressive as we recommend you go is the #83 Dual Action Cleaner Polish with our W-8006 foam polishing pad on a maximum of the 5.0 speed setting.
Just a friendly recommendation.
Mike