I started a similar thread:
debadging thread
Seems taking off the Cooper is easy, but the marque badging is held on with adhesive and pins thru the metal (boot and bonnet), which will need filling in and painting...
BTW I think debading really cleans up a car, makes it a bit smoother, subtler, if you are into the whole sleeper look. Not so much making your car look like more than it is, but getting rid of the noise and letting the lines of the car speak for themselves.
Just as long as you don't replace the logo with a Type R badge...
