Engine Drivetrain 1st Gen Cooper S Most liked posts in thread: Stock S Resonator

Yes, the resonator is located on the passenger side. This mod is most often called the "one-ball" mod.

It will open up the exhaust and make it a bit louder and you can save some weight. If you go to an exhaust shop they usually charge $50-100.

 

This post has some good pictures of the one ball mod.
MINI COOPER :: North American Motoring - One Ball MOD?

The stock exhaust has two muffler looking cans in the rear. One is a resonator and one is a muffler. For the one ball you remove the one can (resonator) and re-route the exhaust pipe.

The JCW exhaust configuration is a little different. The JCW exhaust has a resonator in the straight section of pipe (between the cat and and the y-pipe) plus the JCW has two small mufflers in the rear (one on each side). For the JCW you can replace the resonator with a straight section of pipe and leave the two rear mufflers.