Ed brings up some interesting points about tires/shocks.  I will share my experiences.  Switching from Toyo to Hankook, I notice a much better ride with the Hankook.  Sidewall construction is the main reason for the difference.  Also, recently tried different tire pressure settings and to my surprise, I found running higher pressures in the front (105 to 115) made the ride better, not worse...  On the shocks, I switched from Bilstein to Koni FSDs and they made a huge improvement in ride and handling.  
BTW, you can get much better handling and ride on the Mini Cooper by replacing the "run flats" with a good high performance summer tire.  Be sure you carry a can of tire puncher sealant and air pump for good measure.