Well the 2 boxes at the rear of your exhaust system are your twin back-boxes and you'll be wanting to replace these with a sportier version I should imagine.
Where as that smaller box/device that is fitted towards the front of the car and has heat resistant material fitted to the car (above it), is your cat and you'll need to keep this.
So you need to remove the exhaust system backwards from the cat and fit a suitable (twin-box) exhaust system on to it.
Once fitted it should look something like this:-

So the grimy looking thing on the right is the cat and the shiny silver exhaust boxes on the left are the exhaust (twin-box) system. I'm sure a company like Maniflow or PlayMini will be able to sort you out with the correct system, but I know some people have fitted single back boxes as their much louder, but I've got the twin-box system fitted to my Mini and I find that loud enough and I'm not sure if a single back box would make a difference to the emissions and if it would be allowed on a Twin-Point/MPi Mini?
Oh and don't buy an exhaust system that it too big either (with exhaust pipes the size of drain pipes, but the rear part from the back-box is okay if large though), as it can affect the performance and you don't want anything with pipes larger than around 1"7/8th's and i'd say 1"3/4 diameter would be more than enough.
But Maniflow would have all the answers and supply you with everything you need, well I swear by them as their stuff is top quality, but my back-boxes are classic green with a sporty silver widish tail pipe. But i'm sure they do stainless steel systems too.
Edited by taffy1967, 14 July 2006 - 01:50 PM.