PSP1000(which is also called FAT) and PSP2000 are the ones which you can modify. The new one which is PSP3000 cannot be modified. Thats the reason why 1000 and 2000 became more expensive even thou its an old model. The downside of using PSP3000 is that you have to pay for games instead of just downloading them. If you prefer slim, go for 2000. You can go for secondhand items if you want..