Supposedly you are supposed to uninstall the old drivers and then install the new drivers. I haven't done it that way in years though. I just download and install the new ones over the top like you said.
Right,i agree with the posters above.
The best way to install a new driver is a clean install,here is how:
1_Download and install "Driver sweeper" from Guru3d.com and install
2_Go to add/remove programs and uninstall the driver and reboot
3_Boot to safe mode and open driver sweeper,then click on ATI and then click on clean
4_Reboot and boot normally to windows and install the new drivers after that u need a restart,and its finished