Wireless mouse and sleep mode


Just got a new iMac yesterday, with a wired keyboard, wireless mouse and magic trackpad. Since the mouse and trackpad use batteries, I wanted to turn them off when I put my computer to sleep. The trackpad was fine, but turning the mouse off seemed to wake the computer up because it lost the connection.

Is this not something I can or should do? I have the rechargable batteries, but I still want to conserve them as much as possible.