I think it will do what you want. I use this iMac in the summertime with a dial-up modem. I am using the Apple external USB modem. After I sign off, I often put it to sleep only to find later that it/ someone has awakened it. This has been most annoying but I finally tracked it down to the modem. Any time the phone rings, the modem wakes the computer. I didn't do anything special to either to turn it on so the defaults settings must allow the effect you want. The effect happened in Tiger and now in Leopard. So I'd give it a try. John 24" Intel iMac Leopard 10.5.?