iMac won't remain asleep

My iMac has recently decided to become a recalcitrant child. It cycles through its sleep parameters, but shortly after the screen goes dark it awakens to go through the machinations again. This will continue as long as the unit is on. I've tried the suggested SMC restarting even to the extreme of leaving it unplugged for 15 minutes as well as waiting a minute or longer before restarting it after plugging it back in. The only thing I have done that "may" have contributed to the problem was to trash a .plist in an attempt (successful) to get the Magic Mouse to stop losing signal. Now the mouse works but the sleep gave up the ghost. Is the another .plist thing to trash for this problem?