How to turn off a Cinema Display

[zeb]

I have a new iMac 27" with a 20" Cinema Display connected via a mini display port to dual link DVI adapter. I use the Cinema Display occasionally, and like to keep it off for the majority of the time. The problem is that when I press the power button on the Cinema Display, the screen "turns off" (per the setting in the display prefs), but the computer still registers the second display and my mouse can float off the edge of my main screen to where the secondary screen is. How can I get the computer to stop thinking there is a display connected after I turn it off?

"Detect displays" doesn't work.

I don't want to unplug the screen.