Can you turn off or disable the display on an iMac?

I'd like to turn off my iMac display while connected to it via a remote desktop session. I'm using TeamViewer or LogMeIn, and unfortunately the screen stays on during those sessions when it really doesn't need to be on.

Is there any way to set the screen to off while in use?

Note: I don't want to put the display to sleep because that will only last until I start typing or move the mouse.

You can try RedScreen (I don't have an iMac to test it). I read that it can not only decrease the screen brightness beyond OS X defaults (like others do) but also control the screen backlight. You can bypass the default red tinting mode and just use these brightness controls.