dimmer switch for head unit?

My cd player is a Pionner DEH 720 or something like that. :) Anyway, the face is basically like a mini tv screen, except it's only one color (kinof a indiglo green). It has a little screen saver type deal like Dolphins swimming, or a microphone swinging around a little square that has "on air" written inside. While driving down the road at night, I usually have to flip the face down, b/c it's so bright it's almost like having the interior light on.

What I'm wondering is if it's possible for me to install a dimmer, so I can dim that thing down at night?

Thanks,
Zack

Most Pioneer HU's have dimmer connections already. Doesn't yours?