You need some external source of light somewhere behind your monitor to prevent your pupils from dilating (bias lighting). Adjust screen luminosity so that the screen isn't your reference light source.
I've done that in the past, and it has made no difference. Even in a fully lit room (without reflections on the screens, etc), dark backgrounds are not as comfortable as light backgrounds.
[EDIT] TO clarify a bit more - I use 2x 24" monitors at the recommended distance (arms length). This means that for better or worse, most of my field of view will be taken up by the monitors, and so most of the light that hits my eyes will always be from my monitors.
