f.lux is a sweet free program for any operating system that really helps with eyestrain when working on your computer for long hours.
based on the time of day flux gradually adjusts the tones of your monitor output to be easier on your eyes (including softer, redder colors late at night). This is consistant with the body of literature that suggests avoiding bright blue lights close to bedtime naturally helps you sleep better.
I don't know about sleeping better, but I do appricate the dimming of the screen during night time hours, and f.lux runs flawlessly in the background. You won't even know it's there.
For starters, I'd suggest setting the lighting preferences to "daylight" because it seems to be the least extreme. If that doesn't fade enough, then you can consider switching to another setting.