I have this problem because I have one eye. I do a few things.
1) Make sure my monitor has a high refresh or response rate. Either greater than 75hz or less than 4ms (2 is better) respectively
2) You may be making things worse by setting the contrast down. Your have to do extra work to discern what it's seeing when the contrast is too low.
3) Lighting /fundamentally/ important. Use good lighting, which first means nothing that "flickers," like the average over head office lighting is terrible. You need to use soft lights. I have a rope light strung up behind my monitors so there's a nice soft, yellow glow coming from behind them at all times, plus a larger lamp pointing straight at the back of my central one. That back lighting helps a lot. For overhed, I generally use dilluted sunlight from the windows, but failing that a brightish floor lamp with a nice blub witll work fine.
4) Sit far enough away from the monitor. I sit between 2 and 3 feet back.
5) I use large fonts for everything. When I read web sites, I hit CTRL++ all the time to make the font larger. In my IDE, I use 16 to 18pt font.
6) Whenever possible, /especially/ when programming, I use inverted colors, so black background and light colors for the text. White text generally works, but you might find a light gray to be easier on the eyes.
If you do all that, you'll be fine.