I'm also searching for the solution, but it seems that whenever I do the following things (consistently) my eyes are more white than usual;
-Get enough sleep (7/8 hours)
-Drink plenty of water (about 8 glasses each day)
-Try not to strain your eyes (like staying on the computer/tv too long); whenever I'm on too long it makes my eyes irritated and tired.
-Eat healthy foods and keep a balanced diet (food pyramid!! :D)
Also, one of my friends takes this Rubyred Vitamin superfood stuff (http://www.rubyreds.com/) and her eyes are always stunningly bright and white. So if you feel like it, it might be worth checking into.
Hope this helps :)