I don't think there is any way around soaking your whites to keep them white. What sort of solution a person soaks them in varies, but it always includes soaking. I had been soaking my whites over night about every other time I washed them in Clorox 2. Then I had twin babies and I never could think far enough ahead to get laundry in the washer at night.
About a year and a half later I feel like I have my head back. I also have a lot of dingy whites. Out of Clorox 2, I decided to see what sort of things I could use that I probably already had. A Google search later and I decided to try soaking my whites in hot water over night using 1/4 cup of dishwasher detergent and the regular amount of laundry detergent. I was pleased with the results. My whites looked whiter. And hopefully if I continue to soak them every couple of washes, they'll be the way I like them: white.
Other whitening options:
Baking soda, Vinegar, Hydrogen Peroxide