Brightening White Clothing

Add baking soda to your whites when washing. I use this all the time and they are whiter than when using bleach. For an extra boost, stop the wash and let them soak in the water for a little while.

One thing you can try is bluing. It is on sale in the laundry section of your supermarket, likely. Also, whites should only be washed with whites, If you are washing them with coloreds, they will get dingy In that case, I would bleach them, T-shirts should come quite nicely whiter with about a cup of bleach in the wash water.