As I do church laundry which are all whites, I have always used HOT water, bleach, and Mrs. Stewart's bluing. When I lived in New York City, I bought "Bluette" liquid.
First I start HOT water into wash tub, squeeze in some bluing, add bleach, and detergent. After tub is full, I add clothes and with old, yellowed vestments and communion linens, they come out glistening white. I never use cold water as one of my friends here does and he has a scum ring around his tub and agitator.
One whites that are very old, I may not be able to get them looking like new but with my treatment, they look better than before.
Ross aka "Our Lady of the Laundry Room"