Glasses with compressive stress profiles that allow higher surface compression and deeper depth of layer (DOL) than is allowable in glasses with stress profiles that follow the complementary error function at a given level of stored tension. In some instances, a buried layer or local maximum of increased compression, which can alter the direction of cracking systems, is present within the depth of layer. Theses compressive stress profiles are achieved by a three step process that includes a first ion exchange step to create compressive stress and depth of layer that follows the complimentary error function, a heat treatment at a temperature below the strain point of the glass to partially relax the stresses in the glass and diffuse larger alkali ions to a greater depth, and a re-ion-exchange at short times to re-establish high compressive stress at the surface.