Tailoring, or precisely specifying, the types, amounts, orientations and locations of composite materials in a structure to satisfy specific performance requirements is inherent to the design of efficient composite structures. A simple piece-wise uniform stiffness tailoring concept has previously been shown to increase compressive buckling loads of plates by as much as 138% to 195%, depending on the baseline uniform laminate. The question arises as to what benefits, it any, exist for plates tailored in this way when loaded in the postbuckling regime. This paper presents predictions for global measures of the postbuckling response of plates loaded in compression which have been tailored to maximize the initial buckling load. The analysis shows that postbuckling loads at failure can be increased by 130% to 150% by tailoring. The edge strain at first-ply failure is not significantly affected by tailoring. Postbuckling membrane secant and tangent stiffnesses are much higher for tailored plates than for uniform plates. Out-of-plane postbuckling deflections are shown to be much smaller at a given load level when tailoring is employed. The initial buckling mode shape and the manner in which postbuckling mode changes take place are strongly affected by tailoring. Thus, with this design approach, optimization for initial buckling can provide concurrent benefits in postbuckling response. This improved performance suggests that the skin plate of stiffened composite panels could be tailored using the current approach to significantly improve the postbuckling performance of stiffened panels.