The concept of chemical hardness has been recently adopted in the framework of Kohn-Sham theory as a faithful ab initio measure of pseudopotential transferability. A fully self-consistent hardness theory has been developed and employed to evaluate the transferability of semilocal pseudopotentials. Hardness contains most of the relevant physical information determining the transferability of pseudopotentials, and is an important step forward with respect to the logarithmic derivatives analysis. We discuss the main features of chemical hardness, and the relations between chemical hardness and the original definitions of absolute and local hardness. We then apply the new criterion to investigate the transferability of fully non-local Kleinman-Bylander pseudopotentials. Hardness conservation allows us to obtain a meaningful comparison between them and the conventional norm-conserving ones and give us a criterion to improve the pseudopotential tranferability of fully non-local pseudopotentials by suitably resetting their local part.