A previously derived [J. Chem. Phys. 103, 7645 (1995)] general variational principle, for determining the hardness (or band gap) of electronic systems, is applied to pi-electron systems by a straightforward simple parameterization of the hardness kernel. For conjugated polyenes and annulenes, the hardness (band gaps) are essentially the same as (although no identical with) those predicted by the Huckel method. In contrast with the Huckel method, one need not assume that the total electronic energy is a sum of one-electron energies. Comparisons are made with Nalewajski’s Charge Sensitivity Analysis.