The Hall rule claims that the HMO total pi-electron energy (E) of isomeric benzenoid hydrocarbons is a linear function of the number of Kekule structures (K). We now show that already in the case of benzenoid isomers with a small number of hexagons (4 <= h <= 9), E is better reproduced by a linear function of K-lambda, where the exponent A is significantly smaller than unity. This exponent is found to be a decreasing function of h and its limit value (for h ->infinity) seems to be equal to, or near to, 1/3. A simple model of such a K-dependence of E is constructed. (c) 2006 Elsevier B.V. All rights reserved.