Three novel lower bounds for the total pi-electron energy of benzenoid hydrocarbons have been obtained. These bounds are of (n,m)-type, i.e., they are functions of only the number of carbon atoms (n) and the number of carbon-carbon bonds (m). Two of them are much better than the previously reported estimates of the same kind. The results obtained shed light on the dependence of the thermodynamic stability of benzenoid hydrocarbons on molecular structure. The extension of the results obtained to non-benzenoid alternant hydrocarbons is straightforward, but requires some caution.