The McClelland inequality, E less than or equal to root 2mn, estimates the total pi-electron energy (E) of a conjugated hydrocarbon by means of the number of carbon atoms (n) and the number of carbon-carbon bonds (m). We now show that in the general case 2m/n + root(n - 1)(2m -4m(2)/n(2)) is a better (n,m)-type upper bound for E. An even better estimate, 4m/n + root(n - 2)(2m - 8m(2)/n(2)), holds for alternant hydrocarbons.