  We discuss the renormalization of higher-derivative gravity, both without and
with matter fields, in terms of two primary coupling constants rather than
three. A technique for determining the dependence of the Gauss-Bonnet coupling
constant on the remaining couplings is explained, and consistency with the
local form of the Gauss-Bonnet relation in four dimensions is demonstrated to
all orders in perturbation theory. A similar argument is outlined for the
Hirzebruch signature and its coupling. We speculate upon the potential
implications of instantons on the associated nonperturbative coupling
constants.
