  We extend the $S$-matrix of gravity by the addition of the minimal
three-point amplitude or equivalently adding $R^3$ terms to the Lagrangian. We
demonstrate how Unitarity can be used to simply examine the renormalisability
of this theory and determine the $R^4$ counter-terms that arise at one-loop. We
find that the combination of $R^4$ terms that arise in the extended theory is
complementary to the $R^4$ counter-term associated with supersymmetric
Lagrangians.
