  We apply a number of schemes which variationally improve perturbation theory
for the Kardar-Parisi-Zhang equation in order to extract estimates for the
dynamic exponent z. The results for the various schemes show the same broad
features, giving closer agreement with numerical simulations in low dimensions
than self-consistent methods. They do, however, continue to predict that z=2 in
some critical dimension d_c in disagreement with the findings of simulations.
