  We investigate a tree-level O(a^3)-accurate action, D234c, on coarse
lattices. For the improvement terms we use tadpole-improved coefficients, with
the tadpole contribution measured by the mean link in Landau gauge.
  We measure the hadron spectrum for quark masses near that of the strange
quark. We find that D234c shows much better rotational invariance than the
Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to
smaller finite-lattice-spacing errors than plaquette tadpole improvement. We
obtain accurate ratios of lattice spacings using a convenient ``Galilean
quarkonium'' method.
  We explore the effects of possible O(alpha_s) changes to the improvement
coefficients, and find that the two leading coefficients can be independently
tuned: hadron masses are most sensitive to the clover coefficient, while hadron
dispersion relations are most sensitive to the third derivative coefficient
C_3. Preliminary non-perturbative tuning of these coefficients yields values
that are consistent with the expected size of perturbative corrections.
