  It is hoped that the accuracy of a variety of lattice calculations will be
improved by perturbatively eliminating effects proportional to the lattice
spacing. In this paper, we apply this improvement program to the heavy quark
effective theory currents which cause a heavy quark to decay to a light quark,
and renormalize the resulting operators to order $\alphaS$. We find a small
decrease in the amount that the operator needs to be renormalized, relative to
the unimproved case.
