  In this paper we show that the apparent failure of QCD lattice perturbation
theory to account for Monte Carlo measurements of perturbative quantities
results from choosing the bare lattice coupling constant as the expansion
parameter. Using instead ``renormalized'' coupling constants defined in terms
of physical quantities, like the heavy-quark potential, greatly enhances the
predictive power of lattice perturbation theory. The quality of these
predictions is further enhanced by a method for automatically determining the
coupling-constant scale most appropriate to a particular quantity. We present a
mean-field analysis that explains the large renormalizations relating lattice
quantities, like the coupling constant, to their continuum analogues. This
suggests a new prescription for designing lattice operators that are more
continuum-like than conventional operators. Finally, we provide evidence that
the scaling of physical quantities is asymptotic or perturbative already at
$\beta$'s as low as 5.7, provided the evolution from scale to scale is analyzed
using renormalized perturbation theory. This result indicates that reliable
simulations of (quenched) QCD are possible at these same low $\beta$'s.
