  Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at $\beta=6,$ the `tadpole renormalized' coupling $\tilde g^2 = {4\over
3} g^2,$ to be compared to the non-perturbative numerical value $\tilde g^2 =
1.7 g^2.$
