  In pure gauge SU(3) near beta = 6, weak and strong coupling expansions break
down and the MC method seems to be the only practical alternative. We discuss
the possibility of using a modified version of perturbation theory which relies
on a large field cutoff and has been successfully applied to the double-well
potential (Y. M., PRL 88 141601). Generically, in the case of scalar field
theory, the weak coupling expansion is unable to reproduce the exponential
suppression of the large field configurations. This problem can be solved by
introducing a large field cutoff. The value of this cutoff can be chosen to
reduce the discrepancy with the original problem. This optimization can be
approximately performed using the strong coupling expansion and bridges the gap
between the two expansions. We report recent attempts to extend this procedure
for SU(3) gauge theory on the lattice. We compare gauge invariant and gauge
dependent (in the Landau gauge) criteria to sort the configurations into
``large-field'' and ``small-field'' configurations. %We discuss the effects of
discarding the large field configurations. We discuss the convergence of
lattice perturbation theory and the way it can be modified in order to obtain
results similar to the scalar case.
