  We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge
with the link field U in the 1-direction set to one. The term in the
Hamiltonian containing the square of the electric field in the 1-direction is
non-local. Despite this non-locality, we show that weak-coupling perturbation
theory in this term gives a finite vacuum-energy density to second order, and
suggest that this property holds to all orders. Heavy quarks are confined, the
spectrum is gapped, and the space-like Wilson loop has area decay.
