  We study the ultraviolet problem for QED in d=3 using Balaban's formulation
of the renormalization group. The model is defined on a fine toroidal lattice
and we seek control as the lattice spacing goes to zero. As a first step we
take a bounded field approximation and solve the renormalization problem.
Namely we show that the bare energy density and the bare fermion mass can be
chosen to depend on the lattice spacing, so that under the renormalization
group flow they take preassigned values on unit scale. This is accomplished by
a nonpertubative technique which is insensitive to whether the renormalizations
are finite or infinite.
