We discuss a variational Hamiltonian approach to pure lattice SU(2) gauge theory in the weak-coupling limit. Our variational wave function is similar to the perturbative wave function, but differs in that it is mapped from the perturbative manifold R/sub 3/ onto the correct group manifold S/sub 3/. The mapping generates nonperturbative contributions similar to those predicted by the renormalization group. The paper develops the tools required to complete the calculation, but the requisite lattice sums are not performed in this paper.