  We report the details of our ongoing quenched calculations of weak matrix
elements using the combination of domain-wall fermions and the DBW2 gauge
action on lattices with $a^{-1}\approx 3$ GeV. A strategy to avoid the problem
of fixed topological charge is introduced in generating gauge configurations.
After studying the basic run parameters and elemental quantities, we present a
preliminary result for the kaon B-parameter ($B_K$).
