Quenched Lattice Results for $f_B$ and $f_D$

We have computed the decay constants for the $B$ and $D$ mesons, using quenched lattices at $\beta=6.3$, by interpolating between the static approximation of Eichten and the conventional (``heavy'' Wilson fermion) method. A more careful treatment of the static result using better sources with longer time-displacements and a modification to the Wilson quark normalization to correct approximately for lattice effects in the large-$am$ regime have led to the elimination of the large discrepancy between the two methods which had been previously observed. We report final results, with estimates of various systematic errors.