  We calculate the $B_B$ parameter, relevant for $\overline{B}^0$--$B^0$
mixing, from a lattice gauge theory simulation using the static approximation
for the heavy quark and the Wilson action for the light quark and gauge fields.
Improved sources, produced by an optimized variational technique, {\sc most},
reduce statistical errors and minimize excited-state contamination of the
ground-state signal. Renormalization of four-fermion operator coefficients,
using the Lepage-Mackenzie procedure for estimating typical momentum scales, is
linearized to reduce order $\alpha_s^2$ uncertainties.
