  We introduce an alternative discretization for static quarks on the lattice
retaining the O(a) improvement properties of the Eichten-Hill action. In this
formulation, statistical fluctuations are reduced by a factor which grows
exponentially with Euclidean time, x_0. For the first time, B-meson correlation
functions are computed with good statistical precision in the static
approximation for x_0>1 fm. At lattice spacings a \approx 0.1 fm, a \approx
0.08 fm and a \approx 0.07 fm the B_s-meson decay constant is determined in
static and quenched approximations. A correction due to the finite mass of the
b-quark is estimated by combining these static results with a recent
determination of F_Ds.
