  We improve a previous quenched result for heavy-light pseudoscalar meson
decay constants with the light quark taken to be the strange quark. A finer
lattice resolution (a ~ 0.05 fm) in the continuum limit extrapolation of the
data computed in the static approximation is included. We also give further
details concerning the techniques used in order to keep the statistical and
systematic errors at large lattice sizes L/a under control. Our final result,
obtained by combining these data with determinations of the decay constant for
pseudoscalar mesons around the D_s, follows nicely the qualitative expectation
of the 1/m-expansion with a (relative) 1/m-term of about -0.5 GeV/m_PS. At the
physical b-quark mass we obtain F_{B_s} = 193(7) MeV, where all errors apart
from the quenched approximation are included.
