  Capitalizing on recent advances in lattice QCD, we present a calculation of
the leptonic decay constants f_{B_s} and f_{D_s} that includes effects of one
strange sea quark and two light sea quarks. The discretization errors of
improved staggered fermion actions are small enough to simulate with 3
dynamical flavors on lattices with spacings around 0.1 fm using present
computer resources. By shedding the quenched approximation and the associated
lattice scale ambiguity, lattice QCD greatly increases its predictive power.
NRQCD is used to simulate heavy quarks with masses between 1.5 m_c and m_b. We
arrive at the following results: f_{B_s} = 260 \pm 7 \pm 26 \pm 8 \pm 5 MeV and
f_{D_s} = 290 \pm 20 \pm 29 \pm 29 \pm 6 MeV. The first quoted error is the
statistical uncertainty, and the rest estimate the sizes of higher order terms
neglected in this calculation. All of these uncertainties are systematically
improvable by including another order in the weak coupling expansion, the
nonrelativistic expansion, or the Symanzik improvement program.
