Towards a precision computation of f_Bs in quenched QCD

We present a computation of the decay constant f_Bs in quenched QCD. Our strategy is to combine new precise data from the static approximation with an interpolation of the decay constant around the charm quark mass region. This computation is the first step in demonstrating the feasability of a strategy for f_B in full QCD. The continuum limits in the static theory and at finite mass are taken separately and will be further improved.