  We discuss results for the heavy-light decay constants in the continuum limit
of quenched lattice QCD from finite size scaling techniques. We disentangle the
simultaneous presence of the different energy scales characterizing heavy-light
physics by first performing simulations at the unphysical volume L_0=0.4 fm,
and then evolving the results towards the infinite volume. We find f_{Bs}=
192(6)(4) MeV and f_{Ds}=240(5)(5) MeV. The approach has been developed by the
APE group at the University of Rome ``Tor Vergata''.
