  A visible improvement of the QCD sum-rule framework, achieved only recently
by a slightly more sophisticated consideration of the hadron excitations and
continuum, is applied to the extraction of the decay constants of heavy-light
pseudoscalar mesons from two-point correlators of heavy-light pseudoscalar
currents. This analysis is carried out entirely in terms of the running
heavy-quark mass, for which the perturbative expansion exhibits a passable
convergence. Our main concern is to gain control over both statistical and
systematic uncertainties of the extracted decay constants, the former being
induced by the QCD parameter values requested for input, the latter arising
from the intrinsically limited accuracy of the QCD sum-rule techniques.
