  This talk reviews the recent progress in the extraction of bound-state
characteristics from the operator-product expansion (OPE) for field-theory
correlators, which constitutes the basis of the method of QCD sum rules. This
progress is mainly related to a deeper understanding of one of the key
ingredients of the method of sum rules -- the effective continuum threshold.
The latter determines to a great extent the numerical values of the bound-state
parameters obtained by sum rules. The understanding of properties of the
effective continuum threshold allows one to formulate a new algorithm for fixng
this quantity for various correlators and in this way gain control over the
systematic uncertainties of the bound-state parameters extracted from sum
rules. We start with examples from quantum mechanics, where bound-state
properties may be calculated independently in two ways: exactly, by solving the
Schr\"odinger equation, and approximately, by the method of dispersive sum
rules. Knowing the exact solution is crucial as it allows us to control each
step of the sum-rule extraction procedure. On the basis of this analysis, we
formulate several improvements of the standard procedures adopted in the method
of sum rules in QCD. We then show the impact of these modifications on the
extraction of the decay constants of heavy mesons.
