  The procedure of extracting the ground-state parameters from vacuum-to-vacuum
and vacuum-to-hadron correlators within the method of sum rules is considered.
The emphasis is laid on the crucial ingredient of this method - the effective
continuum threshold. A new algorithm to fix this quantity is proposed and
tested. First, a quantum-mechanical potential model which provides the only
possibility to probe the reliability and the actual accuracy of the sum-rule
method is used as a study case. In this model, our algorithm is shown to lead
to a remarkable improvement of the accuracy of the extracted ground-state
parameters compared to the standard procedures adopted in the method and used
in all previous applications of dispersive sum rules in QCD. As a next step, it
is demonstrated that the procedures of extracting the ground-state decay
constant in the potential model and in QCD are quantitatively very close to
each other. Therefore, the application of the proposed algorithm in QCD
promises a considerable increase of the accuracy of the extracted hadron
parameters.
