  We study the accuracy of the bound-state parameters obtained with the method
of dispersive sum rules, one of the most popular theoretical approaches in
nonperturbative QCD and hadron physics. We make use of a quantum-mechanical
potential model since it provides the only possibility to probe the reliability
and the accuracy of this method: one obtains the bound-state parameters from
sum rules and compares these results with the exact values calculated from the
Schr\"odinger equation. We investigate various possibilities to fix the crucial
ingredient of the method of sum rules -- the effective continuum threshold --
and propose modifications which lead to a remarkable improvement of the
accuracy of the extracted ground-state parameters compared to the standard
procedures adopted in the method. Although the rigorous control of systematic
uncertainties in the method of sum rules remains unfeasible, the application of
the proposed procedures in QCD promises a considerable increase of the actual
accuracy of the extracted hadron parameters.
