  A set of well known chiral sum rules, expected to be valid in QCD, is
confronted with experimental data on the vector and axial-vector hadronic
spectral functions, obtained from tau-lepton decay by the ALEPH collaboration.
The Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and the
electromagnetic pion mass difference sum rule are not well saturated by the
data. Instead, a modified set of sum rules having additional weight factors
that vanish at the end of the integration range on the real axis, is found to
be precociously saturated by the data to a remarkable extent.
