  The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using
ALEPH and OPAL experimental data on the difference between vector and
axial-vector correlators (V-A). The sum rules exhibit poor saturation up to
current energies below the tau-lepton mass. A remarkable improvement is
achieved by introducing integral kernels that vanish at the upper limit of
integration. The method is used to determine the value of the finite remainder
of the (V-A) correlator, and its first derivative, at zero momentum:
$\bar{\Pi}(0) = - 4 \bar{L}_{10} = 0.0257 \pm 0.0003 ,$ and
$\bar{\Pi}^{\prime}(0) = 0.065 \pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and
$d=8$ vacuum condensates in the Operator Product Expansion are also determined:
  $<{\cal {O}}_{6}> = -(0.004 \pm 0.001) {GeV}^6,$ and $<{\cal {O}}_{8}> =
-(0.001 \pm 0.006) {GeV}^8.$
