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 $<{cal {O}}_{8}> = -(0.001 pm 0.006) {GeV}^8.$
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