  We reevaluate the dispersion integrals of the leading order hadronic
contributions to the running of the QED fine structure constant alpha(s) at
s=M_Z^2, and to the anomalous magnetic moments of the muon and the electron.
Finite-energy QCD sum rule techniques complete the data from e+e- annihilation
and tau decays at low energy and at the cc-bar threshold. Global quark-hadron
duality is assumed in order to resolve the integrals using the Operator Product
Expansion wherever it is applicable.
  We obtain delta_alpha_had(M_Z) = (276.3 +/- 1.6)x10^{-4} yielding
alpha^{-1}(M_Z) = 128.933 +/- 0.021, and a_mu^had = (692.4 +/- 6.2)x10^{-10}
with which we find for the complete Standard Model prediction a_mu^SM =
(11659159.6 +/- 6.7)x10^{-10}. For the electron, the hadronic contribution
reads a_e^had = (187.5 +/- 1.8)x10^{-14}.
