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We update our Standard Model predictions for g-2 of the muon and for thehadronic contributions to the running of the QED coupling, Deltaalpha_had^(5)(M_Z^2). Particular emphasis is put on recent changes in thehadronic contributions from new data in the 2pi channel and from the energyregion just below 2 GeV. In particular, for the e+e- -> pi+pi- contribution weinclude the recent `radiative return' data from KLOE and BaBar. We also includethe recent BaBar data on other exclusive channels. We make a detailed study ofthe effect of replacing the measurements of the inclusive cross section,sigma(e+e- -> hadrons), by the sum of the exclusive channels in the energyinterval 1.43 < sqrt{s} < 2 GeV, which includes a QCD sum-rule analysis of thisenergy region. Our favoured prediction for the muon anomalous magnetic momentis (g-2)/2 = (11659182.8 +- 4.9)*10^(-10) which is 3.3 sigma below the presentworld-average measurement. We compare our g-2 value with other recentcalculations. Our prediction for the QED coupling, obtained via Deltaalpha_had^(5)(M_Z^2) = (276.26 +- 1.38)*10^(-4), is alpha(M_Z^2)^(-1) = 128.944+- 0.019.

(g-2)_mu and alpha(M_Z^2) re-evaluated using new precise data