  We critically examine the evaluation of the hadronic contribution to the
running of the QED coupling, $\alpha$, from $Q^2=0$ to $Q^2=M_Z^2$. Using data
for $e^+e^-\to{}$hadrons we find that $\alpha(M_Z^2)^{-1} = 128.99\pm 0.06$, as
compared to the existing value of $128.87\pm 0.12$.
