  We use a new compilation of the hadronic $R$-ratio from available data for
the process $e^+e^-\to$ hadrons below the charm mass to determine the strong
coupling $\alpha_s$, using finite-energy sum rules. Quoting our results at the
$\tau$ mass to facilitate comparison to the results obtained from similar
analyses of hadronic $\tau$-decay data, we find $\alpha_s(m_\tau^2)=0.298\pm
0.016\pm 0.006$ in fixed-order perturbation theory, and
$\alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation
theory, where the first error is statistical, and the second error combines
various systematic effects. These values are in good agreement with a recent
determination from the OPAL and ALEPH data for hadronic $\tau$ decays. We
briefly compare the $R(s)$-based analysis with the $\tau$-based analysis.
