  Using a new result for the first moment of the hadronic production cross
section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and
$\psi'$ resonances for the charm quark, we determine the \msb masses of the
charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and
$\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. We assume that the continuum
contribution to the sum rules is adequately described by pQCD. While we observe
a large reduction of the perturbative error, the shifts induced by the
theoretical input are very small. The main change in the central value of $m_c$
is related to the experimental data. On the other hand, the value of $m_b$ is
not changed by our calculation to the assumed precision.
