  New data for the total cross section sigma(e^+e^- --> hadrons) in the charm
and bottom threshold region are combined with an improved theoretical analysis,
which includes recent four-loop calculations, to determine the short distance
\bar{MS} charm and bottom quark masses. The final result for the
\bar{MS}-masses, m_c(3 GeV)=0.986(13) GeV and m_b(10 GeV)=3.609(25) GeV is
consistent with but significantly more precise than a similar previous study.
