  New data for the total cross section $\sigma(e^+e^-\to{hadrons})$ 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 $\bar{\rm MS}$ charm and bottom quark masses. A detailed discussion of
the theoretical and experimental uncertainties is presented. The final result
for the $\bar{\rm MS}$-masses, $m_c(3 {GeV})=0.986(13)$ GeV and $m_b(10
{GeV})=3.609(25)$ GeV, can be translated into $m_c(m_c)=1.286(13)$ GeV and
$m_b(m_b)=4.164(25)$ GeV. This analysis is consistent with but significantly
more precise than a similar previous study.
