  The QCD up- and down-quark masses are determined from an optimized QCD Finite
Energy Sum Rule (FESR) involving the correlator of axial-vector current
divergences. In the QCD sector this correlator is known to five loop order in
perturbative QCD (PQCD), together with non-perturbative corrections from the
quark and gluon condensates. This FESR is designed to reduce considerably the
systematic uncertainties arising from the hadronic spectral function. The
determination is done in the framework of both fixed order and contour improved
perturbation theory. Results from the latter, involving far less systematic
uncertainties, are: $\bar{m}_u (2\, \mbox{GeV}) = (2.6 \, \pm \, 0.4) \,
{\mbox{MeV}}$, $\bar{m}_d (2\, \mbox{GeV}) = (5.3 \, \pm \, 0.4) \,
{\mbox{MeV}}$, and the sum $\bar{m}_{ud} \equiv (\bar{m}_u \, + \,
\bar{m}_d)/2$, is $\bar{m}_{ud}({ 2 \,\mbox{GeV}}) =( 3.9 \, \pm \, 0.3 \,)
{\mbox{MeV}}$.
