  We compute the conversion factors needed to obtain the MS-bar and RGI up,
down, and strange-quark masses at next-to-next-to-leading order from the
corresponding parameters renormalized in the recently proposed RI/SMOM and
RI/SMOM_gamma_mu renormalization schemes. This is important for obtaining the
MS-bar masses with the best possible precision from numerical lattice-QCD
simulations, because the customary RI(')/MOM scheme is afflicted with large
irreducible uncertainties both on the lattice and in perturbation theory. We
find that the smallness of the known one-loop matching coefficients is
accompanied by even smaller two-loop contributions. From a study of residual
scale dependences, we estimate the resulting perturbative uncertainty on the
light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the
RI/SMOM_gamma_mu scheme. Our conversion factors are given in fully analytic
form, for general covariant gauge and renormalization point. We provide
expressions for the associated anomalous dimensions.
