  We present precise measurements of the eta and K0 masses using the processes
phi to eta gamma, eta to gamma gamma and phi to Ks Kl, Ks to pi+ pi-. The K0
mass measurement, M_K=497.583 +/- 0.005 (stat) +/- 0.020 (syst) MeV, is in
acceptable agreement with the previous measurements but is more accurate. We
find m(eta) = 547.874 +/- 0.007 (stat) +/- 0.031 (syst) MeV. Our value is the
most accurate to date and is in agreement with two recent measurements based on
eta decays, but is inconsistent, by about 10 sigma, with a measurement of
comparable precision based on eta production at threshold.
