We discuss the masses of the top quark and of the Higgs boson in the light of the available precision electroweak data, considering the latest LEP data as well as the latest CCFR measurements of nuN and the SLC measurement of the left-right polarization asymmetry. The high precision reached by the experiments makes now possible to observe for the first time some discrepancies between different sets of data. In particular, the values of m(t) indicated by different subsets of data differ by about 1.3 standard deviations, and the present direct experimental limit on the Higgs mass is somewhat higher than the indirect indications about its mass from the radiative correction effects. Ignoring these discrepancies, we find m(t) < 155 GeV, M(H) < 250 GeV, each at the 95% confidence level, from the precision electroweak data alone.