Six different estimates of the magnetotelluric impedance tensor elements may be computed from measured data by use of auto-power and cross-power density spectra. We show that each of the estimates satisfies a mean-square error criterion. Two of the six estimates are relatively unstable in the one-dimensional case when the incident fields are unpolarized. For the remaining four estimates, it is shown that two are unaffected by random noise on the H signal, but are biased upward by random noise on the E signal. The remaining two estimates are unaffected by random noise on the E signal, but are biased downward by random noise on the H signal. Computation of all of the estimates provides a measure of the total amount of noise present, as indicated by a stability coefficient for the estimates. In the absence of additional information as to the relative signal-to-noise ratios of the E and H signals, we suggest that a mean estimate be used. A numerical example is included.