A waveform inversion algorithm, based on optimal filter theory, has been applied to the P waves from 260 of the largest earthquakes occurring during the years 1981 through 1983. Estimates of average focal depth, scalar moment, and deviatoric source mechanism have been obtained. For all except the largest events (M0 > 1027 dyne-cm), the scalar moments obtained in this study are close to, but somewhat larger than, the Harvard centroid-moment tensor (CMT) scalar moments. The CMT estimates of scalar moment are probably biased to low values due to the way unmodeled lateral heterogeneity affects the fitting procedure. For the largest events, however, source complexity can bias the scalar moments determined in this study to lower values, and the CMT scalar moments are probably more accurate. The moment tensor, CMT, and U.S. Geological Survey first-motion source mechanisms have been objectively compared by computing the locations of the vector representations of the mechanisms on the unit sphere. We find that the similarities and differences between these mechanisms can be related to the uncertainties inherent in each method for certain types of earthquakes: (1) lack of constraint on one of the nodal planes for dip-slip type mechanisms from first-motion analysis; (2) lack of resolution of the moment tensor elements defining the dip-slip component of faulting for shallow-focus earthquakes in the CMT method; and (3) lack of resolution of the moment tensor elements defining the strike-slip component of faulting in the P-wave inversion method used here. Thus, on the average, the first-motion and CMT methods yield the more reliable mechanisms for strike-slip-type earthquakes, and the method used in this study gives a more reliable result for shallow-focus earthquakes with dip-slip-type mechanisms. Finally, both of the moment tensor methods should yield reliable solutions for intermediate- and deep-focus earthquakes.