Recent measurements of peak P-wave amplitudes on World Wide Standardized Seismographic Network short-period instruments by Houston and Kanamori (1986) provided the opportunity to investigate source radiation from great earthquakes at higher frequencies than have previously been available. The dependence on moment magnitude (M) of the amplitude measurements (A) and the dominant period (T) in the P-wave seismograms are compared to predictions from several source-scaling relations. For all of the relations, the radiated energy was assumed to be randomly distributed over a duration proportional to the inverse corner frequency. An ω-square source-scaling relation with a constant stress parameter of 50 bars gives a good fit to both observed quantities (A and T) for earthquakes up to M 9.5. This model, with the same stress parameter, also fits peak acceleration and peak velocity data for earthquakes with moment magnitude as low as 0.5. Predictions using the source spectra derived by Gusev (1983), which are representative of several published relations featuring regions of reduced spectral decay after an initial ω−2 attenuation beyond the corner frequency, do not fit the various high-frequency observations quite as well as do those using the ω-square model, although the differences between the predicted motions are generally within a factor of 2 to 3. Although the ω-square model successfully predicts a wide variety of time-domain measures over an extraordinary magnitude range, it fails to fit the Ms, M correlation for large earthquakes; Gusev's spectral scaling relation, on the other hand, fits this correlation, but was constrained in advance to do so. This failure of the ω-square model is of little practical concern, occurring as it does at periods longer than those of usual engineering importance. An ω-cube model fails completely to explain the seismic moment dependence of the observations.