Characterization of near-source crustal properties for underground nuclear explosions using distant seismic observations can potentially improve nuclear test monitoring capabilities. Previous analyses of the relative spectral content of direct P waves and P-wave coda have suggested that important physical parameters such as source overburden velocity and shot point velocity can be inferred from teleseismic signals. Such observations have the potential to both improve yield estimation (by indicating coupling conditions) and to shed light on the basic mechanisms of coda excitation. Reliable isolation of any near-source influences requires thorough suppression of propagation and near-receiver effects on the signals, which are shown herein to be significant for comparisons of P and P coda. A spectral factoring procedure is used to determine event-averaged source spectra from which propagation and receiver terms have been removed for both direct P signals and early P coda. A large short-period waveform data set (2457 signals) for 71 events at the Nevada and Novaya Zemlya test sites is analyzed with the event-averaging procedure. Spectral ratios and slopes of spectral ratios for the event-averaged P and P-coda source terms are examined for dependence on event magnitude, burial depth, overburden velocity, and other known source characteristics. The slopes of P/P-coda ratios over the frequency band 0.3 to 2.5-Hz for NTS events show only weak dependence on near-source properties for the event-averaged spectra, while individual stations sometimes show strong systematic trends, as discovered by Gupta and Bland-ford (1987). The tendency is for larger, deeper events (with higher average overburden velocities) to have relative enrichment of high frequency P-wave energy compared to the coda. Single-frequency P/P-coda spectral amplitude ratios increase with increasing magnitude, depth, and overburden velocity for frequencies less than 0.5 Hz, with these trends being reversed near 0.8 Hz. For Novaya Zemlya, the slope of P/P-coda shows a strong variation with magnitude, but P waves from larger events have relatively depleted high-frequency content. Differences in magnitude-depth scaling may contribute to this difference between test sites. Single-frequency P/P-coda spectral ratios at frequencies less than 1.0 Hz increase with magnitude for Novaya Zemlya similarly to the NTS events, possibly as a result of enhanced coda excitation for shallower events combined with low-frequency pP interference. These variations are not yet quantitatively understood but may ultimately provide empirical procedures for characterizing the near-source environment of isolated events or additional test site explosions.