Spectral analyses of short-period P arrivals on teleseismic recordings of nuclear explosions at Yucca Flats and Pahute Mesa regions of the Nevada Test Site seem to provide explosion source medium information. The spectral ratio P/P coda on short-period vertical component records at NORSAR shows significant correlation with explosion medium velocity. For a given yield, spectrum of the initial P waves from an explosion within a high-velocity medium is richer in high frequencies as compared to that for P waves from an explosion within a low-velocity medium. The spectra of P codas, on the other hand, are considerably less sensitive to the near-source velocity differences from one shot to another so that the spectral ratio P/P coda is diagnostic of the shot medium velocity. Relative insensitivity of the P-coda spectra and amplitudes to the overburden velocity is perhaps due to several factors, including an effective source function controlled by average properties of rock within a fairly large nonlinear region around the shot point. The study provides valuable insight into effects of the shot medium on the spectra and amplitudes of compressional arrivals and offers the exciting possibility of extracting near-source information from teleseismic observations.