An extensive data set of more than 1600 teleseismic short-period P waves from 46 underground nuclear explosions is analyzed to establish near-source contributions to the first 15 sec of the P signals. The near-source components are isolated by event-to-event comparisons of first-cycle magnitudes, RMS amplitudes in the first 5 and next 10 sec of the waveforms, and energy temporal centroid measurements. Events from the Nevada, Amchitka, and Novaya Zemlya test sites are analyzed separately in order to characterize overall source region variations. Event-averaged waveform complexity variations between explosions within a given site are tested for dependence on source strength, burial depth, location within the site, and tectonic release. Azimuthal patterns of the individual event complexity anomalies are used to discriminate between possible near-source influences. For events at Pahute Mesa, a strong azimuthal amplitude pattern in both the direct P waves and the P coda for all of the events is produced principally by deep mantle variations. Defocusing by a high velocity anomaly in the crust and uppermost mantle beneath the site has a stronger effect on the direct P signals than on the early P coda, resulting in a systematic, spatially varying relative pattern. Events PIPKIN and SCOTCH have the most pronounced waveform complexity anomalies, which may be related to either their position in the site or to their respective burial above the water table (PIPKIN) and deep overburial (SCOTCH). The Amchitka events show variations between direct arrival and P coda amplitudes that are similar to the Pahute Mesa data, which can be attributed to focusing and defocusing associated with the subducting Aleutian slab. Novaya Zemlya events exhibit a strong inverse relation between waveform complexity and event size, as well as having much lower early coda amplitudes relative to the direct P arrivals than the Nevada Test Site events. There is very little evidence of significant tectonic release contribution to either the direct P arrivals or early P coda for any of the test sites.