Based on waveform data from a profile of aftershocks following the north-south trace of the 28 June 1992 Landers rupture across the Mojave desert, we construct a new velocity model for the Mojave region that features a thin, slow crust. Using this model, we obtain source parameters, including depth and duration, for each of the aftershocks in the profile and, in addition, any significant (M > 3.7) Joshua Tree-Landers aftershock between April 1992 and October 1994 for which coherent TERRAscope data were available. In all, we determine source parameters and stress drops for 45 significant (Mw > 4) earthquakes associated with the Joshua Tree and Landers sequences, using a waveform grid-search algorithm. Stress drops for these earthquakes appear to vary systematically with location, with respect to previous seismic activity, proximity to previous rupture (i.e., with respect to the Landers rupture), and with tectonic province. In general, for areas north of the Pinto Mountain fault, stress drops of aftershocks located off the faults involved with the Landers rupture are higher than those located on the fault, with the exception of aftershocks on the newly recognized Kickapoo (Landers) fault. Stress drops are moderate south of the Pinto Mountain fault, where there is a history of seismic swarms but no single throughgoing fault. In contrast to aftershocks in the eastern Transverse ranges, and related to the 1992 Big Bear, California, sequence, Landers events show no clear relationship between stress drop and depth. Instead, higher stress-drop aftershocks appear to correlate with activity on nascent faults or those that experienced relatively small slip during mainshock rupture.