We determine the source time histories of five recent (1994--1996) large, deep-focus earthquakes using a method that inverts for fault slip from far-field moment rate functions. The moment rate functions are obtained through the deconvolution of multiple body wave phases using broadband records from Global Seismic Network (GSN) and GEOSCOPE stations. Tests of this method on synthetic data indicate that it is successful in determining the low-frequency rupture characteristics of deep earthquakes under a variety of complicating conditions. We find that source parameters such as average rupture velocity and stress drop are highly variable among the events studied and that some unusual characteristics exhibited by the June 9, 1994, great Bolivian earthquake are also found for other events. Comparison of the slip distributions with background seismicity and aftershock locations indicates that most of the moment release for large deep-focus earthquakes is probably occurring within the active slab interior. This provides further evidence that temperature-controlled mechanisms (such as transformational faulting) play a large role in deep earthquake faulting. Most of the events studied also show a tendency for horizontal rupture propagation, suggesting that isobaric processes may be an important factor in controlling progression of the rupture. Large gaps in the slip distributions point to possible occurrence on multiple fault planes. ¿ 1999 American Geophysical Union