To constrain dynamic source properties of deep earthquakes, we have systematically constructed broadband time functions of deep earthquakes by stacking and scaling teleseismic P waves from U.S. National Seismic Network, TERRAscope, and Berkeley Digital Seismic Network broadband stations. We examined 42 earthquakes with depths from 100 to 660 km that occurred between July 1, 1992 and July 31, 1995. To directly compare time functions, or to group them by size, depth, or region, it is essential to scale them to remove the effect of moment, which varies by more than 3 orders of magnitude for these events. For each event we also computed short-period stacks of P waves recorded by west coast regional arrays. The comparison of broadband with short-period stacks yields a considerable advantage, enabling more reliable measurement of event duration. A more accurate estimate of the duration better constrains the scaling procedure to remove the effect of moment, producing scaled time functions with both correct timing and amplitude. We find only subtle differences in the broadband time-function shape with moment, indicating successful scaling and minimal effects of attenuation at the periods considered here. The average shape of the envelopes of the short-period stacks is very similar to the average broadband time function. The main variations seen with depth are (1) a mild decrease in duration with increasing depth, (2) greater asymmetry in the time functions of intermediate events compared to deep ones, and (3) unexpected complexity and late moment release for events between 350 and 550 km, with seven of the eight events in that depth interval displaying markedly more complicated time functions with more moment release late in the rupture than most events above or below. The first two results are broadly consistent with our previous studies, while the third is reported here for the first time. The greater complexity between 350 and 550 km suggests greater heterogeneity in the failure process in that depth range. Copyright 1998 by the American Geophysical Union.