Short-period, teleseismic ScP phases from events in the Tonga-Fiji region recorded at the short-period, small-aperture Warramunga Array in Australia are used to study structure at the core-mantle boundary (CMB). We examine the data for evidence of precursors and postcursors to ScP. Such additional arrivals are generated by the interaction of ScP with structure at the reflection and conversion point at or near the CMB. We show precursors and postcursors to ScP, indicating an ultralow-velocity zone (ULVZ) at the CMB in the region between Tonga-Fiji and Australia. One-dimensional forward modeling of the short-period data leads to models of the ULVZ with thickness varying between 5 and 20 km, velocity reductions of 0--10% and 10--30% for P velocity and S velocity, respectively, and 0--50% density increase. Many events, however, show simple waveforms, consistent with a locally simple CMB. Models for proximal events can vary greatly, indicating very complex, three-dimensional structure with scale lengths of a few tens of kilometers. These results point to complex chemical and physical processes in the lowermost mantle.