Mining of the database produced by seismic array stations of the International Monitoring System has resulted in hundreds of new observations of precritical reflections from Earth's inner core. Here we present short-period amplitude ratios between these PKiKP phases and corresponding reflections (PcP) from the core-mantle boundary (CMB). PKiKP/PcP amplitude ratios are one of the few seismic observations that directly constrain the change in S velocity and density across the inner core-outer core boundary. We measure the amplitude ratios from optimally tuned array beams and use a bootstrap technique to estimate observational uncertainties. We also use a model resampling technique to estimate uncertainties associated with the background reference model. The optimal models have S velocities at the top of the inner core less than about 2.5 km/s and density jumps across the inner core-outer core boundary of less than about 0.45 g/cm3. These values can be reconciled with the higher estimates from normal mode constraints if strong radial gradients are present in the top of the inner core or if the outermost inner core has material properties distinct from the bulk of the inner core. We also find evidence for an ultralow-velocity zone in the lowermost mantle beneath the eastern coast of Australia. A unique, best fitting model cannot be determined, but an example that is consistent with the data has a reduction in P velocity of 10%, a reduction in S velocity of 35%, and an increase in density of 20%. This type of structure could be explained by the presence of partial melt and increased iron content just above the CMB.