Precursors to the SS wave have been analyzed extensively to characterize seismic discontinuities in the upper mantle. We examine the influence of shear-velocity heterogeneity on the amplitude of underside shear wave reflections off the 410 (i.e., S410S) and 660 (i.e., S660S) discontinuities using waveform data from global seismic networks and spectral element method synthetics for four tomographic models of the crust and mantle. On average, the S660S/SS amplitude ratio is smaller than values predicted for the Preliminary Reference Earth Model (PREM) and tomographic models of shear velocity perturbations from PREM. The variation of S410S/SS and S660S/SS ratios determined for the 3-D models is significant. Its amplitude depends on the amplitude of shear-velocty heterogeneity in the mantle and on the incorporated model for the crust. The S410S/SS and S660S/SS amplitude variations are stronger in the data and do not correlate spatially with the simulated ratios. It is therefore not certain that the spatial variation of S410S/SS and S660S/SS, as expressed by cap averaging, can be related to compositional heterogeneity in the mantle, given the profound influence of the heterogeneous crust and mantle.