Slant stacking of broadband seismograms recorded in the western United States for two 1993 intermediate-depth earthquakes that occurred near the Bolivia-Argentina-Chile borders reveals small but clear precursors to both the compressional (P) wave and shear (S) wave depth phases. We interpret and model these precursors as underside reflections from the thickened Andean Altiplano crust. We model the crustal structure of the Altiplano with a grid-search technique to match the timing and amplitudes of the depth phases and precursors in the waveforms of both the P wave and S wave. Our best-fit model has an average crustal velocity of 5.9-6.0 km/s, a crustal Vp/Vs of 1.6, a crustal thickness of 75-80 km, and a high-velocity (Vp = 8.4 km/s), high-Vp/Vs (1.9) mantle wedge. Assuming isotropy, the low Vp/Vs ratio of 1.6 for the crust corresponds to an anomalously low Poisson's ratio of 0.18. Such a low value, in conjunction with the low average Vp estimate, is consistent only with a felsic composition and high upper-crustal temperatures. The finding of a thick felsic crust overlying a high-velocity mantle supports models of Altiplano uplift due predominantly to crustal shortening as opposed to mafic magmatic addition and is inconsistent with recent mantle delamination.