Coherent precursors to shear phases (S, SKS, ScS) observed on long-period seismograms recorded at LASA are interpreted as shear-to-P type mode conversions, or Sdp phases, from mantle discontinuities at depth d. Polarization analysis on three-component beam traces confirm that the precursors are compressional phases. Mode conversions are distinguished from multiple surface reflections on the basis of apparent slownesses, constant lead times of mode-converted phases relative to the shear phases for different focal depths, and amplitude considerations. The waveform shapes of mode conversions are modeled using the matrix propagator method. Two mode conversions from the top and bottom of a low-velocity zone between 171 and 226 km depth explain the waveform shape immediately in front of the primary shear waves. The strongest mode conversion is produced by a discontinuity at about 451 km and has a velocity contrast of about 10 per cent. The variation in the measured S451p-to-primary-S amplitude ratio recorded at the subarrays strongly correlates with the variation in the P-to-S amplitude ratios and is probably caused by focusing and defocusing effects in the lithosphere beneath the array. A 556 km discontinuity is inferred from the partial interference of S556p with S451p. Interfering S671p and S770p phases seem to be present on one of the beam traces. However, the presence of these mode conversions is problematic because they do not appear on all the beam and subarray traces.