The recently discovered phase transition for (Mg,Fe)SiO3 from perovskite to post-perovskite structure for pressure-temperature conditions in the lowermost mantle provides a plausible mechanism to explain a several percent shear velocity increase detected at the top of the D″ region in many regions. The phase transition has a large positive Clapeyron slope, and given the likely presence of a strong temperature increase just above the core-mantle boundary, D″ conditions may reintersect the phase boundary, resulting in a thin layer of perovskite below a lens of post-perovskite, separated by a few percent velocity decrease. Detection of such a velocity decrease is shown to be much harder than detection of the shallower velocity increase due to fundamental properties of seismic waves; purported observations in support of a double-discontinuity are re-evaluated based on waveform modeling. Waveform stacking procedures are required for reliable detection of the lower half of any double-crossing of the phase boundary.