The vertical coherence of mantle structure is of importance for a range of dynamic issues including convective mass transport and the geochemical evolution of Earth. Here, we use seismic data to infer the most likely depth ranges of strong, global changes in the horizontal pattern of mantle heterogeneity. We apply our algorithm to a comprehensive set of measurements, including various shear- and compressional-wave delay times and Love- and Rayleigh-wave fundamental mode and overtone dispersion, so that tomography resolution is as high as possible at all mantle depths. We find that vertical coherence is minimum at ∼100 km and ∼800 km depths, corresponding to the base of the lithosphere and the transition between upper and lower mantle, respectively. The D″ layer is visible, but not as prominent as the shallower features. The rest of the lower mantle is, essentially, vertically coherent. These findings are consistent with slab stagnation at depths around, and perhaps below, the 660-km phase transition, and inconsistent with global, chemically distinct, mid-mantle layering.