Abstract The recent determination of high-quality, short-period P-wave amplitude profiles near the core shadow zone for three source-receiver combinations allows an exploration of lateral variations in P velocity structure at the base of the mantle. Various radially symmetric models are tested by comparison of the data with amplitudes measured from generalized ray theory synthetics. The assumption necessary to justify one-dimensional modeling—that each of the profiles is most sensitive to scales of heterogeneity larger than the discrete regions sampled—is well supported by the coherence of the individual profiles. The observed amplitude versus distance profiles exhibit significant regional variations of the apparent shadow zone boundary, with as much as a 5° shift in onset distance, but it is possible to model the overall behavior using simple, regionally varying, positive P velocity gradients in the lowermost mantle. Velocity models with pervasive negative velocity gradients in the D″ layer are not consistent with the data. The modeling indicates that D″ velocities beneath the North Pole are ∼ 2% slower than those beneath the central Pacific, while velocities beneath the North Pacific are ∼ 1% faster. Although the simplest class of successful models begins to deviate from the PREM reference Earth model as much as 690 km above the core-mantle boundary, these models do not violate global mantle velocity constraints, and the theoretical slowness values calculated for the three models are consistent with slowness measurements for the same general regions. More complex, multiple-gradient lower mantle velocity structures with a thinner zone of lateral heterogeneity may be compatible with the P wave data, but such detailed structures cannot be resolved by our modeling (though bounds can be placed on viable structures). The strong lateral variations required by the data support the presence of compositional heterogeneity in D″, and the data require that at least in several locations the predominant P velocity gradients in D″ are positive.