SUMMARY The effects of complex structure in the deep mantle and D �� on PKP differential traveltimes should be estimated accurately in order to reach reliable conclusions concerning the physical and chemical properties of the Earth’s inner and outer core. In particular, it is important to assess how much of the data can be explained by mantle structure alone. For this purpose, we have assembled global data sets of high-quality PKP(AB‐DF), PKP(BC‐DF) and PcP‐P differential traveltimes measured on mostly broad-band records. The PKP(AB‐DF) data were inverted alone or jointly with PcP‐P data, to retrieve P-velocity maps of the lowermost 300 km of the mantle. Corrections for mantle structure above D �� were performed prior to inversion using recent tomographic models and the fit to the PKP(BC‐DF) data set was used to constrain damping in the inversions. We compare models obtained with and without polar PKP paths and find that their inclusion or exclusion does not significantly affect the resulting D �� model except under North America, where coverage is poor without polar paths. Our preferred model, obtained using PKP(AB‐DF) and PcP‐P data combined, explains over 80 per cent of the variance in PKP(AB‐DF), almost 60 per cent of the variance in PcP‐P and 27 per cent of the variance in PKP(BC‐DF)—a significant portion considering that the PKP(BC‐DF) data set was not used in the inversion. Our models are characterized by prominent fast features under mid-America and east Asia, a fast belt across the Pacific, a slow region under the southwestern Pacific and southern Africa, as well as sharp transitions from fast to slow, for instance under Alaska and the South Atlantic. The anomalous South Sandwich to Alaska data cannot fully be explained by D �� structure alone, unless very short-wavelength lateral vari