The mapping of variations in P wave speed in the deep mantle is restricted by the uneven sampling of P waves, in particular beneath the Southern Hemisphere. To enhance data coverage, we augmented the ~1.6 million summary rays of P, pP, and pwP that we used in previous studies with differential travel times of diffracted and refracted core phases. For the core-refracted differential travel time residuals (PKPAB-PKPDF and PKPAB-PKPBC) we used 1383 cross-correlated digital waveforms as well as ~27,000 routinely processed bulletin data. We used the waveform data to define quality criteria for the selection and reduction of the bulletin PKP data. For PKPDF-Pdiff we only considered 543 records derived from waveform cross correlation. No PcP data were used in this study. We used optical ray theory to calculate the ray paths associated with the P, pP, pwP, and PKP data, which are measured at 1 Hz. However, to account for the large Fresnel zones of the low-frequency (~50 mHz) PKPDF-Pdiff data we estimated the three-dimensional shape of the Fr¿chet sensitivity kernels from kernels calculated by normal mode summation. The use of these kernels allows us to properly distribute the sensitivity for a given seismic phase over a large mantle volume while allowing the high-frequency data to constrain small-scale structure. The differential times are relatively insensitive to source mislocation and to structure in the shallow mantle beneath source and receivers, and they have previously been interpreted exclusively in terms of lateral structure directly above the core mantle boundary (CMB). However, images thus obtained can be contaminated by effects of small scale structure elsewhere in the mantle. Here, we do not make a priori assumptions about the mantle source of anomalous time differentials. From test inversions we conclude that (both upper and lower) mantle structures that are poorly resolved by P data can be mapped into the core along PKP paths but that the effect of outer core structures, if any, on the mantle model is small. Compared to the inversion of the P, pP, and pwP alone, the inclusion of the PKPAB-PKPDF and PKPAB-PKPBC and PKPDF-Pdiff data improves the resolution of structure beneath 2200 km depth. In particular, the joint inversion puts better constraints on the long-wavelength variations in the very deep mantle and yields an increase in the amplitude of velocity perturbations near the CMB that is in agreement with but still smaller than inferences from shear wave studies. Resolution tests indicate that in some regions the enhanced definition of structure is significant, but in most regions the improvements are subtle and structure remains poorly resolved in large regions of the mantle. ¿ 2001 American Geophysical Union