High-quality P and S travel times are now available from careful reprocessing of data reported to international agencies. A restricted data set has been extracted, for which comparable ray coverage is achieved for P and S, and used for a joint inversion to produce a three-dimensional model for shear and bulk sound velocities represented in terms of 2¿¿2¿ cells and 18 layers in depth through the mantle. About 106 times for each of P and S are combined to produce 312,549 summary rays for each wave type. Linearizing about the ak135 reference model, 583,200 coupled tomographic equations are solved using an iterative partitioned scheme. Clear high-resolution images are obtained for both bulk-sound speed and shear wavespeed. The bulk and shear moduli have differing sensitivity to temperature and mineral composition, and so the images of the two velocity distributions help to constrain the nature of the processes which produce the variations. Different heterogeneity regimes can be recognised in the upper mantle, the transition zone, most of the lower mantle, and the lowermost mantle. In the upper mantle, many features can be explained by thermal effects; but in some orogenic zones (e.g. western North America), the opposite sense of the bulk-sound and shear wave speed variation requires compositional effects or volatiles to outweigh any thermal effects. In the lower mantle, pronounced narrow structures which may represent remnant subduction are most marked in shear. The level of large-scale variations in bulk sound speed compared to shear diminishes with depth in the lower mantle reaching a minimum near 2000 km. Below this depth, the variability of both wave speeds increases. Near the core-mantle boundary the variations of the two wave speeds show little concordance, suggesting the presence of widespread chemical heterogeneity. ¿ 1998 American Geophysical Union