Joint inversions of seismic and geodynamic data are carried out in which we simultaneously constrain global-scale seismic heterogeneity in the mantle as well as the amplitude of vertical mantle flow across the 670 km seismic discontinuity. These inversions reveal the existence of a family of three-dimensional (3-D) mantle models that satisfy the data while at the same time yielding predictions of layered mantle flow. The new 3-D mantle models we obtain demonstrate that the buoyancy forces due to the undulations of the 670 km phase-change boundary strongly inhibit the vertical flow between the upper and lower mantle. The strong stabilizing effect of the 670 km topography also has an important impact on the predicted dynamic topography of the Earth's solid surface and on the surface gravity anomalies. The new 3-D models that predict strongly or partially layered mantle flow provide essentially identical fits to the global seismic data as previous models that have, until now, predicted only whole-mantle flow. The convective vertical transport of heat across the mantle predicted on the basis of the new 3-D models shows that the heat flow is a minimum at 1000 km depth. This suggests the presence at this depth of a globally defined horizon across which the pattern of lateral heterogeneity changes rapidly. Copyright 1997 by the American Geophysical Union.