The ability of phase transitions and a viscosity jump at 660 km depth to induce long-wavelength flow in the mantle is systematically investigated using three-dimensional numerical simulations of internally-heated convection at convective vigors (as indicated by the Rayleigh number Ra) ranging from mildly supercritical to greater than the Earth's current regime. Cases with neither a viscosity jump nor phase changes display a steadily decreasing wavelength with increasing Ra, as expected. Increasing the lower mantle viscosity by a factor of 30 induces significantly longer wavelengths, but the ''reddening'' effect decreases with increasing Ra; this is explained in large part by the decrease in effective Rayleigh number due to increasing the lower mantle viscosity. In contrast, the effect of phase transitions is minor at low Ra but increases sharply at geodynamically relevant Ra, potentially increasing the mean wavelength of thermal heterogeneity by factors of greater than 10. Conclusions regarding the relative importance of the two effects are thus highly dependent on Ra. ¿ American Geophysical Union 1996