Numerical simulations of compressible, isochemical mantle convection are used to investigate the effect of the perovskite to post-perovskite phase transition at around 2700 km depth, which has recently been discovered by high-pressure experiments and ab initio calculations, on the convective planform, temperature, and heat transport characteristics of the mantle. The usual phase transitions at 410 km (olivine-spinel) and 660 km (spinel-perovskite) are also included. The exothermic post-perovskite phase change at 2700 km depth destabilizes the lower thermal boundary layer, increasing the heat flow, increasing interior mantle temperature, and increasing the number and time-dependence of upwelling plumes. The resulting weak, highly time-dependent upwellings also have a smaller horizontal spacing than the plumes that occur in the absence of the phase transition. While the influence of post-perovskite phase change may be smaller than that of some other complexities, such as compositional stratification, it appears to have an important enough effect that it should not be ignored in dynamical studies of mantle convection.