Recent geophysical evidences from seismology and geoid inversions have pointed out the existence of some layering between 900 and 1000 km depth and the possibilities of a low viscosity zone between 660 and 1000 km depth. Using a finite-difference and spectral code, we have conducted 3-D calculations of thermal convection with the endothermic phase transition at 670 km depth and a family of viscosity profiles with emphasis on the presence of two low viscosity zones, one in the upper mantle between 100 and 250 km depth and the second one between 670 and 1000 km depth. Below 1000 km the viscosity increases with depth. The surface Rayleigh number used was in the range of 107. The dominating effect is that due to the second low viscosity zone below the phase change. Layered convection is induced by the presence of this second asthenosphere, which causes horizontal flow to develop in there. Alternatively, a viscosity increase at 670 km depth would shift convection to the single-layer regime. The potential sharp variations of the viscosity structure between 670 and 1000 km depth can greatly influence the global flow dynamics of the mantle.