The effects on the dynamics of compressible mantle convection from increasing Rayleigh number, viscosity stratification and internal heating are investigated in a time-dependent, 3-D spherical shell model. Resolution of up to spherical harmonics of degree 192 and 150 higher-order finite difference grid points unevenly distributed in the radial direction have been employed. Surface Rayleigh number varies from 5 × 104 to O(107). The viscosity profiles used range from constant to a depth-dependent viscosity profile. The Adams-Williamson adiabatic assumption is adopted for describing the equation of state. Both depth dependences of thermal expansivity and thermal conductivity are included. We have focused on the viscosity stratification in the lower mantle. The mean temperature profiles are very sensitive to the input parameters, such as the amount of internal heating and the dissipation number. In the isoviscous model the number of hot plumes decreases for low Rayleigh number (5 × 104) and increases dramatically with higher Rayleigh number (106). In the model with a high-viscosity zone in the lower mantle, the number of plumes is small and does not change too much, when the Rayleigh number varies from 3 × 106 to 8 × 106. In the purely base-heated, viscously stratified models well-organized triple junctions of the downwelling sheets are developed near the surface and interconnected cold walls of downwellings are produced around upwelling plumes. The presence of internal heating increases the number of upwelling plumes and breaks up the interconnection of downwelling sheets. Strong viscous heating in the compressible solutions is found near the top and bottom. At the higher values of Rayleigh number the laterally averaged value of viscous dissipation is comparable with the chondritic strength of internal heating. Whether the maximum viscous heating is found in upwelling plumes or downwelling flows depends on the presence of internal heating and the mechanical boundary conditions. The effects of compressibility on local structures and plume morphologies can be significant. However, these compressible effects are moderate on the global patterns.