Current numerical solutions of population balance problems including growth are limited by the Courant condition time step constraint. As a result, particle size ranges must be restricted and limited growth rate mechanisms can be solved. A thorough analysis of growth rate mechanisms and dynamics is presented that relates the growth rate mechanisms and particle size ranges to the time step limit. These relationships reveal a method for producing the optimal time step for any growth rate model, which can increase the time step by a factor of 10(7). When these methods are combined with previous approaches, new hybrid methods are developed that allow the user to flexibly choose the optimal time step given the resolution requirements of the problem, producing solutions that are 10(4)-10(7) times faster than conventional solutions. The numerical accuracy of these solutions compares favorably against analytical solutions, demonstrating their applicability across a wide range of problems.