Population balance equations for microbial or cell cultures contain a state-dependent fission intensity function which is such that the product of this function, evaluated at a given state, and a differential increment of time is the fraction of cells of the given state that divide in that increment of time. Ways to determine experimentally how the fission intensity function depends on cell state have been proposed but, so far as is known to the authors, no one has yet proposed a model that would predict what the state dependence of the fission intensity function is for any population. If one wants to take account of the existence of cell cycle phases, one will have to write a population balance equation for each phase, a transition intensity function for each phase will have to be introduced. and the problem of making models for these functions will arise again, and in multiplied fashion. In this paper, we describe a new and different approach which circumvents the necessity of having intensity functions for transitions between cell cycle phases, and for which the fission intensity function is state-independent.