A new formulation is developed of the popular Discretized Population Balance due to Hounslow and co-workers. This new formulation is simpler and permits some variations in the method; three variations are put forward and tested. It also allows more flexibility in the choice of discretization, so that detail can be added at small sizes. The method is applied to the case of free-molecular aggregation Of SiO2 molecules inflames. The SiO2 is in equilibrium with SiO, which is assumed not to participate in aggregation; SiO2 molecules are, therefore, continuously created during aggregation. This source term complicates the resulting particle-size distributions compared to the self-preserving size distribution. Four parameters are used to summarize the PSDs, and their rates of change are found by approximations. This summarized model, a quasi-self-preserving size distribution, matches the detailed simulations very well. The cause of the stiffness of the differential equations is shown to be collisions between small and large particles. (C) 2004 American Institute of Chemical Engineers.