The method of successive generations used in Monte Carlo simulations of nuclear reactor models is known to suffer from intergenerational correlation between the spatial locations of fission sites. One consequence of the spatial correlation is that the convergence rate of the variance of the mean for a tally becomes worse than O(N–1). In this work, we consider how the true variance can be minimized given a total amount of work available as a function of the number of source particles per generation, the number of active/discarded generations, and the number of independent simulations. We demonstrate through both analysis and simulation that under certain conditions the solution time for highly correlated reactor problems may be significantly reduced either by running an ensemble of multiple independent simulations or simply by increasing the generation size to the extent that it is practical. However, if too many simulations or too large a generation size is used, the large fraction of source particles discarded can result in an increase in variance. We also show that there is a strong incentive to reduce the number of generations discarded through some source convergence acceleration technique. Furthermore, we discuss the efficient execution of large simulations on a parallel computer; we argue that several practical considerations favor using an ensemble of independent simulations over a single simulation with very large generation size.