Informal impressions or formal estimates of the size of prehistoric populations are often distorted by counting as if contemporary remains that, although dating to the same general period, were not in fact contemporary in a strict sense. In this paper, I evaluate a number of methods for mitigating this problem and propose a new solution. In the process, fundamental questions are raised concerning the nature of period boundaries, the life-cycles of sites, and how these phenomena affect estimates of the size of prehistoric populations. It is suggested that the growth cycles of most sites can be approximated by a relatively simple mathematical formula, or a series of such formulae, each expressed as a function of time. The total population can then be estimated at any point in time. A computer program to perform this task is given as an appendix, and the suggested procedure is illustrated with an example using data from SW Iran.