We introduce REJECTOR, software for parameter estimation and comparison of alternate models of population history from genetic data via a rejection algorithm. Through coalescent simulation, REJECTOR generates numerous gene genealogies, and hence simulated data, under a model of population history specified by the user. Summary statistics derived from such simulated data are compared with observed statistics, leading to acceptance or rejection of a given set of parameter values. We performed tests of the software using known parameter values in order to assess the inferential power provided by each summary statistic. The tests demonstrate the precision and accuracy of estimation made possible using this approach.