Our understanding of population history in deep time has been assisted by fitting admixture graphs (AGs) to data: models that specify the ordering of population splits and mixtures, which along with the amount of genetic drift and the proportions of mixture, is the only information needed to predict the patterns of allele frequency correlation among populations. The space of possible AGs relating populations is vast, and thus most published studies have identified fitting AGs through a manual process driven by prior hypotheses, leaving the majority of alternative models unexplored. Here, we develop a method for systematically searching the space of all AGs that can incorporate non-genetic information in the form of topology constraints. We implement thisfindGraphstool within a software package,ADMIXTOOLS 2, which is a reimplementation of theADMIXTOOLSsoftware with new features and large performance gains. We apply this methodology to identify alternative models to AGs that played key roles in eight publications and find that in nearly all cases many alternative models fit nominally or significantly better than the published one. Our results suggest that strong claims about population history from AGs should only be made when all well-fitting and temporally plausible models share common topological features. Our re-evaluation of published data also provides insight into the population histories of humans, dogs, and horses, identifying features that are stable across the models we explored, as well as scenarios of populations relationships that differ in important ways from models that have been highlighted in the literature.