Abstract Repeated runs of the same program can generate different molecular phylogenies from identical data sets under the same analytical conditions. This lack of reproducibility of inferred phylogenies casts a long shadow on downstream research employing these phylogenies in areas such as comparative genomics, systematics, and functional biology. We have assessed the relative accuracies and log-likelihoods of alternative phylogenies generated for computer-simulated and empirical data sets. Our findings indicate that these alternative phylogenies reconstruct evolutionary relationships with comparable accuracy. They also have similar log-likelihoods that are not inferior to the log-likelihoods of the true tree. We determined that the direct relationship between irreproducibility and inaccuracy is due to their common dependence on the amount of phylogenetic information in the data. While computational reproducibility can be enhanced through more extensive heuristic searches for the maximum likelihood tree, this does not lead to higher accuracy. We conclude that computational irreproducibility plays a minor role in molecular phylogenetics.