Reconstruction artifacts are a serious hindrance to the elucidation of phylogenetic relationships and a number of methods have been devised to alleviate them. Previous studies have demonstrated a striking disparity in the evolutionary rates of the mitochondrial (mt) genomes of squamate reptiles (lizards, worm lizards and snakes) and the reconstruction artifacts that may arise from this. Here, to examine basal squamate relationships, we have added the mt genome of the blind skink Dibamus novaeguineae to the mitogenomic dataset and applied different models for resolving the squamate tree. Categorical models were found to be less susceptible to artifacts than were the commonly used noncategorical phylogenetic models GTR and mtREV. The application of different treatments to the data showed that the removal of the fastest evolving sites in snakes improved phylogenetic signal in the dataset. Basal divergences remained, nevertheless, poorly resolved. The proportion of both fast-evolving and conserved sites in the squamate mt genomes relative to sites with intermediate rates of evolution suggests rapid early divergences among squamate taxa and at least partly explains the short internal relative to external branches in the squamate tree. Thus, mt and nuclear trees may never reach full agreement because of the short branches characterizing these divergences.