The Genealogical Sorting Index (gsi) has been widely used in species-delimitation studies, where it is usually interpreted as a measure of the degree to which each of several predefined groups of specimens display a pattern of divergent evolution in a phylogenetic tree. Here we show that the gsi value obtained for a given group is highly dependent on the structure of the tree outside of the group of interest. By calculating the gsi from simulated datasets we demonstrate this dependence undermines some of desirable properties of the statistic. We also review the use of the gsi delimitation studies, and show that the gsi has typically been used under scenarios in which it is expected to produce large and statistically significant results for samples that are not divergent from all other populations and thus should not be considered species. Our proposed solution to this problem performs better than the gsi in under these conditions. Nevertheless, we show that our modified approach can produce positive results for populations that are connected by substantial levels of gene flow, and are thus unlikely to represent distinct species. We stress that the properties of gsi made clear in this manuscript must be taken into account if the statistic is used in species-delimitation studies. More generally, we argue that the results of genetic species-delimitation methods need to be interpreted in the light the biological and ecological setting of a study, and not treated as the final test applied to hypotheses generated by other data.