This paper shows that despite evidence of structural convergence between some of the Austronesian and non-Austronesian (Papuan) languages of Island Melanesia, statistical methods can detect two independent genealogical signals derived from linguistic structural features. Earlier work by the author and others has presented a maximum parsimony analysis which gave evidence for a genealogical connection between the non-Austronesian languages of island Melanesia. Using the same data set, this paper demonstrates for the non-statistician the application of more sophisticated statistical techniques—including Bayesian methods of phylogenetic inference, and shows that the evidence for common ancestry is if anything stronger than originally supposed.