This paper builds on a previous work in which we attempted to retrieve a phylogenetic signal using abstract structural features alone, as opposed to cognate sets, drawn from a sample of Island Melanesian languages, both Oceanic (Austronesian) and (non-Austronesian) Papuan (Science 2005[309]: 2072-75 ). Here we clarify a number of misunderstandings of this approach, referring particularly to the critique by Mark Donohue and Simon Musgrave (in this same issue of Oceanic Linguistics), in which they fail to appreciate the statistical principles underlying computational phylogenetic methods. We also present new analyses that provide stronger evidence supporting the hypotheses put forward in our original paper: a reanalysis using Bayesian phylogenetic inference demonstrates the robustness of the data and methods, and provides a substantial improvement over the parsimony method used in our earlier paper. We further demonstrate, using the technique of spatial autocorrelation, that neither proximity nor Oceanic contact can be a major determinant of the pattern of structural variation of the Papuan languages, and thus that the phylogenetic relatedness of the Papuan languages remains a serious hypothesis.