Supertree methods are fairly widely used to build comprehensive phylogenies for particular groups, but concerns remain over the adequacy of existing approaches. Steel and Rodrigo recently introduced a statistical model of incongruence between trees, allowing maximum-likelihood supertree inference. This approach to supertree construction will enable hypothesis-testing and model-choice methods that are now routine in sequence phylogenetics to be applied in this setting, and might form an important part of future phylogenetic inference from genomic data.