Three-taxon statement matrices can be analysed using the maximum-likelihood method. In the present paper, it is demonstrated that groups based solely on putative reversals are always recognisable after maximum-likelihood analysis of three-taxon statement matrices, even without a priori recoding of the putative reversals as new character states or fractional weighting of three-taxon statements. Parametric implementations of three-taxon statement analysis still require more investigation. However, it must be highlighted that a focus on the set of hypotheses, rather than on the ‘actual data’, is required.