We have performed detailed first-principles calculations to determine the eigenvectors of the zone-centre modes of hexagonal BaTiO₃ and shown that the experimentally relevant soft modes can be represented as suitable combinations of basic local distortions taken directly from the better known perovskite phase. The hexagonal structure provides a testing ground for the analysis of the influence of the stacking of TiO₆ octahedra; in particular, its effect on the energetics of the chains of dipoles which are the essential element in the instabilities of the perovskite BaTiO₃.