Computer-based group-theoretical methods are used to enumerate structures arising in A₂BB'X₆ perovskites, with either rock-salt or checkerboard ordering of the B and B' cations, under the additional assumption that one of these two cations is Jahn–Teller active and thereby induces a distortion of the BX₆ (or B'X₆) octahedron. The requirement to match the pattern of Jahn–Teller distortions to the cation ordering implies that the corresponding irreducible representations should be associated with the same point in the Brillouin zone. Effects of BX₆ (and B'X₆) octahedral tilting are included in the usual way. Finally, an analysis is presented of more complex models of ordering and distortion as might lead to the doubling of the long axis of the common Pnma perovskite, observed in systems such as Pr₁₋ xCaxMnO₃(x ≃ 0.5). The structural hierarchies derived in this work should prove useful in interpreting experimental results.