The structure of the salts MBr₃, where M³⁺ denotes Dy³⁺, Y³⁺, Ho³⁺ or Er³⁺, was investigated by using neutron diffraction. On heating DyBr₃, YBr₃ and HoBr₃, a phase transition from the FeCl₃-type crystal structure to possibly the YCl₃-type crystal structure was observed. The liquids were studied at the total-structure-factor level and difference function methods were also applied to DyBr₃ and YBr₃ by assuming isomorphous structures. The melts are found to comprise distorted MBr₆^3- octahedra with M-Br distances comparable to the sum of the ionic radii and there is evidence for a substantial number of edge-sharing configurations. The octahedra pack to give intermediate-range ionic ordering as manifested by the appearance of a first sharp diffraction peak at 0.79(2)-0.87(2) Å^-1 which is associated with cation correlations