Variable temperature X-ray and neutron powder diffraction techniques have been used to identify structural phase transitions in Cu-rich A(3)A'BO6 phases. A transition from monoclinic to rhombohedral symmetry was observed by X-ray diffraction between 700 and 500 K in Sr3Cu1-xMxIrO6 (M = Ni, Zn; 0 less than or equal to x less than or equal to 0.5). The temperature of the phase change decreased in a linear manner with Cu-content and was essentially independent of the nature of M. Ca3.1Cu0.9MnO6 was shown to pass from a rhombohedral phase to a triclinic phase on cooling below 290 K; the structure of the triclinic phase was refined against neutron diffraction data collected at 2 K. Ca3.1CU0.9RuO6 undergoes a transition between a disordered rhombohedral phase and an ordered monoclinic phase when cooled below 623 K. Neutron diffraction has been used to determine the structure as a function of temperature in the range 523 less than or equal to T/K less than or equal to 723 and hence to determine an order parameter for the low temperature phase; the second-order transition is shown to be incomplete 100 K below the critical temperature.