The ordered double perovskite Ba2BiTaO6 is shown to undergo a first-order rhombohedral (�3¯) to monoclinic (I2/m) phase transition, which can be induced by either lowering the temperature or through the application of pressure. The structures in both phases have been refined from high resolution neutron powder diffraction data at various temperatures, while the high pressure measurements utilised synchrotron X-ray diffraction data. The rhombohedral structure is characterised by out-of-phase tilts about the [111] axis. In the monoclinic structure the tilt axis has changed to be about the [110] axis; however, the magnitude of the tilts in the two structures is remarkably similar.