Mirabilite (Na2SO4.10H2O) is relevant to many areas of geology, planetary science, and even the construction industry. It occurs naturally in evaporite deposits, and even as microscopic inclusions in polar ice sheets; moreover, it is thought to be a major rock-forming mineral on the solar system¿s icy moons. It has been used as an energy storage material, and its formation on weathering causes structural damage to building stones. In 1978, Levy & Lisensky reported a single-crystal neutron study of protonated mirabilite. They identified orientational disorder in some Na-coordinated water molecules, and also in the sulfate tetrahedra. However, our recent neutron powder study of deuterated mirabilite found no evidence of this sulfate disorder. We wish to determine the reasons for this difference in behaviour by single-crystal measurements of both protonated and deuterated mirabilite.