The isostructural family of compounds that includes the familiar copper sulfate pentahydrate and the two less familiar title materials, has for decades been a model for studying a range of structural and magnetic phenomena. Our understanding of the magnetic transitions on cooling below 1 K have hitherto been based on an assumption that there is no preceding structural change, an assumption we now know to be false. We have shown that CuSO4.5D2O undergoes a loss...