Single crystals of Lu(ClO4)3 · 3 H2O were obtained by slow dehydration of Lu(ClO4)3 · 6 H2O at 140 °C under flowing argon. The compound crystallizes in the triclinic crystal system (P1, Z = 2, a = 750.3(1), b = 838.4(1), c = 1054.6(2) pm, α = 79.77(2)°, β = 79.18(2), γ = 63.83(2), Rall = 0.0426) with Lu3+ eightfold coordinated by oxygen atoms, which belong to five ClO4– groups and three H2O molecules. The [LuO8] polyhedra and ClO4– groups are connected to form chains which are held together only via hydrogen bridges. Er(ClO4)3 · H2O can also be prepared by dehydration of the respective hexahydrate but only at higher temperature and under vacuum. The triclinic compound (P1, Z = 2, a = 678.31(9), b = 783.4(1), c = 955.9(1) pm, α = 77.29(1)°, β = 75.71(1)°, γ = 78.31(1)°, Rall = 0.0292) contains Er3+ ions which are coordinated by seven ClO4– groups and one H2O molecule. The linkage of the [ErO8] polyhedra and ClO4– tetrahedra results in a three‐dimensional network. Attempts to dehydrate Sc(ClO4)3 · 6 H2O led to the basic perchlorate Sc(OH)(ClO4)2 · H2O. In the monoclinic structure (P21/n, Z = 4, a = 942.8(1), b = 735.16(8), c = 1157.9(2) pm, β = 93.76(2)°, Rall = 0.0579), Sc3+ is surrounded by six oxygen atoms which belong to three ClO4– ions, two OH– groups and one H2O molecule. These octahedra are connected via common edges which are formed by the OH– groups to pairs according to [Sc2(OH)2(ClO4)6(H2O)2]2–. Four of the six ClO4– groups link the pairs to two‐dimensional infinite sheets, which are held together via hydrogen bonds.