Transparent, needle-like single crystals of the isostructural compounds [Sb4O7+3δX4][Zn3]1+δ (X = Cl, Br, I) δ ≈ 0.2 were obtained from chemical reactions in evacuated and sealed silica tubes. First, the average structure was solved in P21/n but the model refined poorly and a lowering of the symmetry to the 3 + 1 dimensional space group P21(α0γ)0 gave a significantly better fit to the data. This model used second order positional modulations for all the atoms. Whereas Sb, Cl (Br, I) and most O positions were well behaved, there was a mismatch with Zn that was better described in a sub-cell, thus yielding a composite structure. The composite nature of the structure leads to a charge imbalance that is compensated by oxygen vacancies.