We report X-ray diffraction measurements in CdIn ₂S ₄, MgIn ₂S ₄, and MnIn ₂S ₄ thiospinels at room temperature and high pressures. The pressure dependences of the structural parameters have been determined and compared to those from theoretical calculations. It is found that the three thiospinels have similar bulk moduli (B ₀) between 75 and 80 GPa (B ₀́ ∼ 3). The degree of inversion of these thiospinels has also been determined. The three thiospinels undergo a phase transition toward a defect LiTiO ₂-type structure above 9.5, 8.3, and 6.8 GPa in CdIn ₂S ₄, MgIn ₂S ₄, and MnIn ₂S ₄, respectively. Interestingly, the low- and high-pressure phases belong to the same symmetry group (Fd-3m), the transition mechanism being associated to the migration of the tetrahedrally coordinated cations to a Wyckoff position of higher multiplicity, where these cations present an octahedral environment. The new postspinel phase exhibits a larger compressibility than the spinel phase for the three compounds, likely due to the presence of stoichiometric vacancies in the unit cell as it occurs for defect chalcopyrites and stannites. The relation between the bulk and the polyhedral compressibilities is discussed as well.