The pressure‐temperature phase diagram of InSb is refined to show the boundaries between the high‐pressure tetragonal (InSb II) and orthorhombic (InSb IV) phases and extended to about 125 kbar to locate the boundary of the new phase (InSb III). The existence of these structures as stable phases in their phase fields is demonstrated by high‐pressure, high‐temperature x‐ray studies and by x‐ray studies and superconductivity measurements on these phases retained by quenching to 77°K. The structures of InSb II and InSb IV are confirmed, and a hexagonal structure for InSb III is proposed. The hexagonal cell has the dimensions (at ∼90 kbar) ofa=6.10 Å andc=5.71 Å with a calculated density of 8.5 g/cc. Values are reported for the compressibility of phases InSb I, InSb III, and InSb IV and for the thermal expansion coefficients, under pressure, of phases InSb I and InSb IV.