Using single crystal X-ray methods, the structural phase sequence of (C3H7NH3)2CuBr4 (abbreviated to C3CuBr) has been studied at 100 K < T < 420 K. The perovskite-type layer structure, distorted by the Jahn-Teller effect, exhibits four phases: δ phase: Pbca, (4); ε phase: P21/b11, (2); ζ phase: IC (P21/b11); η phase; P 1, (4); the number of formula units per primitive cell is given in brackets. Remarkably, the ζ phase is incommensurate (IC), and the normal phase (ε phase) appears upon heating only: The changes in lattice symmetry at the strongly discontinuous δ → ζ and ε → δ phase transitions point to a spontaneous rearrangement of the octahedral JT-distortion pattern within every second layer. Upon cooling, this process is triggered by the onset of the modulation of the IC ζ phase. The wave vector is given by q ζ = (1/2 - δ2)b* m - δ3 c* m, with the irrational parts δ2 and δ3 in the cooling (c) and heating (h) case: δ c 2 ≈ 0.009, δh 2 ≈ 0;δ c,h 3 ≈ 0.09.δ3 decreases slightly with temperature, both δ2 and δ3 jump to zero at the ζ → η transition.