The structural behavior of BiMnO3 under pressure was studied in a quantitative way by single-crystal synchrotron X-ray diffraction up to 36 GPa. Two phase transitions were observed at moderate pressures (1 and 6 GPa, respectively), leading the system at first to the P21/c and then to the Pnma symmetry. The breaking of C-centering in the first transition does not affect significantly Jahn-Teller (JT) distortion and orbital order (OO) but determines a significant change in the cooperative tilting of the MnO6 octahedra. The second transition increases the symmetry to orthorhombic, leading to a Pnma structure similar to the O' structure of LaMnO3, characterized by a > c > b/√2. No symmetry change was observed above 7.1 GPa, but the different compressibility of the lattice parameters (in particular, the b axis) leads at first to a pseudocubic phase (≈30 GPa) and then to different parameter ratios (b/√2 > c > a). Even if the JT distortion is continuously reduced with increasing pressure, it is retained, together with the resulting OO, until the highest measured pressure, pointing out the relevant role of the distortion induced by the Bi(3+) lone pair in stabilizing the JT distortion.