alpha(R)-In2Se3 has been experimentally and theoretically studied under compression at room temperature by means of X-ray diffraction and Raman scattering measurements as well as by ab initio total-energy and lattice-dynamics calculations. Our study has confirmed the alpha (R3m) -> beta' (C2/m) ? beta (R (3) over barm) sequence of pressure-induced phase transitions and has allowed us to understand the mechanism of the monoclinic C2/m to rhombohedral R (3) over barm phase transition. The monoclinic C2/m phase enhances its symmetry gradually until a complete transformation to the rhombohedral R (3) over barm structure is attained above 10-12 GPa. The second-order character of this transition is the reason for the discordance in previous measurements. The comparison of Raman measurements and lattice-dynamics calculations has allowed us to tentatively assign most of the Raman-active modes of the three phases. The comparison of experimental results and simulations has helped to distinguish between the different phases of In2Se3 and resolve current controversies.