High pressure single crystal X-ray diffraction measurements that have been performed over the 0–2.5 GPa pressure range with the 3D metal–organic hybrid material {[Cu(CO₃)₂](CH₆N₃)₂}_n (1) are discussed. Compound 1 contracts over the 0–4 GPa pressure range, but exhibits reversible softening at pressures in excess of 2.5 GPa. The mechanisms by which these structural rearrangement processes occur have been elucidated. Furthermore, an extensive evaluation of the elastic properties of 1 has been performed. The room temperature isothermal bulk modulus for 1 is 36.1(3) GPa, and the axial compressibilities for the tetragonal unit cell of 1 are 7.7(1) × 10⁻³ and 1.23(1) × 10⁻²GPa⁻¹ for the a- and c-axes, respectively.