Cs4O6 adopts two distinct crystal structures at ambient pressure. At temperatures below ∼200 K, its ground state structure is tetragonal, incorporating two symmetry-distinct dioxygen anions, diamagnetic peroxide, O22-, and paramagnetic superoxide, O2-, units in a 1:2 ratio, consistent with the presence of charge and orbital order. At high temperatures, its ground state structure is cubic, comprising symmetry-equivalent dioxygen units with an average oxidation state of -4/3, consistent with the adoption of a charge-disordered state. The pressure dependence of the structure of solid Cs4O6 at 300 K and at 13.4 K was followed up to ∼12 GPa by synchrotron X-ray powder diffraction. When a pressure of ∼2 GPa is reached at ambient temperature, an incomplete phase transition that is accompanied by a significant volume reduction (∼2%) to a more densely packed highly anisotropic tetragonal structure, isostructural with the low-temperature ambient-pressure phase of Cs4O6, is encountered. A complete transformation of the cubic (charge-disordered) to the tetragonal (charge-ordered) phase of Cs4O6 is achieved when the hydrostatic pressure exceeds 6 GPa. In contrast, the pressure response of the Cs4O6 cubic/tetragonal phase assemblage at 13.4 K is distinctly different with the cubic and tetragonal phases coexisting over the entire pressure range (to ∼12 GPa) accessed in the present experiments and with only a small fraction of the cubic phase converting to tetragonal. Pressure turns out to be an inefficient stimulus to drive the charge disorder-order transition in Cs4O6 at cryogenic temperatures, presumably due to the high activation barriers (much larger than the thermal energy at 13.4 K) associated with the severe steric hindrance for a rotation of the molecular oxygen units necessitated in the course of the structural transformation.