This study investigates the effect of hydrostatic pressure on the luminescence properties of CsPbBr3 single crystals at 12 K. The luminescence at the edge of the band gap reveals a structure attributed to free excitons, phonon replica of the free excitons, and Rashba excitons. Changes in the relative intensity of the free and Rashba excitons were observed with increasing pressure, caused by changes in the probability of nonradiative deexcitation. At pressures around 3 GPa, luminescence completely fades away. The red shift of the energy position of the maximum luminescence of free and Rashba excitons in pressure ranges of 0-1.3 GPa is attributed to the length reduction of Pb-Br bonds in [PbBr6]4- octahedra, while the high-energy shift of the Rashba excitons at pressures above 1.3 GPa is due to [PbBr6]4- octahedra rotation and changes in the Pb-Br-Pb angle.