We report the size-dependent pressure response for CsPbBr3 perovskite nanocrystals in the size range 5.7-10.9 nm using photoluminescence spectroscopy in a diamond anvil cell. As the nanocrystal size decreases below ca. 7.5 nm, we observe a decrease in the transition pressure at which there is a change in the mode of deformation concomitant with an isostructural phase transition. We hypothesize that surface fluctuations regarding the tilt and distortion of surface PbBr6 octahedra facilitate the change in the mode of deformation and phase transition at lower pressures for smaller nanocrystals.