Mixing iodide and bromide in halide perovskite semiconductors is an effective strategy to tune their band gap; therefore, mixed-halide perovskites hold great promise for color-tunable LEDs and tandem solar cells. However, the band gap of mixed-halide perovskites is unstable under (sun-)light, since the halides segregate into domains of different band gaps. Using pressure-dependent ultrafast transient absorption spectroscopy, we find that high external pressure increases the range of stable halide mixing ratios. Chemical compression, by inserting a smaller cation, has the same effect, which means that any iodide:bromide ratio can be stabilized by tuning the crystal volume and compressibility. We interpret these findings as an increased thermodynamic stabilization through alteration of the Gibbs free energy via the largely overlooked PΔV term.