Solution-processable metal halide perovskites show immense promise for use in photovoltaics and other optoelectronic applications. The ability to tune their bandgap by alloying various halide anions (for example, in CH3NH3Pb(I1-xBrx)3, 0 < x < 1) is however hampered by the reversible photoinduced formation of sub-bandgap emissive states. We find that ion segregation takes place via halide defects, resulting in iodide-rich low-bandgap regions close to the illuminated surface of the film. This segregation may be driven by the strong gradient in carrier generation rate through the thickness of these strongly absorbing materials. Once returned to the dark, entropically driven intermixing of halides returns the system to a homogeneous condition. We present approaches to suppress this process by controlling either the internal light distribution or the defect density within the film. These results are relevant to stability in both single- and mixed-halide perovskites, leading the way toward tunable and stable perovskite thin films for photovoltaic and light-emitting applications.