Bandgap instability due to light-induced phase segregation in mixed-halide perovskites presents a major challenge for their future commercial use. Here we demonstrate that photoinduced halide-ion segregation can be completely reversed at sufficiently high illumination intensities, enabling control of the optical bandgap of a mixed-halide perovskite single crystal by optimizing the input photogenerated carrier density. We develop a polaron-based two-dimensional lattice model that rationalizes the experimentally observed phenomena by assuming that the driving force for photoinduced halide segregation is dependent on carrier-induced strain gradients that vanish at high carrier densities. Using illumination sources with different excitation intensities, we demonstrate write-read-erase experiments showing that it is possible to store information in the form of latent images over several minutes. The ability to control the local halide-ion composition with light intensity opens opportunities for the use of mixed-halide perovskites in concentrator and tandem solar cells, as well as in high-power light-emissive devices and optical memory applications.