In halide perovskites, photocarriers can have strong polaronic interactions with point defects. For iodide-deficient MAPbI3, we found that the Fermi level can shift significantly by 0.6-0.7 eV upon light illumination. This energy level shift is accompanied by the formation of deep electron traps. These experimental observations are consistent with the formation of a Pb-Pb dimer when photoexcited electrons are trapped at an iodide vacancy. Interestingly, we found that this polaronic interaction is suppressed when a portion of MA+ cations is replaced by smaller Cs+ ions. Density functional theory calculations reveal that Cs-doping can reduce the distance between two Pb atoms across an iodide vacancy, even without electron trapping. The predistortion of the lattice induced by cation replacement resembles the Pb-Pb dimer formed by electron trapping at the defect site, which explains the suppression of light-induced effects observed in the experiment. Our finding unveils a counterintuitive strategy to enhance the photostability of halide perovskites by preintroducing distortions into its lattice.