The performance of lead-halide perovskites in optoelectronic devices is due to a unique combination of factors, including highly efficient generation, transport, and collection of photogenerated charge carriers. The mechanism behind efficient charge generation in lead-halide perovskites is still largely unknown. Here, we investigate the factors that influence the exciton binding energy (Eb) in a series of metal-halide perovskites using accurate first-principles calculations based on solution of the Bethe-Salpeter equation, coupled to ab initio molecular dynamics simulations. We find that Eb is strongly modulated by screening from low-energy phonons, which account for a factor ∼2 Eb reduction, while dynamic disorder and rotational motion of the organic cations play a minor role. We calculate Eb = 15 meV for MAPbI3, in excellent agreement with recent experimental estimates. We then explore how different material combinations (e.g., replacing Pb → Pb:Sn→ Sn; and MA → FA → Cs) may lead to different Eb values and highlight the mechanisms underlying Eb tuning.