The tunable bandgaps and facile fabrication of perovskites make them attractive for multi-junction photovoltaics(1,2). However, light-induced phase segregation limits their efficiency and stability(3-5): this occurs in wide-bandgap (>1.65 electron volts) iodide/bromide mixed perovskite absorbers, and becomes even more acute in the top cells of triple-junction solar photovoltaics that require a fully 2.0-electron-volt bandgap absorber(2,6). Here we report that lattice distortion in iodide/bromide mixed perovskites is correlated with the suppression of phase segregation, generating an increased ion-migration energy barrier arising from the decreased average interatomic distance between the A-site cation and iodide. Using an approximately 2.0-electron-volt rubidium/caesium mixed-cation inorganic perovskite with large lattice distortion in the top subcell, we fabricated all-perovskite triple-junction solar cells and achieved an efficiency of 24.3 per cent (23.3 per cent certified quasi-steady-state efficiency) with an open-circuit voltage of 3.21 volts. This is, to our knowledge, the first reported certified efficiency for perovskite-based triple-junction solar cells. The triple-junction devices retain 80 per cent of their initial efficiency following 420 hours of operation at the maximum power point.