A run-flat tire (11) comprising a crown comprising a crown reinforcement (21, 22) surmounted by a tread (30); two sidewalls (40) extending the crown radially inward; two beads (50) radially inward to the sidewalls and each comprising an annular reinforcing structure (60); at least one carcass reinforcement (71, 72) anchored in each of the beads and extending from the beads through the sidewalls toward the crown; and at least one sidewall insert (80) axially on the inside of the carcass reinforcement, comprising at least one polymer compound; wherein at least one sidewall of the tire further comprises: at least one additional sidewall reinforcement (90) comprising reinforcing elements, positioned axially on the outside of the carcass reinforcement, the radially inside end (91) of the additional sidewall reinforcement being, in any radial section, radially on the inside of the axial straight line (100) that passes through those points in the sidewalls at which the carcass reinforcement has its greatest axial width when the tire is mounted on a rim; and a layer (110) of polymer compound positioned between the additional sidewall reinforcement and the carcass reinforcement, over at least a portion of the additional sidewall reinforcement.