Tire (10) comprising a radial carcass reinforcement (2) anchored in beads, the tire (10) comprising two sidewalls (1), each sidewall (1) extending between a bead (4) and a crown (3), the two sidewalls comprising a first additional reinforcement (6) positioned either between the carcass reinforcement and the internal cavity of the tire or axially on the outside of the carcass reinforcement and at least one of the sidewalls comprising a second additional reinforcement (5), this tire being characterized in that the first additional reinforcement comprises a plurality of reinforcing elements of textile nature oriented at an angle at least equal to 80° and at most equal to 90° to the circumferential direction, and in that the second additional reinforcement (5) comprises, in the circumferential direction and in an alternating manner, a plurality of first parts (51) and of second parts (52), these second parts (52), having a mean width at least equal to 20 mm, these first and second parts having ultimate tensile strengths, that is to say forces at break per unit width of reinforcement, which are such that the ultimate tensile strength of the second parts (52) is lower than the ultimate tensile strength of the first parts, and in that the first and second additional reinforcements are positioned one on each side of the carcass reinforcement.