A tire designed to be mounted on a mounting rim J of maximum diameter Dc the type comprising beads designed to cooperate with seats of the mounting rim, the beads comprising at least one annular bead reinforcement structure; a crown comprising a reinforcement structure, this crown being surmounted radially on the outside by a tread; on either side of the tire's crown, a sidewall providing connection to each bead; a carcass reinforcement extending between the crown and the beads; wherein at least one sidewall comprises at least two additional annular reinforcement structures, each additional annular structure having an inner diameter at least equal to the maximum diameter Dc of the rim; the carcass reinforcement is anchored at least partially on each annular bead reinforcement structure and on each additional annular sidewall reinforcement structure; the difference between the inner diameter of the radially innermost additional annular reinforcement structure in each sidewall and the diameter Dj of the rim seat on the same side as the sidewall containing the annular structure is at least equal to 20% of the diameter Dj.