A tire is formed with two treads spaced transversely from each other, two sidewalls terminating in beads reinforced with bead wires, and, between the treads, a connection comprising in its center a wire rod forming a closed loop of diameter intermediate between that of the bead wires and that of the treads. Each tread has its own independent reinforcement, and each sidewall has a rigid zone close to the bead and a flexible zone close to the tread. The connection has on opposite sides of the central wire rod substantially the same structure and the same equilibrium profile when the tire is inflated, and therefore the same radial flexibility, as the flexible zones of the two sidewalls.