A tire includes two beads and a carcass reinforcement anchored in the beads. The carcass reinforcement has at least two circumferential alignments of first reinforcing threads. Each such circumferential alignment is, within each bead, bordered axially inwardly and outwardly by second circumferential reinforcing threads having an elasticity modulus at least equal to that of the first threads. The first and second threads are separated by a rubber mix of high elasticity modulus. The outer surface of each bead includes a seat which includes an arc-shaped wall section having a geometrical center arranged axially outwardly relative to the bead. Considering an imaginary straight line passing through both the center and the bead at an angle α=+45±5 degrees relative to the tire axis, all of the second threads are spaced from that axis by a radial distance no larger than the locus of the imaginary line.