A tire intended to be mounted on a drop-center rim with a flange height G and a radius of curvature R1 has first and second beads each having an annular reinforcing structure having a radially innermost point, the radial distance between the radially innermost point and the mounting rim being A, and a carcass reinforcement anchored in the two beads by being turned back around the annular reinforcing structure forming, within each bead, a main strand and a turned-back strand, in which the thicknesses EB1 of the first bead and EB2 of the second bead are the distance separating (i) the point on the main strand that is at a distance R from the radially innermost point, where R=G+(R1)/2−A, and (ii) the point on the exterior surface of the bead that is at the distance R from the radially innermost point, and in which |EB1−EB2|≧1 mm.