A tire intended to be mounted on a drop-center rim with a flange height G and a radius of curvature R1, comprising a first and a second bead, each comprising at least one annular reinforcing structure having a radially innermost point, the radial distance between the radially innermost point and the mounting rim being denoted by A; a carcass reinforcement anchored in the two beads by being turned back around the annular reinforcing structure so as to form, within each bead, a main strand and a turned-back strand, in which the first bead has a thickness EB1 and the second bead has a thickness EB2, the thicknesses EB1 and EB2 defined as the distance separating (i) the point on the main strand that is at a distance R from said point, where R=G+R1/2−A, and (ii) the point on the exterior surface of the bead that is at this same distance R from said point, and in which the absolute value of the difference between the thicknesses EB1 and EB2 is greater than or equal to 1 mm.