Tire comprising two beads and a carcass reinforcement anchored in each bead, each bead comprising a plurality of annular reinforcing structures forming at least one anchoring alignment, parallel to a portion of the carcass reinforcement, and an additional stiffening reinforcement formed by one single alignment of at least two annular reinforcing structures and extending between a first end situated a distance H1 from the tangent to the seat-forming bead portion being 20-70% of the anchoring alignment minimum distance H0, the first end lying an axial distance L1 from the interior surface of the tire being 50-85% of the maximum axial width L0 of the bead; and a second end, the second end being radially and axially at the same level as or on the outside of the first end such that the distance LA separating the first and second ends is ≧30% of the mean anchoring alignment length.