Tire comprising a crown surmounted by a tread, a crown reinforcement, two sidewalls and two beads, a carcass reinforcement passing into the two sidewalls and anchored by means for anchoring in the two beads, said anchoring means comprising, in at least one bead, a circumferential alignment of at least one anchoring reinforcing member oriented circumferentially and cooperating with a rubber composition referred to as ‘anchoring rubber’; this tire is characterized in that this anchoring reinforcing member is a metal cable having two layers of construction M+N comprising an inner layer C1 of M wires of diameter d1 wound together in a helix at a pitch p1, this layer C1 itself being surrounded by an outer layer C2 of N wires of diameter d2 wound together in a helix at a pitch p2, this anchoring cable furthermore having the following characteristics (d1, d2, p1 and p2 in mm):2≦M≦4M+3≦N≦M+70.25<d1<0.40;0.25<d2<0.40;3.5<p1<7<p2<14.The invention also relates to a metal / rubber composite comprising the above two-layered metal cable associated with a rubber matrix of high rigidity, having, in the vulcanized state, a secant tensile modulus at 10% elongation which is greater than 20 MPa.