Crown reinforcement for a tire

A tire with radial carcass reinforcement, having a crown reinforcement comprising at least two working crown plies formed of inextensible metallic reinforcement elements, crossed from one ply to the next, forming angles of between 10° and 45° with the circumferential direction, characterized in that, in the absence of any ply formed of inextensible reinforcement elements forming an angle greater than 45° with the circumferential direction, an additional, axially continuous, ply formed of undulating reinforcement elements is placed radially between the working plies, said ply having an axial width L33 of at least 50% of the maximum axial width S0 of the carcass reinforcement, the undulations of the cables being parallel to each other, in phase and oriented parallel to the circumferential direction, and the ratio of the rigidity per unit length of the additional ply to the total of the rigidity per unit length of the other plies of the crown reinforcement being at most 0.10.