The invention relates to a tire in which at least one first profiled element P of rubber mix separates the axially widest ply of reinforcement elements from at least one end of a second ply, axially narrower than the axially widest ply, the axially outer end of said first profiled element P being located at a distance from the equatorial plane of the tire which is less than the distance between said plane and the end of the axially widest ply of reinforcement elements, said profiled element P being radially separated at least in part from the liner C of said axially narrower ply of reinforcement elements by a second profiled element of rubber mix G, and said first and second profiled elements of rubber mix P and G and said liner C having secant modules of elasticity under tension at 10% elongation MP, MG, MC respectively such that MC≧MG>MP.