Tire having crown reinforcement with profiled element and edging rubber

A tire having a radial carcass reinforcement, which is anchored within each bead to at least one bead wire, and is surmounted by a crown reinforcement comprising at least two plies of reinforcement elements, which are parallel to each other within each ply and are crossed from one ply to the next, said two plies being of unequal axial widths, each edge of the ply which is axially less wide of at least a pair of crossed plies being separated from the axially widest ply of the same pair by a profiled element P of rubber mix, the axially outer end of which is located at a distance from the equatorial plane of the tire which is at least equal to the distance between said plane and the end of the widest ply, said profiled element P itself being separated from the liner C contacting the reinforcement elements of the least wide ply by an edging rubber G, the axially outer end of which is located at a distance from said plane which is at least equal to half the width of the least wide ply, the tire characterized in that said profiled element P, said edging rubber G and said liner C have respectively secant moduli of elasticity under tension at 10% relative elongation MP, MG, MC such that MC≧MG>MP, the thickness of the edging rubber being at least equal to 15% of the total thickness of rubber mix between generatrices of cables respectively of the two plies.