A tire includes two beads configured to come into contact with a mounting rim and two sidewalls extending the beads radially to the outside, the two sidewalls being joined together in a crown. A crown reinforcement extends axially between two axial ends and is surmounted by a tread. The crown includes, radially on the inside of the tread and radially on the outside of a carcass reinforcement, at least one first layer of rubber mix having a modulus of elasticity which is greater than or equal to 50 MPa, this first layer extending from the median plane of the tire axially to the outside, on both sides of the median plane, only as far as an axial distance from the median plane which is less than the axial distance of the axial end of the crown reinforcement from the median plane.