Tyre having an axis of rotation and comprising: two beads designed to come into contact with a mounting rim, each bead comprising at least one annular reinforcement structure having a point that is radially innermost, two sidewalls extending the beads radially outwards, the two sidewalls coming together in a crown comprising a crown reinforcement (80, 90) radially surmounted by a tread; a radial carcass reinforcement consisting of threadlike reinforcing elements having an elongation at break EB C and a force at break FB C, placed at a pitch P C and coated with a rubber composition, the carcass reinforcement extending from one bead to the other, passing through the crown, the carcass reinforcement being anchored in each bead by a turn-up around the said at least one annular reinforcement structure, so as to form an main portion and a wrapped-around portion, each sidewall of the tyre also comprising an additional reinforcement extending between a radially inner end that is close to the said at least one annular reinforcement structure of the bead extended by the sidewall, and a radially outer end situated radially between the carcass reinforcement and the crown reinforcement, characterized by the carcass reinforcement being designed so as to satisfy the inequality: FB C P C ≤ 1.5 ⋅ 10 6 ⋅ R S 2 − R E 2 R T; where FB C is expressed in Newton, R S is the radial distance between the axis of rotation of the tyre and the radially outermost point of the carcass reinforcement, R E is the radial distance between the axis of rotation of the tyre and the axial position at which the tyre reaches its maximum axial width, and R T is the radial distance between the axis of rotation of the tyre and the radially innermost point of the said at least one annular reinforcement structure, the pitch P C and the radial distances R S, R E and R T being expressed in metres; the additional reinforcement consisting of threadlike reinforcing elements having an elongation at break EB A and a force at break FB A, placed at a pitch P A and coated with a rubber composition, wherein EB A, FB A, P A, EB C, FB C and P C are chosen such that FB A P A ≥ 1.3 ⋅ FB C P C, and EB C ≥ EB A, it being understood that the forces at break FB A and FB C, and the elongations at break EB C and EB A correspond to the values the reinforcing elements exhibit before they are incorporated into the tyre. two beads designed to come into contact with a mounting rim, each bead comprising at least one annular reinforcement structure having a point that is radially innermost, two sidewalls extending the beads radially outwards, the two sidewalls coming together in a crown comprising a crown reinforcement (80, 90) radially surmounted by a tread; a radial carcass reinforcement consisting of threadlike reinforcing elements having an elongation at break EB C and a force at break FB C, placed at a pitch P C and coated with a rubber composition, the carcass reinforcement extending from one bead to the other, passing through the crown, the carcass reinforcement being anchored in each bead by a turn-up around the said at least one annular reinforcement structure, so as to form an main portion and a wrapped-around portion, each sidewall of the tyre also comprising an additional reinforcement extending between a radially inner end that is close to the said at least one annular reinforcement structure of the bead extended by the sidewall, and a radially outer end situated radially between the carcass reinforcement and the crown reinforcement, characterized by the carcass reinforcement being designed so as to satisfy the inequality: FB C P C ≤ 1.5 ⋅ 10 6 ⋅ R S 2 − R E 2 R T; where FB C is expressed in Newton, R S is the radial distance between the axis of rotation of the tyre and the radially outermost point of the carcass reinforcement, R E is the radial distance between the axis of rotation of the tyre and the axial position at which the tyre reaches its maximum axial width, and R T is the radial distance between the axis of rotation of the tyre and the radially innermost point of the said at least one annular reinforcement structure, the pitch P C and the radial distances R S, R E and R T being expressed in metres; the additional reinforcement consisting of threadlike reinforcing elements having an elongation at break EB A and a force at break FB A, placed at a pitch P A and coated with a rubber composition, wherein EB A, FB A, P A, EB C, FB C and P C are chosen such that FB A P A ≥ 1.3 ⋅ FB C P C, and EB C ≥ EB A, it being understood that the forces at break FB A and FB C, and the elongations at break EB C and EB A correspond to the values the reinforcing elements exhibit before they are incorporated into the tyre.