Radial tyre, defining three main directions, circumferential, axial and radial, comprising a crown surmounted by a tread, two sidewalls, two beads, each sidewall connecting each bead to the crown, a carcass reinforcement that is anchored in each of the beads and extends in the sidewalls to the crown, a crown reinforcement or belt (10, 20) that extends in the crown in the circumferential direction and is situated radially between the carcass reinforcement and the tread, the said belt comprising a multilayer composite laminate (10a, 10b, 10c; 20a, 20b, 20c) comprising at least three superposed layers of reinforcers (110, 120, 130; 111, 125, 135), the said reinforcers being unidirectional within each layer and embedded in a thickness of rubber (C1, C2, C3, respectively), with: - on the tread side, a first layer (10a, 20a) of rubber comprising a first row of reinforcers (110, 111) which are oriented at an angle alpha of -5 to +5 degrees with respect to the circumferential direction, these reinforcers (110, 111), referred to as first reinforcers, being made of a heat-shrinkable textile material; - in contact with the first layer (10a, 20a) and disposed beneath the latter, a second layer (10b, 20b) of rubber comprising a second row of reinforcers (120, 125) which are oriented at a given angle beta, which is positive or negative, of between 10 and 30 degrees with respect to the circumferential direction, these reinforcers (120, 125), referred to as second reinforcers, having a diameter or thickness, denoted D2, of between 0.20 mm and 0.50 mm; - in contact with the second layer (10b, 20b) and disposed beneath the latter, a third layer (10c, 20c) of rubber comprising a third row of reinforcers (130, 135) which are oriented at an angle gamma the opposite of the angle beta, itself being between 10 and 30 degrees with respect to the circumferential direction, these reinforcers (130, 135), referred to as third reinforcers, having a diameter or thickness, denoted D3, of between 0.20 mm and 0.50 mm, characterized in that all or part of the second and/or third reinforcers are composite reinforcers comprising steel monofilaments (120a, 130a; 125a, 135a) which are covered with a sheath (120b, 130b; 125b, 135b) of a thermoplastic material the glass transition temperature Tg of which is higher than 20°C. - on the tread side, a first layer (10a, 20a) of rubber comprising a first row of reinforcers (110, 111) which are oriented at an angle alpha of -5 to +5 degrees with respect to the circumferential direction, these reinforcers (110, 111), referred to as first reinforcers, being made of a heat-shrinkable textile material; - in contact with the first layer (10a, 20a) and disposed beneath the latter, a second layer (10b, 20b) of rubber comprising a second row of reinforcers (120, 125) which are oriented at a given angle beta, which is positive or negative, of between 10 and 30 degrees with respect to the circumferential direction, these reinforcers (120, 125), referred to as second reinforcers, having a diameter or thickness, denoted D2, of between 0.20 mm and 0.50 mm; - in contact with the second layer (10b, 20b) and disposed beneath the latter, a third layer (10c, 20c) of rubber comprising a third row of reinforcers (130, 135) which are oriented at an angle gamma the opposite of the angle beta, itself being between 10 and 30 degrees with respect to the circumferential direction, these reinforcers (130, 135), referred to as third reinforcers, having a diameter or thickness, denoted D3, of between 0.20 mm and 0.50 mm,