Method for manufacturing a tyre comprising a crown, two sidewalls and two beads, each sidewall respectively connecting each bead to the crown, the tyre comprising a carcass reinforcement that is anchored in each bead and extends in each sidewall and radially on the inside of the crown, the carcass reinforcement comprising at least one carcass layer, the crown comprising: - a tread intended to come into contact with the ground when the tyre is running, - a crown reinforcement arranged radially between the tread and the carcass reinforcement, the crown reinforcement comprising a working reinforcement comprising a single working layer, the working layer being delimited axially by two axial edges (18A, 18B) of the working layer and comprising working filamentary reinforcing elements that extend axially from one axial edge (18A, 18B) to the other axial edge (18A, 18B) of the working layer substantially parallel to one another along a main direction of each working filamentary reinforcing element that forms, with the circumferential direction of the tyre, an angle AT, wherein, in this method: - a carcass assembly intended to form the at least one carcass layer is arranged around a support having a substantially cylindrical shape about a main axis, the carcass assembly being delimited axially by two axial edges (52A, 52B) of the carcass assembly and comprising carcass filamentary reinforcing elements that extend substantially parallel to one another axially from one axial edge (52A, 52B) to the other axial edge (52A, 52B) of the carcass assembly, each carcass filamentary reinforcing element extending, in the carcass assembly, along a main direction of each carcass filamentary reinforcing element that forms, with the circumferential direction (x) of the support, an initial angle A3 that ranges, in terms of absolute value, from 80° to 90°, - a working assembly intended to form the working layer is arranged radially on the outside of the carcass assembly, the carcass assembly and the working assembly forming an assembly with a substantially cylindrical shape about the main axis of the support, - the assembly with a substantially cylindrical shape about the main axis of the support is deformed so as to obtain an assembly with a substantially toric shape about the main axis of the support, - a green form of tyre obtained from the assembly with a substantially toric shape is crosslinked in order to obtain the tyre, characterized in that the angle AT ranges, in terms of absolute value, from 30° to 37°. - a tread intended to come into contact with the ground when the tyre is running, - a crown reinforcement arranged radially between the tread and the carcass reinforcement, the crown reinforcement comprising a working reinforcement comprising a single working layer, the working layer being delimited axially by two axial edges (18A, 18B) of the working layer and comprising working filamentary reinforcing elements that extend axially from one axial edge (18A, 18B) to the other axial edge (18A, 18B) of the working layer substantially parallel to one another along a main direction of each working filamentary reinforcing element that forms, with the circumferential direction of the tyre, an angle AT, - a carcass assembly intended to form the at least one carcass layer is arranged around a support having a substantially cylindrical shape about a main axis, the carcass assembly being delimited axially by two axial edges (52A, 52B) of the carcass assembly and comprising carcass filamentary reinforcing elements that extend substantially parallel to one another axially from one axial edge (52A, 52B) to the other axial edge (52A, 52B) of the carcass assembly, each carcass filamentary reinforcing element extending, in the carcass assembly, along a main direction of each carcass filamentary reinforcing element that forms, with the circumferential direction (x) of the support, an initial angle A3 that ranges, in terms of absolute value, from 80° to 90°, - a working assembly intended to form the working layer is arranged radially on the outside of the carcass assembly, the carcass assembly and the working assembly forming an assembly with a substantially cylindrical shape about the main axis of the support, - the assembly with a substantially cylindrical shape about the main axis of the support is deformed so as to obtain an assembly with a substantially toric shape about the main axis of the support, - a green form of tyre obtained from the assembly with a substantially toric shape is crosslinked in order to obtain the tyre,