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 reinforcing structure, so as to define a median plane of the tyre that separates a first half of the tyre and a second half of the tyre, this medium plane being defined as the plane perpendicular to the axis of rotation which lies equidistant from the annular reinforcing structures of the two beads; and two sidewalls extending the beads radially outwards, the two sidewalls meeting in a crown comprising a crown reinforcement comprising a first reinforcing ply and a second reinforcing ply, the second reinforcing ply being positioned radially on the outside of the first reinforcing ply, the crown reinforcement being surmounted by a hooping reinforcement made up of circumferentially orientated reinforcing elements, preferably wound in a spiral, the hooping reinforcement being itself surmounted by a tread; characterised in that the second reinforcing ply has, in any radial section, a first axial end situated in the first half of the tyre, and a second axial end, situated in the second half of the tyre, the absolute value of the difference D between the distance D1 of the first axial end from the median plane and the distance D2 of the second axial end from the median plane being greater than or equal to 4 mm and less than or equal to 10 mm, 4 mm ≤ |1D| = |D1-D2| ≤ 10 mm; and in that, in any radial section, ∑ j = 1 N 2 MA 2 j = K × ∑ i = 1 N 1 MA 1 i where K is greater than or equal to 1.15 and less than or equal to 1.50, N1 is the number of hooping reinforcing elements situated in the first half of the tyre and MA1 i denotes the modulus at 2% elongation of an individual reinforcing element situated in the first half of the tyre, N2 is the number of hooping reinforcing elements situated in the second half of the tyre, and MA2 j denotes the modulus at 2% elongation of an individual reinforcing element situated in the second half of the tyre. two beads designed to come into contact with a mounting rim, each bead comprising at least one annular reinforcing structure, so as to define a median plane of the tyre that separates a first half of the tyre and a second half of the tyre, this medium plane being defined as the plane perpendicular to the axis of rotation which lies equidistant from the annular reinforcing structures of the two beads; and two sidewalls extending the beads radially outwards, the two sidewalls meeting in a crown comprising a crown reinforcement comprising a first reinforcing ply and a second reinforcing ply, the second reinforcing ply being positioned radially on the outside of the first reinforcing ply, the crown reinforcement being surmounted by a hooping reinforcement made up of circumferentially orientated reinforcing elements, preferably wound in a spiral, the hooping reinforcement being itself surmounted by a tread; characterised in that the second reinforcing ply has, in any radial section, a first axial end situated in the first half of the tyre, and a second axial end, situated in the second half of the tyre, the absolute value of the difference D between the distance D1 of the first axial end from the median plane and the distance D2 of the second axial end from the median plane being greater than or equal to 4 mm and less than or equal to 10 mm, 4 mm ≤ |1D| = |D1-D2| ≤ 10 mm; and in that, in any radial section, ∑ j = 1 N 2 MA 2 j = K × ∑ i = 1 N 1 MA 1 i where K is greater than or equal to 1.15 and less than or equal to 1.50, N1 is the number of hooping reinforcing elements situated in the first half of the tyre and MA1 i denotes the modulus at 2% elongation of an individual reinforcing element situated in the first half of the tyre, N2 is the number of hooping reinforcing elements situated in the second half of the tyre, and MA2 j denotes the modulus at 2% elongation of an individual reinforcing element situated in the second half of the tyre.