Tire formed of two halves separated by a median plane, comprising a crown comprising a crown reinforcement comprising a first reinforcing ply (80) and a second reinforcing ply (90) having two axial ends, which is situated radially on the outside of the first reinforcing ply and surmounted by a hooping reinforcement (100) made up of circumferentially orientated reinforcing elements, in which tire the absolute value of the difference D between the distance D1 of the first axial end (92) from the median plane and the distance D2 of the second axial end (93) from the median plane is greater than or equal to 4 mm and less than or equal to 10 mm (4 mm≦|D|=|D1−D2|≦10 mm).