- Tyre intended to be fitted on a drop-centre rim of the "15° drop-centre" type, comprising a radial carcass reinforcement made up of a single carcass reinforcement layer formed by reinforcement elements, said tyre comprising a crown reinforcement, which is radially capped by a tread, said tread being connected to two beads via two sidewalls, the layer of reinforcement elements of the carcass reinforcement being anchored in each of the beads by being turned up around a bead wire to form a main part of the carcass reinforcement layer extending from one bead wire to the other and a turn-up of the carcass reinforcement layer in each of the beads, said turn-up of the carcass reinforcement being reinforced by at least one layer of reinforcement elements or a stiffening element, characterized in that in a meridian cross section of said tyre: - any point of the profile of the outer surface of the tyre, between a first point, which is defined by the intersection of an axially orientated straight line, passing through the axially outermost point of the main part of the carcass reinforcement layer and the outer surface of the tyre, and a point is at a constant distance D from the main part of the carcass reinforcement layer, said distance D being measured at any point in a direction normal to the main part of the carcass reinforcement layer; - the point is radially outside a first circle of radius R1, centred on the end of the turn-up of the carcass reinforcement layer, with R1 being between 8 and 13 mm; - radially inside the point, the outer surface of the tyre extends by an arc of a circle of radius R2, which is strictly greater than R1 and for which the centre is axially outside the surface of the tyre; - the arc of a circle of radius R2 is tangent to its radially innermost end with an arc of a circle of radius R1 centred on the radially outermost end of the stiffening element, extending the outer surface of the tyre radially towards the inside up to the axially outermost point of the circle of radius R1 centred on the radially outermost end of the stiffening element. - any point of the profile of the outer surface of the tyre, between a first point, which is defined by the intersection of an axially orientated straight line, passing through the axially outermost point of the main part of the carcass reinforcement layer and the outer surface of the tyre, and a point is at a constant distance D from the main part of the carcass reinforcement layer, said distance D being measured at any point in a direction normal to the main part of the carcass reinforcement layer; - the point is radially outside a first circle of radius R1, centred on the end of the turn-up of the carcass reinforcement layer, with R1 being between 8 and 13 mm; - radially inside the point, the outer surface of the tyre extends by an arc of a circle of radius R2, which is strictly greater than R1 and for which the centre is axially outside the surface of the tyre; - the arc of a circle of radius R2 is tangent to its radially innermost end with an arc of a circle of radius R1 centred on the radially outermost end of the stiffening element, extending the outer surface of the tyre radially towards the inside up to the axially outermost point of the circle of radius R1 centred on the radially outermost end of the stiffening element.