-Tyre intended to be mounted on a hollow rim of the " 15° drop centre" type, comprising a radial carcass reinforcement made up of a single carcass reinforcement layer formed of reinforcing elements, said tyre comprising a crown reinforcement, itself capped radially by a tread, said tread being joined to two beads via two sidewalls, the layer of reinforcing elements of the carcass reinforcement being anchored in each of the beads by being turned up around a bead wire so as 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 reinforcing elements or stiffener, 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, itself defined by the intersection of an axially oriented 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 T from the main part of the carcass reinforcement layer, said distance being measured at any point in a direction normal to the main part of the carcass reinforcement layer, - the point is radially on the outside of a first circle of radius R1 that is centred on the end of the turn-up of the carcass reinforcement layer, R1 being between 8 and 13 mm, - radially on the inside of the point, the outer surface of the tyre is continued by a circular arc of radius R2, the centre of which is axially on the outside of the surface of the tyre, and the radius R2 of which is between 50% and 125% of the distance between the point and the centre of gravity of the bead wire, - the circular arc of radius R2 is tangent at its radially innermost end to a circular arc of radius R3, the centre of which is axially on the inside of the surface of the tyre, and continues the outer surface of the tyre radially inwards as far as the point, said point being a point of contact between the circular arc of radius R3 and the circle of radius R1 centred on the radially outermost end of the stiffener, - said point being radially on the inside of the axially outermost point of the circle, - the radius R3 being between 50% and 125% of the distance between the point and the centre of gravity of the bead wire. - any point of the profile of the outer surface of the tyre, between a first point, itself defined by the intersection of an axially oriented 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 T from the main part of the carcass reinforcement layer, said distance being measured at any point in a direction normal to the main part of the carcass reinforcement layer, - the point is radially on the outside of a first circle of radius R1 that is centred on the end of the turn-up of the carcass reinforcement layer, R1 being between 8 and 13 mm, - radially on the inside of the point, the outer surface of the tyre is continued by a circular arc of radius R2, the centre of which is axially on the outside of the surface of the tyre, and the radius R2 of which is between 50% and 125% of the distance between the point and the centre of gravity of the bead wire, - the circular arc of radius R2 is tangent at its radially innermost end to a circular arc of radius R3, the centre of which is axially on the inside of the surface of the tyre, and continues the outer surface of the tyre radially inwards as far as the point, said point being a point of contact between the circular arc of radius R3 and the circle of radius R1 centred on the radially outermost end of the stiffener, - said point being radially on the inside of the axially outermost point of the circle, - the radius R3 being between 50% and 125% of the distance between the point and the centre of gravity of the bead wire.