Tyre having a radial carcass reinforcement, consisting of at least one layer of reinforcing elements, said tyre comprising a crown reinforcement, which is itself covered radially with a tread, said tread being joined to two beads via two sidewalls, said at least one layer of reinforcing elements of the carcass reinforcement being anchored in each of the beads by an upturn around a bead wire, said carcass reinforcement upturn being reinforced by at least one layer of reinforcing elements or stiffener, characterized in that the relative density of sulfur bridges measured according to the equilibrium swelling method is less than 5% in at least 30% of the elastomer compounds present in the surface of at least one zone in a meridian plane, in that said at least one zone is defined in a meridian plane by the combination of two ovals O1, O2: - a first oval O1 consisting, on the one hand, in its radially innermost portion, of a semi-ellipse, centred on the end of the upturn of said at least one carcass reinforcement layer, the major axis of which is tangent to the end at the upturn of said at least one carcass reinforcement layer, the length of the major axis being equal to 30 mm and the length of the minor axis being equal to 12 mm and, on the other hand, in its radially outermost portion, of a semicircle, of diameter D1 equal to 12 mm, centred on the end of the upturn of said at least one carcass reinforcement layer, - a second oval 02 consisting, on the one hand, in its radially innermost portion, of a semi-ellipse, centred on the outermost end of said at least one layer of reinforcing elements or stiffener, the major axis of which is tangent to the end at said at least one layer of reinforcing elements or stiffener, the length of the major axis being equal to 30 mm and the length of the minor axis being equal to 12 mm and, on the other hand, in its radially outermost portion, of a semicircle, of diameter D2 equal to 12 mm, centred on the outermost end of said at least one layer of reinforcing elements or stiffener, and in that said elastomer compounds present in the surface of said at least one zone in a meridian plane are compositions based on at least one diene elastomer selected from the group of diene elastomers consisting of polybutadienes (abbreviated to "BR"), synthetic polyisoprenes, natural rubber, isoprene copolymers, butadiene copolymers with the exception of butadiene-nitrile copolymers, apart from diene elastomers bearing carboxyl functions, and mixtures of these diene elastomers. - a first oval O1 consisting, on the one hand, in its radially innermost portion, of a semi-ellipse, centred on the end of the upturn of said at least one carcass reinforcement layer, the major axis of which is tangent to the end at the upturn of said at least one carcass reinforcement layer, the length of the major axis being equal to 30 mm and the length of the minor axis being equal to 12 mm and, on the other hand, in its radially outermost portion, of a semicircle, of diameter D1 equal to 12 mm, centred on the end of the upturn of said at least one carcass reinforcement layer, - a second oval 02 consisting, on the one hand, in its radially innermost portion, of a semi-ellipse, centred on the outermost end of said at least one layer of reinforcing elements or stiffener, the major axis of which is tangent to the end at said at least one layer of reinforcing elements or stiffener, the length of the major axis being equal to 30 mm and the length of the minor axis being equal to 12 mm and, on the other hand, in its radially outermost portion, of a semicircle, of diameter D2 equal to 12 mm, centred on the outermost end of said at least one layer of reinforcing elements or stiffener, and