Tyre comprising: - two beads designed to come into contact with a rim, each bead comprising at least one annular reinforcing structure; - two sidewalls extending the beads radially outwards, the two sidewalls meeting in a crown comprising a crown reinforcement (80, 90) surmounted by a tread; - one single carcass reinforcement extending from the beads through the sidewalls as far as the crown, the carcass reinforcement comprising a plurality of carcass reinforcing elements, the carcass reinforcement being anchored in the two beads by a turn-up around the annular reinforcing structure so as to form, within each bead, a main portion and a wrapped-around portion, each wrapped-around portion extending radially outwards as far as an end situated a radial distance DEC from the innermost point of the annular reinforcing structure of the bead; wherein each bead comprises an apex made from a rubber composition, the apex being situated essentially radially on the outside of the annular reinforcing structure and at least partially between the main portion and the wrapped-around portion of the carcass reinforcement, the apex extending radially as far as a radially outer end of the apex, the radially outer end of the apex being situated a radial distance DEE1 from the radially innermost point of the annular reinforcing structure of the bead, wherein each bead further comprises an outer strip made of a rubber composition that has an elastic modulus G' less than or equal to 15 MPa and a viscous modulus G" such that: Gʺ MPa ≤ 0.2 ⋅ Gʹ MPa - 0.2 ⁢ MPa, the elastic and viscous moduli being measured at 23°C, the outer strip being situated axially on the outside of the wrapped-around portion of the carcass reinforcement, the outer strip extending between a radially inner end of the outer strip and a radially outer end of the outer strip, the radially inner end of the outer strip being situated at a radial distance DEI2 from the radially innermost point of the annular reinforcing structure of the bead, the radial distance DEI2 being less than or equal to 20% of the radial height H of the tyre, the radially outer end of the outer strip being situated at a radial distance DEE2 from the radially innermost point of the annular reinforcing structure of the bead, the radial distance DEE2 being greater than or equal to 25% of the radial height H of the tyre, wherein the apex has an axial thickness E(r), this axial thickness corresponding to the length of the intersection of the apex with an axial direction, r denoting the distance separating the point of intersection of the said axial direction with the main portion of the carcass reinforcement from the radically innermost point of the annular reinforcing structure, the thickness E(r) being a substantially linear function of r, wherein the entity formed by the apex and the outer strip has a thickness ET(r), this thickness corresponding to the length of the intersection of the direction perpendicular to the main portion of the carcass reinforcement with the said entity, r denoting the distance separating the point of intersection of the said direction perpendicular to the main portion of the carcass reinforcement with the main portion of the carcass reinforcement from the radially innermost point of the annular reinforcing structure, wherein the thickness ET(r) changes in such a way that, in the range of distances r comprised between 25 and 45% of the height H of the tyre, the variation in thickness ∂ ET r ∂ r is negative and has an absolute value that is greater than or equal to 0.25 mm/mm over at least 4% of the height H of the tyre; and wherein the said at least one annular reinforcing structure has a maximum axial width DE such that the ratio ET ⁢ r max - DE ET ⁢ r max, wherein ET(r) max is the maximum value of the thickness ET(r), is less than or equal to 10% characterised in that the radial distance DEC is less than or equal to 10% of the radial height H of the tyre, in that the rubber composition from which the apex is made has an elastic modulus greater than or equal to 40 MPa, and in that the radial distance DEE1 is greater than or equal to 10% and less than or equal to 15% of the radial height H of the tyre. - two beads designed to come into contact with a rim, each bead comprising at least one annular reinforcing structure; - two sidewalls extending the beads radially outwards, the two sidewalls meeting in a crown comprising a crown reinforcement (80, 90) surmounted by a tread; - one single carcass reinforcement extending from the beads through the sidewalls as far as the crown, the carcass reinforcement comprising a plurality of carcass reinforcing elements, the carcass reinforcement being anchored in the two beads by a turn-up around the annular reinforcing structure so as to form, within each bead, a main portion and a wrapped-around portion, each wrapped-around portion extending radially outwards as far as an end situated a radial distance DEC from the innermost point of the annular reinforcing structure of the bead;