Tire having two beads each comprising an annular reinforcing structure and a carcass reinforcement which is anchored in the two beads by being wrapped around the annular reinforcing structure so as to form, in each bead, a main portion and a wrapped-around portion, wherein each bead comprises an apex situated between the main portion and the wrapped-around portion of the carcass reinforcement, and an outer strip positioned axially on the outside of the carcass reinforcement and of the apex, the apex and the outer strip being made of a rubber compound that has an elastic modulus G′ less than or equal to 15 MPa and a viscous modulus G″ such that: G″[MPa]≦0.2·G′[MPa]−0.2 MPa, the elastic and viscous moduli being measured at 23° C.; wherein the entity formed by the apex and the outer strip has a thickness E(r), the thickness E(r) varying such that, in the range of distances r comprised between 25 and 45% of the height H of the tire, the variation in thickness ∂ E ⁡ ( r ) ∂ r is less than or equal to −0.25 mm/mm over at least 4% of the height H of the tire, that, in the range of distances r comprised between 15 and 35% of the height H, the variation in thickness ∂ E ⁡ ( r ) ∂ r is greater than or equal to 0.20 mm/mm over at least 2% of the height H of the tire, and that, in the range of distances r comprised between 10 and 20% of the height H of the tire, the variation in thickness ∂ E ⁡ ( r ) ∂ r is greater than or equal to −0.10 mm/mm and less than or equal to 0.0 mm/mm over at least 5% of the height H of the tire.