A tire has a sub-layer (7) made up substantially of a first base layer (71) disposed radially on the crown reinforcement (5) and axially between the median plane (CP) and a transition edge (711), the transition edge (711) being situated axially between the median plane (CP) and a shoulder (60), said first base layer (71) being made up of a rubber compound of given stiffness A, a second base layer (72) disposed radially on the crown reinforcement (5) and axially between the transition edge (711) and a shoulder end (721), said second base layer (72) being made up of a rubber compound of given stiffness B, a covering layer (73) disposed radially on the first base layer (71) and on the second base layer (72) and radially on the inside of the tread (6) and axially at least in sections situated between the median plane (CP) and the shoulder end (721), said covering layer (73) being made up of a rubber compound of given stiffness C, the stiffness B being less than the stiffness A, which is less than the stiffness C, and the stiffness C being greater than the stiffness M.