Tyre having an axis of rotation and a median plane perpendicular to the axis of rotation, comprising: • a crown reinforcement, • a tread radially on the outside of the crown reinforcement, the tread extending axially between two shoulders, the tread comprising a contact face intended to come into contact with the roadway when the tyre is being driven on, the tread being made up of at least one rubber compound of given stiffness M, the tread having furrows oriented substantially circumferentially, the material visible at the bottom of the furrow is the same material as the material of which the tread is made and, • a sub-layer disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, at least on one side axially with respect to the median plane, the sub-layer comprising: • a base layer disposed radially on the outside of the crown reinforcement and extending axially continuously from one shoulder to the other one, said base layer being made up of a rubber compound of given stiffness A, • a covering layer disposed radially on the base layer and radially on the inside of the tread and axially at least in portions situated between the median plane and the shoulder end, said covering layer being made up of a rubber compound of given stiffness B, the covering layer is formed by several portions that are separated axially, said covering layer being interrupted under the furrows, • the stiffness A being less than the stiffness B, and the stiffness B being greater than the stiffness M, each stiffness A, B, and M of each compound respectively of the base layer, of the covering layer, and the tread, being the dynamic shear modulus G ∗ of each compound respectively of the base layer, of the covering layer, and the tread, measured at 23°C, under an alternating shear stress at a frequency of 10 Hz and at 10% deformation, characterized in that, the dynamic shear modulus G ∗ of the material of the base layer, measured at 23°C and under an alternating shear stress at a frequency of 10 Hz and at 10% deformation, being less than 0.6 MPa. • a crown reinforcement, • a tread radially on the outside of the crown reinforcement, the tread extending axially between two shoulders, the tread comprising a contact face intended to come into contact with the roadway when the tyre is being driven on, the tread being made up of at least one rubber compound of given stiffness M, the tread having furrows oriented substantially circumferentially, the material visible at the bottom of the furrow is the same material as the material of which the tread is made and, • a sub-layer disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, at least on one side axially with respect to the median plane, the sub-layer comprising: • a base layer disposed radially on the outside of the crown reinforcement and extending axially continuously from one shoulder to the other one, said base layer being made up of a rubber compound of given stiffness A, • a covering layer disposed radially on the base layer and radially on the inside of the tread and axially at least in portions situated between the median plane and the shoulder end, said covering layer being made up of a rubber compound of given stiffness B, the covering layer is formed by several portions that are separated axially, said covering layer being interrupted under the furrows, • the stiffness A being less than the stiffness B, and the stiffness B being greater than the stiffness M, each stiffness A, B, and M of each compound respectively of the base layer, of the covering layer, and the tread, being the dynamic shear modulus G ∗ of each compound respectively of the base layer, of the covering layer, and the tread, measured at 23°C, under an alternating shear stress at a frequency of 10 Hz and at 10% deformation,