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 dynamic shear modulus M, and • a sub-layer disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, characterized in that, at least on one side axially with respect to the median plane, the sub-layer has: • a first base layer disposed radially on the crown reinforcement and axially between the median plane and a transition edge, the transition edge being situated axially between the median plane and a shoulder, said first base layer being made up of a rubber compound of given dynamic shear modulus A, • a second base layer disposed radially on the crown reinforcement and axially between the transition edge and a shoulder end, said second base layer being made up of a rubber compound of given dynamic shear modulus B, • a covering layer disposed radially on the first base layer and on the second 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 dynamic shear modulus C, • the dynamic shear modulus B being less than the dynamic shear modulus A, which is less than the dynamic shear modulus C, and the dynamic shear modulus C being greater than the dynamic shear modulus M, each dynamic shear modulus 1, B, C and M being measured at 23°C at 10 Hz and under an alternating shear deformation of 10%. • 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 dynamic shear modulus M, and • a sub-layer disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, • a first base layer disposed radially on the crown reinforcement and axially between the median plane and a transition edge, the transition edge being situated axially between the median plane and a shoulder, said first base layer being made up of a rubber compound of given dynamic shear modulus A, • a second base layer disposed radially on the crown reinforcement and axially between the transition edge and a shoulder end, said second base layer being made up of a rubber compound of given dynamic shear modulus B, • a covering layer disposed radially on the first base layer and on the second 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 dynamic shear modulus C, • the dynamic shear modulus B being less than the dynamic shear modulus A, which is less than the dynamic shear modulus C, and the dynamic shear modulus C being greater than the dynamic shear modulus M,