Tyre having an axis of rotation and a median plane perpendicular to the axis of rotation, and comprising: • a crown reinforcement, • a tread radially on the outside of the crown reinforcement, and axially between two shoulders, the tread comprising a contact face intended to come into contact with the roadway while the tyre is being driven on, the tread having a plurality of furrows oriented substantially circumferentially, each furrow having a furrow bottom, the tread being primarily made up of at least one rubber compound of given stiffness M, • a sub-layer (7, 71, 72, 73, 74) disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, the sub-layer being flush with each furrow bottom, the sub-layer being made up of at least one rubber compound of given stiffness A, • the stiffness of a rubber compound being defined by the dynamic shear modulus measured at 23°C, under an alternating shear stress at a frequency of 10 Hz and at 10% deformation, characterized in that, at least on one side axially with respect to the median plane: • each of the furrows is bordered axially on either side by a reinforcing element that extends radially from the sub-layer (7, 71, 72, 73, 74) towards the outside of the tread to a radial height greater than 75% of the radial thickness of the tread, said reinforcing element having a variable axial width, from a maximum value of less than 30% of the axial width of said tread block, said axial width decreasing radially upwardly, each reinforcing element being made up of a rubber compound of given stiffness B, • a covering layer is disposed radially on the sub-layer (7, 71, 72, 73, 74) and axially covering the sub-layer between the reinforcing elements away from the furrows, and in each case between a reinforcing element and the shoulder, said covering layer being made up of the same material as the material of the reinforcing elements, • the stiffnesses satisfying the following inequalities: A < M < B. • a crown reinforcement, • a tread radially on the outside of the crown reinforcement, and axially between two shoulders, the tread comprising a contact face intended to come into contact with the roadway while the tyre is being driven on, the tread having a plurality of furrows oriented substantially circumferentially, each furrow having a furrow bottom, the tread being primarily made up of at least one rubber compound of given stiffness M, • a sub-layer (7, 71, 72, 73, 74) disposed radially on the outside of the crown reinforcement and radially on the inside of the tread, the sub-layer being flush with each furrow bottom, the sub-layer being made up of at least one rubber compound of given stiffness A, • the stiffness of a rubber compound being defined by the dynamic shear modulus measured at 23°C, under an alternating shear stress at a frequency of 10 Hz and at 10% deformation, • each of the furrows is bordered axially on either side by a reinforcing element that extends radially from the sub-layer (7, 71, 72, 73, 74) towards the outside of the tread to a radial height greater than 75% of the radial thickness of the tread, said reinforcing element having a variable axial width, from a maximum value of less than 30% of the axial width of said tread block, said axial width decreasing radially upwardly, each reinforcing element being made up of a rubber compound of given stiffness B, • a covering layer is disposed radially on the sub-layer (7, 71, 72, 73, 74) and axially covering the sub-layer between the reinforcing elements away from the furrows, and in each case between a reinforcing element and the shoulder, said covering layer being made up of the same material as the material of the reinforcing elements, • the stiffnesses satisfying the following inequalities: A < M < B.