Tyre having an axis of rotation and comprising: - two beads and two sidewalls connected to the beads; - a crown, the crown having a first side connected to the radially outer end of one of the two sidewalls and having a second side connected to the radially outer end of the other of the two sidewalls, the crown comprising a radially outer tread, the tread comprising: ∘ at least one first sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially as far as a first sector contact face intended to come into contact with the roadway when the tyre is running; ∘ at least one second sector axially adjacent to the said at least one first sector, the said at least one second sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially towards a second sector contact face intended to come into contact with the roadway when the tyre is running; ∘ a plurality of circumferential grooves formed starting from one of the said contact faces intended to come into contact with the roadway when the tyre is running, each circumferential groove having circumferential groove sidewalls and a circumferential groove bottom, each circumferential groove having a depth P measured in a radial direction between the bottom and the said contact face; characterized in that, on the second sector or on one of the second sectors at least, the tread comprises a plurality of cavities oriented at least partly axially, and extending radially inwards from the said second sector contact face as far as a depth p equivalent to at least 25% of the depth P, the said plurality of cavities being distributed over the entire circumference of the tyre, and in that each second sector is made of a rubber compound of dynamic shear modulus G* at least a factor of two higher than the dynamic shear modulus G* of the rubber compound of each first sector, said modulus being measured at 60°C at 10 Hz and under an alternating shear stress of 0.7 MPa. - two beads and two sidewalls connected to the beads; - a crown, the crown having a first side connected to the radially outer end of one of the two sidewalls and having a second side connected to the radially outer end of the other of the two sidewalls, the crown comprising a radially outer tread, the tread comprising: ∘ at least one first sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially as far as a first sector contact face intended to come into contact with the roadway when the tyre is running; ∘ at least one second sector axially adjacent to the said at least one first sector, the said at least one second sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially towards a second sector contact face intended to come into contact with the roadway when the tyre is running; ∘ a plurality of circumferential grooves formed starting from one of the said contact faces intended to come into contact with the roadway when the tyre is running, each circumferential groove having circumferential groove sidewalls and a circumferential groove bottom, each circumferential groove having a depth P measured in a radial direction between the bottom and the said contact face; characterized in that, on the second sector or on one of the second sectors at least, the tread comprises a plurality of cavities oriented at least partly axially, and extending radially inwards from the said second sector contact face as far as a depth p equivalent to at least 25% of the depth P, the said plurality of cavities being distributed over the entire circumference of the tyre, and in that each second sector is made of a rubber compound of dynamic shear modulus G* at least a factor of two higher than the dynamic shear modulus G* of the rubber compound of each first sector, said modulus being measured at 60°C at 10 Hz and under an alternating shear stress of 0.7 MPa. ∘ at least one first sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially as far as a first sector contact face intended to come into contact with the roadway when the tyre is running; ∘ at least one second sector axially adjacent to the said at least one first sector, the said at least one second sector extending axially over a portion of the total width of the tread, extending circumferentially over the entire circumference of the tyre, and extending radially towards a second sector contact face intended to come into contact with the roadway when the tyre is running; ∘ a plurality of circumferential grooves formed starting from one of the said contact faces intended to come into contact with the roadway when the tyre is running, each circumferential groove having circumferential groove sidewalls and a circumferential groove bottom, each circumferential groove having a depth P measured in a radial direction between the bottom and the said contact face;