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: o 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 to a first sector contact face intended to come into contact with the roadway when the tyre is running, said first sector essentially consisting of a base material; o 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 to a second sector contact face intended to come into contact with the roadway when the tyre is running, said second sector essentially consisting of a rigid reinforcing material, the dynamic shear modulus G* of which is at least two times greater than the dynamic shear modulus G* of the base material; o a plurality of grooves made starting from one of said contact faces intended to come into contact with the roadway when the tyre is running, each groove having groove sidewalls and a groove bottom, each groove having a depth P measured along a radial direction between the bottom and said contact face; characterized in that, on the second sector or on one of the second sectors at least, the second sector contact face comprises a recess having a depth p of less than 2 mm. - 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: o 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 to a first sector contact face intended to come into contact with the roadway when the tyre is running, said first sector essentially consisting of a base material; o 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 to a second sector contact face intended to come into contact with the roadway when the tyre is running, said second sector essentially consisting of a rigid reinforcing material, the dynamic shear modulus G* of which is at least two times greater than the dynamic shear modulus G* of the base material; o a plurality of grooves made starting from one of said contact faces intended to come into contact with the roadway when the tyre is running, each groove having groove sidewalls and a groove bottom, each groove having a depth P measured along a radial direction between the bottom and said contact face; characterized in that, on the second sector or on one of the second sectors at least, the second sector contact face comprises a recess having a depth p of less than 2 mm. o 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 to a first sector contact face intended to come into contact with the roadway when the tyre is running, said first sector essentially consisting of a base material; o 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 to a second sector contact face intended to come into contact with the roadway when the tyre is running, said second sector essentially consisting of a rigid reinforcing material, the dynamic shear modulus G* of which is at least two times greater than the dynamic shear modulus G* of the base material; o a plurality of grooves made starting from one of said contact faces intended to come into contact with the roadway when the tyre is running, each groove having groove sidewalls and a groove bottom, each groove having a depth P measured along a radial direction between the bottom and said contact face;