A tire is provided with a tread that includes first and second sectors and grooves. The second sectors are formed of a rigid reinforcing compound. Each of the first and second sectors has a contact face intended to contact a road surface when the tire is in use. Each groove includes sidewalls and a bottom, and extends from an end of an adjacent contact face. A depth P of each groove is measured in a radial direction between its bottom and a position corresponding to a radial height of the adjacent contact face. At least one of the second sectors has a contact face that includes a recess having a depth p of less than 2 mm, as measured in a radial direction from a surface of the recess to a position corresponding to a radial height of an adjacent first sector.