A bumper, which comprises a bumper crossmember having an outer shell and having at least one sensor holder arranged therein, and an outer cladding shell. The at least one sensor holder is implemented as an impressed pocket originating from the front-side termination of the outer shell and having an upper wall, a lower wall and a base connecting the two walls. On the side of the outer cladding shell pointing toward the bumper crossmember, in the region of a sensor holder, the outer cladding shell carries at least one sensor engaging in the sensor holder.