Abstract: A method of reducing surface irregularities in paper machine headbox components such as the apron floor. A lap having a working surface diameter greater than the dominant dimensional characteristic of the irregularities is provided. The lap's working surface is machined flat to a tolerance equivalent to a desired flatness tolerance of the apron floor. A central, circular portion of the lap's working surface is counterbored to define an outer, annular cutting region on the lap's working surface. The apron floor is levelly supported and measured to obtain an initial profile of surface irregularity as a function of position on the apron floor. The lap is then driven to rotate its cutting region levelly on and over the apron floor while abrasive material in solid form and a coolant are applied between the lap and the apron floor. The apron floor is again measured to obtain an updated profile of surface irregularity as a function of position on the apron floor.