Process for producing a line of weakness in a cover element comprising at least one slit. This slit is produced through a plurality of machining cycles in which a pulsed laser beam is guided in each instance over the cover element along an imaginary line so that the energy of the laser pulses is introduced into the cover element. The slits are produced in two segments. More energy is introduced over the machining cycles in the first, comparatively short segments than in the second, comparatively long segments. The residual wall below the slits decreases with each machining cycle until the first residual wall segment thickness in the first segment is so small that energy portions transmit through the first residual wall segment and are detected by a sensor arrangement arranged downstream. Accordingly, the first residual wall segment thickness is detected, and inferences can be drawn from this about the second residual wall segment thickness.