Gripper jaws for an insulation stripper have a gripping surface and an attachment extension with ribs which run transversely to a longitudinal direction of a cable to be gripped when the gripping surfaces are fitted, and have groove-like recesses corresponding to the ribs and running between the latter. When the gripper jaws are fitted, the ribs can enter into the recesses of the opposing gripper jaw in accordance with the thickness of the cable to be gripped. Blades for an insulation stripper have, on their free ends that run into a blade tip with an acute angle in cross-section, a contour line which has a depression, when seen from a side view in which the contour line forms the termination line of the blade.