A disc brake for a commercial vehicle is equipped with a wear adjustment device having two adjustment spindles and a slip clutch actuated when a certain torque is exceeded. The slip clutch is designed such that it can be installed in existing installation spaces. The slip clutch is a safety adapter that is pressed onto the end region of each adjustment spindle via a press fit. In order to achieve the press fit, an inner contour of the safety adapter deviates from a circular shape and that an oversize is selected such that sufficient press forces are generated. The disc brake is particularly suited for heavy trucks and cantilevers.