Blind rivet sleeve for a blind rivet, having a sleeve head which has a bearing face for bearing against a visible workpiece surface, and having a sleeve shank, wherein the blind rivet sleeve has a through-opening through which a mandrel can be guided, wherein the sleeve shank has a head forming portion which, during the setting of the blind rivet, is designed to form a blind head, and has a folding portion which is arranged between the head forming portion and the sleeve head and which, during the setting of the blind rivet, is designed to form a sleeve fold for the purpose of achieving a clamping thickness compensation.In this arrangement, the sleeve head has in the region of the bearing face an axial recess for receiving at least part of the sleeve fold formed during the setting.