A cutting insert having a front cutting edge and a connecting surface including male- and/or female-like engagement portions, in order to rigidly secure the cutting insert, a geometrically predetermined reference locus serving as a force-application spot for the clamping of the cutting insert. Simultaneously active engagement portions are of only two types—a first, elongate engagement portion, which is located between the front cutting edge and the reference locus, and a second, elongate engagement means, which is oriented at an angle to the first engagement portion and situated at a greater distance from the front cutting edge than the reference locus. In such a way, it is guaranteed that a tightening force always is applied to the cutting insert in a substantially triangular area, which is defined by the free ends of the engagement portions. Furthermore, a tool for chip removing machining, as well as an attachment, e.g., a shim plate, for such tools is provided.