A cutting insert, intended for chip removing machining, includes a body delimited by two opposite, first and second surfaces, which in the operative state of the cutting insert form an actively chip removing top surface and a bottom surface, respectively. The insert also includes at least one side surface, serving as a flank surface, which extends between the first and second surfaces. A cutting edge is formed between the flank surface and at least one of said first and second surfaces, in which a segment is included, which has the purpose of smoothening and facing the machined surface of the workpiece. The smoothening edge segment is divided into at least three different part edge segments, a first of which forms a tangent point and is surrounded by two part edge segments having longer radii (R22, R23) than the first edge part segment.