A cutting insert with a substantially triangular or square basic form is particularly suited for face milling at high feed rates. It has convex cutting edges, which are each made up of a circular arc and at least one straight portion. Each cutting edge has, adjoining a cutting corner, a straight face cutting edge that merges with a main cutting edge, having 1 to 3 straight portions, a circular portion with a radius of at most 80% of the radius Ri of the inscribed circle. The cutting edges have an all-round cutting edge chamfer with a chamfer angle α. This chamfer angle α has along the cutting corners a value in the range from −10° to −20° and changes continuously along sub-portions of the face cutting edge and main cutting edge and along the circular portion to a constant value in the range from 0° to −10°.