A cutting insert (10) has an upper surface (12) bounded by a cutting edge (14), a base (16), and a peripheral flank surface (18). The shape of the peripheral flank surface (18) varies along the height of the cutting insert (10). Near the top of the peripheral flank surface, it conforms to round or polygonal geometry of the cutting edge (14) so as to provide support for the cutting edge. Lower down the cutting insert (10), the peripheral flank surface (18) is shaped to provide transverse bearing surfaces (38) which have considerably lower pressure angles, i.e., resistance to turning moments, than would be provided by the inherent geometry of the cutting edge. Preferably, these transverse bearing surfaces (38) are formed by recessed features such as channels (40, 42), and most preferably, as chevron-type channels.