A square-shaped bar-peeling insert and insert-holder designed with pockets to hold two such square-shaped inserts. Each insert has four peripheral sub-surfaces and corners. Between each adjacent pair of corners is a cutting edge which includes a straight wiper sub-edge and two at least partially curved peeling sub-edges respectively located on opposing sides of the wiper sub-edge. The corners of the insert are inwardly disposed relative to an imaginary square formed by the sub-edges.