A planing machine (or simply “planer”) which may have two planer heads, each head containing the conventional knives and supporting apparatus to perform the actual cutting of material. To improve yield, the board is centered vertically as it progresses longitudinally through the planer. This is accomplished using either or (preferably) both of two systems: (1) a segmented self-centering drive roll system to feed the boards into the machine; and (2) a shoe mechanism which is controlled by a linkage such that the retracting segmented shoe assembly moves away from the planer head as it moves vertically to compensate for varying material thicknesses. The result is a more efficient use of the workpiece because less waste is created.