Machines and methods suitable for performing cutting operations on products to yield a reduced-size product, for example, slicing and strip-cutting elongate food products. Such a method includes simultaneously delivering products to annular-shaped cavities of a rotating impeller. The products are simultaneously delivered with a feed unit that has a feed chute extension that protrudes into an interior of the impeller. The feed chute extension defines feed chutes that are aligned with the annular-shaped cavities of the impeller and direct the products to circumferential series of pockets within the annular-shaped cavities. The products are held within the pockets by centrifugal force as the products are carried past a slicing knife to form a first longitudinal cut through each of the products during a rotation of the impeller and to produce therefrom a substantially longitudinally sliced product.