Abstract: A sharpener has two sharpening members pivotally mounted on opposite sides of a reference plane. Each sharpening member includes a counterweight portion below its pivot and a sharpening portion above its pivot. The sharpening portions have convex sharpening edges which overlap laterally to form a vertically movable V-shaped slot for receiving a cutting blade. A cutting blade is placed in the slot and moved lengthwise and downwardly. The downward movement causes the vertex of the V-shaped slot to move down, but the slot's vertex angle remains substantially constant because the curvatures of the sharpening edges increase progressively from upper regions to lower regions of the sharpening edges. The centers of gravity of the sharpening members are laterally inboard of the pivots, and the sharpening edges are higher than the pivots. The sharpening forces exerted by the sharpening edges against a cutting blade increase in response to downward movement of the slot vertex.