Method for sharpening a cutting tool. In some embodiments, a first abrasive belt is advanced along a belt path between first and second rollers. A cutting tool inserted into a v-shaped slot is drawn across the belt as a cutting edge is supported by a limit stop of the slot. The first abrasive belt is deflected at a first radius of curvature in relation to a first linear stiffness of the belt and a tension applied to the first roller. The first abrasive belt is replaced with a second abrasive belt, and the cutting tool is again inserted into the v-shaped slot and drawn across the belt as the cutting edge is supported by the limit stop of the slot. The second abrasive belt is deflected at a second radius of curvature in relation to a second linear stiffness of the belt and the tension applied to the first roller.