Abstract: A method and apparatus for cutting a longitudinally advancing a rod of tobacco-containing material into lengths including a cut-off wheel having two or more blades equally spaced around the wheel periphery, a sharpening stone driven independently by a motor at a fixed location to sharpen one side of each blade as the wheel rotates, and a deburring stone oscillating in a path between two points at a frequency such that the stone intersects the path of travel of each blade for deburring the other side of each blade. The deburring stone may be located on the ledger device of a cigarette manufacturing machine where the ledger is oscillating at a frequency that is a multiple of the number of blades of the cutoff wheel for each revolution of the wheel.