An atherectomy burr has an operating diameter that is larger than the diameter of a catheter in which the burr is routed. The burr may include a polymeric balloon that is coated with an abrasive and that expands when the burr is rotated. Alternatively, the burr may include a polymeric tube that is coated with an abrasive and secured to the proximal end of the burr. When the burr is rotated, the polymeric tube expands by centrifugal force. Alternatively, the burr may comprise a metallic strip wound over a mandrel. When the strip is tightly coiled to the mandrel, its outer diameter decreases. The outer diameter of the burr increases as the metallic strip expands. In addition, the burr can be formed as a wire spring wound over a drive tube. The distal end of the spring is coupled to a nose cone that can move within a distal lumen in the drive tube. The maximum expansion of the burr is controlled by the distance that the nose cone can be retracted into the lumen. In addition, the present invention includes a burr having an indexable outer diameter. Various indexing mechanisms are disclosed for selectively increasing or decreasing the distance between a proximal and distal end of the burr. As the length of the burr changes, the outer diameter of a number of cutting blades is changed to allow a physician to create different sized lumens in a patient's vessel.