Apparatus and methods are provided for treating a lesion within a body lumen using a catheter including a balloon on its distal end and an abrasive distal tip extending distally beyond the balloon. The distal tip may terminate in a sharpened tip for penetrating occlusive material, e.g., a beveled tip, and includes abrasive material on an outer surface thereof, e.g., abrasive grit, cutting elements, and the like, for abrading occlusive material adjacent the distal tip. The abrasive material may be arranged in a predetermined pattern, e.g., an axial, circumferential, or helical pattern, to facilitate abrading occlusive material. The distal tip may have a substantially uniform diameter or tapered shape along its length.