Dilating an obstructed region in a narrow, highly torturous lumen with a dilatation catheter (10) having near its distal end an inflatable balloon (12) with a dilatation section (26), a proximal taper section (24), and a distal taper section (28). The dilatation section is generally cylindrical in shape when the balloon is inflated. The distal taper section has a relatively abrupt slope, and the proximal taper section has a relatively gradual slope.
