A catheter for insertion into a bodily conduit, especially an artery. The catheter comprises a shaft (26) having at least one lumen (24) for delivery of a fluid inflation media and a double balloon (12) including an array (20) of a plurality of inflatable secondary chambers (22) radially disposed in a cylindrical array around an inflatable primary chamber (16). Each of the secondary chambers (22) shares a common wall (38) with adjacent secondary chambers (22) and a common wall (14) with the primary chamber (16). The secondary chambers (22) are inflated by an array of channels (32) which are separated from each other by webs (40). One or more of the secondary chambers (22) may be in communication with a pressure transducer for measurement of the resistance of, e.g., a stenosis to dilation by the balloon (12). Alternately, a triple balloon (60) has inner secondary chambers (22a) and outer secondary chambers (22b). Also alternately, one or more of the secondary chambers (22) may be adapted to dispense medication. A method for treating a constricted bodily conduit using the catheter is also disclosed.