A cryoplasty catheter and method for preventing or slowing reclosure of a lesion following angioplasty. The cryoplasty catheter includes a shaft having proximal and distal ends and a dilatation balloon disposed at the distal end. An intake lumen and exhaust lumen are defined by the shaft to deliver coolant to the balloon and to exhaust or drain coolant from the balloon. The method in accordance with the present invention includes cooling a lesion to aid in remodeling the lesion through dilatation and/or freezing a portion of the lesion adjacent the dilatation balloon to kill cells within the lesion to prevent or retard restenosis.