An angioplasty balloon having an elastic constraining structure that partially expands with the balloon so that, at maximum balloon inflation, the constraining structure forms a pattern of channels or "pillows" on the balloon. Such discrete protruding regions will each separately engage a segment of the lesion when the balloon is inflated so that the pressure and degree of balloon expansion applied against that segment is controlled and limited, thus reducing the risk of trauma while assuring that all segments of the lesion are adequately treated.
