A cutting or scoring balloon (26) is provided with a plurality of cutting or scoring elements (34) and is wrapped onto a balloon catheter (12) such that the cutting or scoring elements (34) overlie the balloon wall (36) with the balloon wall (36) pleated underneath the cutting or scoring elements (34). The cutting or scoring elements (34) remain exposed when the balloon (26) is pleated and wrapped onto the balloon catheter (12) and in a tightly wrapped configuration.
