A cutting balloon catheter, comprising: a balloon mounted on a distal portion of a catheter shaft; a cutting member (320; 620) mounted on an exterior surface of the balloon, the cutting member (320; 620) having a length from a first end of the cutting member (320; 620) to a second end of the cutting member (320; 620), and including at least one discrete region of enhanced flexibility (375; 675) at a location along the length of the cutting member (320; 620) connecting a first portion of the cutting member (320; 620) to a second portion of the cutting member (320; 620); the discrete region of enhanced flexibility (375; 675) permitting the first portion of the cutting member (320; 620) to flex relative to the second portion of the cutting member (320; 620) without fracturing the first portion from the second portion; wherein the cutting member (320; 620) has a cutting edge (344; 644) and a base portion (342; 642), the base portion (342; 642) including a plurality of slots (350; 650) alternating with a plurality of tabs (360; 660), wherein the plurality of slots (350; 650) have a T-shape and form a plurality of small T-shaped slots (350; 650) extending along the base portion (342; 642) of the cutting member (320; 620) and opening out to a lower surface (336; 636) of the cutting member (320; 620), characterized in that the discrete region of enhanced flexibility (375; 675) includes a large T-shaped slot larger than each of the small T-shaped slots (350; 650), the large T-shaped slot opening out to the lower surface (336; 636) of the cutting member (320; 620) between adjacent small T-shaped slots (350; 650). a balloon mounted on a distal portion of a catheter shaft; a cutting member (320; 620) mounted on an exterior surface of the balloon, the cutting member (320; 620) having a length from a first end of the cutting member (320; 620) to a second end of the cutting member (320; 620), and including at least one discrete region of enhanced flexibility (375; 675) at a location along the length of the cutting member (320; 620) connecting a first portion of the cutting member (320; 620) to a second portion of the cutting member (320; 620); the discrete region of enhanced flexibility (375; 675) permitting the first portion of the cutting member (320; 620) to flex relative to the second portion of the cutting member (320; 620) without fracturing the first portion from the second portion; wherein the cutting member (320; 620) has a cutting edge (344; 644) and a base portion (342; 642), the base portion (342; 642) including a plurality of slots (350; 650) alternating with a plurality of tabs (360; 660), wherein the plurality of slots (350; 650) have a T-shape and form a plurality of small T-shaped slots (350; 650) extending along the base portion (342; 642) of the cutting member (320; 620) and opening out to a lower surface (336; 636) of the cutting member (320; 620), characterized in that the discrete region of enhanced flexibility (375; 675) includes a large T-shaped slot larger than each of the small T-shaped slots (350; 650), the large T-shaped slot opening out to the lower surface (336; 636) of the cutting member (320; 620) between adjacent small T-shaped slots (350; 650).