A catheter balloon having improved steerability is disclosed having a transition between a soft distal tip and a relatively stiffer working portion of a balloon carrying a stent, in the form of a support sleeve on the inner member. The support sleeve provides stiffness to the taper portion of the balloon and also allows precise location of a radio opaque marker. The support sleeve can have a varying thickness or be made of a combination of materials to yield an increasing or decreasing stiffness along the support sleeve to provide an even smoother transition along the balloons length.
