A rapid-exchange balloon catheter or stent delivery system, for medically treating a patient, has a proximal hub, a balloon, and an improved shaft design. The catheter shaft has a tubular outer body that includes a hypotube extending from the catheter proximal end to a position at or near the proximal leg of the balloon. An inner tubular body defines a guidewire lumen and extends from a distal guidewire port at the catheter distal end to proximal guidewire port located between the balloon and the proximal hub. The hypotube has an aperture for accepting the inner body proximal end and a circumferential cut pattern. The cut pattern adds flexibility and may have any desired shape, including a spiral, a helical undulating path, or an overlapping serpentine path with inflection points, for example. The proximal guidewire port may be positioned on or in between the individual portions of the cut pattern.