A balloon catheter or stent delivery system for medical treatment of a patient has a proximal hub, a balloon, and an improved shaft design. The catheter shaft has a rapid-exchange configuration, and a tubular outer body that includes a hypotube extending from the catheter proximal end to a position at or near a proximal leg of the balloon. An inner tubular body defines a guidewire lumen extending from a distal guidewire port at the catheter distal end to a proximal port located at a position between the balloon and the hub. A distal leg of the balloon is directly or indirectly affixed to the inner body, and a proximal leg of the balloon is affixed to the distal end of the outer body. The hypotube has an aperture for accepting the inner body proximal end, and a circumferential cut pattern. The cut pattern adds flexibility, and may extend from the hypotube distal end to a position proximal of the proximal guidewire port. The cut pattern may have any desired shape, including a spiral, a helical undulating path, or an overlapping serpentine path with inflection points, for example. The hypotube has a fluid-tight covering such as a heat-shrink polymer, so the outer body supports pressure of an inflation medium. The proximal guidewire port may be positioned on or between the individual portions of the cut pattern, or at a position beyond the cut pattern.