A balloon catheter for medical treatment of a patient, including therapeutic dilatation or deployment of medical devices such as stents or grafts. The balloon catheter has an "over-the-wire configuration, including a proximal hub defining an inflation port and a guidewire port, a flexible shaft defining an inflation lumen and a guidewire lumen, a balloon near a distal end of the catheter, and a distal guidewire port. At least a portion of the shaft has an inner tubular body defining at least a portion of the guidewire lumen, surrounded by an outer tubular body defining at least a portion of the inflation lumen. A proximal portion of the inner body is reinforced by a hypotube, which provides much greater column strength and torsional stiffness. A distal end of the hypotube provides a graduated flexibility transition with a distal spiral-cut segment, in which the pitch of the spiral cut pattern decreases to provide increasing flexibility.