The intravascular catheter has two segments; a proximal segment with high stiffness and a distal segment with lower stiffness. The catheter can also have an intermediate segment of lower stiffness than the proximal segment and higher stiffness than the distal segment. The catheter comprises a polymeric inner tube, a reinforcing inner jacket which is spirally wound over the inner tube and which becomes progressively softer from a proximal end to a distal end, and a polymeric outer sheath extruded over the inner jacket according to the teachings of U.S. Pat. No. 5,445,624. The reinforcing jacket comprises helical coiled wires or fibers of various materials and layers wound over the inner tube in order to provide improved multi-axial mechanical properties, such as torque, compression, tension and anti-kinking characteristics. Stainless steel, carbon, glass, platinum, platinum/tungsten or palladium wire in either oval, round or flat geometry are used together with single or dual layers to achieve a graduated stiffness with the reinforcing jacket being stiffer at a proximal end and softer at a distal end. Methods for making the catheter and for annealing ends of the wound wire are also disclosed.