The present invention relates to a catheter having a soft distal tip that can be manufactured at lower cost than catheters in the prior art. In one embodiment, the catheter is produced by coupling a soft sleeve to the distal end of a catheter tube. The sleeve may affixed to the catheter tube under temperature and pressure conditions that cause the proximal end of the sleeve to taper against the outer surface of the catheter tube, avoiding or minimizing discontinuities in the insertion profile of the catheter, and that also cause the inner wall of the sleeve to taper against the distal end of the catheter tube, avoiding or minimizing discontinuities in the lumen of the catheter.