A catheter includes a catheter tube extending to a distal end portion that terminates at a terminal end of the catheter tube, the distal end portion including a tapered portion extending between the terminal end and a transition region on the distal end portion set back slightly from the terminal end. The tapered portion has a cross sectional area that decreases toward the terminal end to define a frustoconically-shaped outer surface extending from the transition region to the terminal end on which a soft tip member is mounted. The tip member has a size and shape adapted to be placed over the tapered portion coaxially, and a composition softer than that of the distal end portion that is suitable for bonding to the frustoconically-shaped outer surface.
