A multiple lumen catheter having a soft, tapered multiple lumen distal tip for insertion into a body vessel. One of the lumens is sized to pass over a guidewire such that the catheter can be inserted into the body vessel using the Seldinger technique. At least one medical implement lumen is used for placement or positioning of a biomedical sensor or other medical implement. For example, at least one optical fiber passing through the medical implement lumen may transmit and receive light at the distal tip for measuring oxygen saturation of the blood. The catheter may have a cylindrical catheter body to which the soft distal tip attaches. The soft tip reduces the possibility of vessel or tissue puncture and abrasion. The tip is constructed of a soft plastic or pliable material that yields easily when force is applied. For example, the tip may be made of a softer material than the catheter body, or if made of the same material, the tip can be configured with thinner walls or a higher air-to-material ratio cross-section. Various geometrical configurations and combinations of materials can be used to decrease the resistance of the tip to an applied load. One particular useful application for the catheter of the present invention is as a central venous catheter equipped with fibers for measuring oximetry. The fibers extend to the distal end of the tip and are preferably secured therein with minimal adhesive so as to limit the stiffness added to the tip. One particular useful construction is to secure the fibers within the medical implement lumen using adhesive only along a length of between about 0.5-3.5 mm.