A multi-lumen catheter having a guidewire for each lumen, the catheter having a proximal-end assembly and an elongate tube including a multi-lumen medial portion and a distal-end portion. Each guidewire extends from the proximal end assembly through the medial portion to a lumen convergence portion which merges the lumens into a single output lumen. The distal-end portion includes (a) the lumen convergence portion, (b) an intermediate section surrounding the output lumen, and (c) a tapered tip surrounding the output lumen, with the diameter of each lumen of the multiple lumens other than the output lumen being sized to match the guidewire therein such that the guidewire is able to move therealong while being constrained laterally and remaining substantially coaxial with its lumen, and the diameter of the single output lumen being equal to the diameter of the largest diameter lumen of the multiple lumens.