A tunneler (100,800) having a shaft (102,802) with an advancement end (106) and a connection end portion (104,804) having a lumen insertion tip (108,806) that may define a locating pin. At least one lumen-gripping section (120,818) is defined on the connection end portion spaced from the lumen insertion tip (108,806), and may be a barb section having at least one discrete barb (120), or an array of barbs (124), each with a sharp lumen-biting edge and a tapered lead-in surface (128) extending from the sharp edge toward the locating pin. Also, the lumen-gripping section (818) may be an annulus having a rounded lumen-engaging surface, or may be a circumferential array of nubs having rounded lumen-engaging surfaces. The connection end portion may have a plurality of axially spaced lumen-gripping sections (220,230818) that may have the same diameters or different maximum dimensions for use with a range of sizes of catheter lumens.