A method of making a portion of a bicycle frame including positioning a low-friction mandrel adjacent a flexible mandrel with a first fibrous material in between. The mandrels are wrapped with second fibrous material, and the mandrels are inserted into a mold. The second fibrous material is cured to produce a cured assembly, the cured assembly is withdrawn from the mold, and the low-friction mandrel is removed from the cured assembly to produce an internal passageway. The flexible mandrel can includes a recess, and the step of positioning can include inserting the low-friction mandrel into the recess of the flexible mandrel. Preferably, the low-friction mandrel has a cross sectional shape that substantially matches a cross-sectional shape of the recess. The invention is also embodied in a portion of a bicycle frame, such as a portion of the frame during the manufacturing process, and having similar features as recited above.