Abstract: Catheters and related methods for supporting a guidewire or delivering an agent through a vessel stenosis or other tortuous anatomy are disclosed. A catheter can comprise an elongate shaft body and a polymer tip member disposed at a distal end of the shaft body. The shaft body and the tip member can include a liner, one or both of a braid member or a coil member surrounding the liner, and a polymer cover surrounding the braid member or the coil member. The tip member can further include one or more filaments extending from a position overlapping, underlapping, or abutting a distal end of the braid member or the coil member on their proximal ends to a position distal to the braid member or the coil member on their distal ends. The one or more filaments can include a plurality of filaments arranged in a series of contacting helical windings about the liner, the braid member, or the coil member.