Catheters and methods for supporting a guidewire or delivering a radiopaque, diagnostic or therapeutic agent through a vessel stenosis or other tortuous anatomy are disclosed. A catheter can comprise an elongate shaft body and a tip member disposed at a distal end of the shaft body. The shaft body can extend from a proximal end to the distal end and can define an inner lumen. The shaft body can include a liner, a braid member surrounding the liner, a multi-layer coil surrounding the braid member, and a polymer cover surrounding the multi-layer coil. An outer surface portion of the polymer cover can include one or more helical threads, which can be enveloped in an outer wrapper. The tip member can be made from a metal or a polymer. Polymer tip members can include a hard or semi-hard distal tip.
