Catheters, sheaths, or other tubular devices are provided that include a proximal end 12, a distal end 14 sized for introduction into a patient's body, and a steerable distal portion 24. The tubular device includes primary lumen 18a extending between the proximal and distal ends； an auxiliary lumen 18b adjacent the primary lumen； and one or more reinforcement members 43 including windings extending helically along at least the distal portion, at least some of the windings passing between the primary and steering element lumens and at least some of the windings surrounding both the primary and steering element lumens. In one embodiment, a steering element is slidably disposed with the auxiliary lumen. Apparatus and methods for making such tubular devices are also provided.
