Catheters, sheaths, or other tubular devices are provided that include a proximal end, a distal end sized for introduction into a patient's body, and a steerable distal portion. The tubular device includes a primary lumen extending between the proximal and distal ends; an auxiliary lumen adjacent the primary lumen; and one or more reinforcement members 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 within the auxiliary lumen. Apparatus and methods for making such tubular devices are also provided.