Abstract: Apparatus are provided for performing a procedure within a patient's body that include a tubular member including proximal and distal ends, a central axis or region extending therebetween, and a distal portion extending distally from an intermediate portion to the distal end. One or more accessory lumens and a steering element lumen extend between the proximal and distal ends, the steering element lumen offset from the central region within the distal portion such that a steering plane intersects the steering element lumen and the central axis. The distal portion includes a core member extending between the intermediate portion and the distal end, and stabilization elements embedded in the core member adjacent the accessory lumen and defining a stabilization plane that intersects the steering plane at a location offset from the central region, e.g., closer to the accessory lumen than the steering element lumen.