Devices intended for deployment into interior body regions employ a catheter tube, which carries an expandable structure. The catheter tube extends along a first axis, while the expanded geometry of the structure is oriented about a second axis, which is not aligned with the first axis. The asymmetry between the two axes permits deployment of the expandable structure in a symmetric fashion with respect to the natural axis of a targeted interior body region, even when the targeted interior body region is either asymmetric in geometry or otherwise requires access along a path that is not aligned with the natural axis. The structure can include spaced apart end regions, which provide a non-conical diameter transition between the diameter of the catheter tube and the larger diameter of the expanded structure. The non-conical diameter transition mitigates the tradeoff, present in conventional structures, between achieving a desired maximum expanded diameter without undesired reduction in the effective length of the structure.