Flexible, tip-steerable needles promise to enhance physicians' abilities to accurately reach targets and maneuver inside the human body while minimizing patient trauma. Here, we present a functional needle steering system that integrates two components: (1) a patient-specific 2D pre- and intra-operative planner that finds an achievable route to a target within a planar slice of tissue (Stochastic Motion Roadmap), and (2) a low-level image-guided feedback controller that keeps the needle tip within that slice. The planner generates a sequence of circular arcs that can be realized by interleaving pure insertions with 180° rotations of the needle shaft. This preplanned sequence is updated in realtime at regular intervals. Concurrently, the low-level image-based controller servos the needle to remain close to the desired plane between plan updates. Both planner and controller are predicated on a previously developed kinematic nonholonomic model of bevel-tip needle steering. We use slighly different needles here that have a small bend near the tip, so we extend the model to account for discontinuities of the tip position caused by 180° rotations. Further, during large rotations of the needle base, we maintain the desired tip angle by compensating for torsional compliance in the needle shaft, neglected in previous needle steering work. By integrating planning, control, and torsion compensation, we demonstrate both accurate targeting and obstacle avoidance.