A mapping and/or ablation catheter , comprising: - a tubular member comprising a proximal end , a distal end sized for introduction into a patient's body, a central axis extending therebetween, and a distal portion extending distally from an intermediate portion to the distal end , wherein an electrode is arranged on the distal portion ; - an accessory lumen and a steering element lumen extending between the proximal end and the distal end , the steering element lumen offset from the central axis within the distal portion , thereby defining a steering plane intersecting the steering element lumen and the central axis , wherein the accessory lumen is disposed opposite the central axis from the steering element lumen within the distal portion , wherein a conductor extends through the accessory lumen from the proximal end to the distal portion and is coupled to the electrode; - the distal portion comprising a core member extending between the intermediate portion and the distal end comprising a portion of the steering element lumen therein offset from and extending substantially parallel to the central axis , wherein the steering element lumen is arranged above a midline of the core member , and a pair of stabilization elements embedded in the core member creating a stabilization plane extending between the stabilization elements that intersects the steering plane , wherein the stabilization elements are arranged below the midline such that the stabilization plane intersects the steering plane at a location closer to the accessory lumen than the steering element lumen ; and - a steering element slidably disposed within the steering element lumen comprising a distal end fixed to the tubular member distal end and a proximal end coupled to an actuator on the tubular member proximal end such that, actuation of the actuator applies axial tension or compression to the steering element , thereby causing the distal portion to deflect substantially within the steering plane . - a tubular member comprising a proximal end , a distal end sized for introduction into a patient's body, a central axis extending therebetween, and a distal portion extending distally from an intermediate portion to the distal end , wherein an electrode is arranged on the distal portion ; - an accessory lumen and a steering element lumen extending between the proximal end and the distal end , the steering element lumen offset from the central axis within the distal portion , thereby defining a steering plane intersecting the steering element lumen and the central axis , wherein the accessory lumen is disposed opposite the central axis from the steering element lumen within the distal portion , wherein a conductor extends through the accessory lumen from the proximal end to the distal portion and is coupled to the electrode; - the distal portion comprising a core member extending between the intermediate portion and the distal end comprising a portion of the steering element lumen therein offset from and extending substantially parallel to the central axis , wherein the steering element lumen is arranged above a midline of the core member , and a pair of stabilization elements embedded in the core member creating a stabilization plane extending between the stabilization elements that intersects the steering plane , wherein the stabilization elements are arranged below the midline such that the stabilization plane intersects the steering plane at a location closer to the accessory lumen than the steering element lumen ; and - a steering element slidably disposed within the steering element lumen comprising a distal end fixed to the tubular member distal end and a proximal end coupled to an actuator on the tubular member proximal end such that, actuation of the actuator applies axial tension or compression to the steering element , thereby causing the distal portion to deflect substantially within the steering plane . <EOS>