A catheter includes an elongated body, a distal assembly with a shape-memory member defining a generally helical form, and a control handle. The control handle may be adapted to actuate a deflection puller wire for deflecting a portion of the elongated body and a contraction wire for contracting the generally helical form. The generally helical form carries irrigated ablation ring electrodes. A nitinol support member with shape memory extends through the distal assembly and into the elongated body to provide the helical form. The support member may have a varying stiffness along its length, for example, a decreasing stiffness toward a distal end of the support member. The support member can also be hollow so that it can receive a mandrel whose stiffness is greater than that of the support member.