A catheter includes an elongated body, a distal assembly with a shape-memory member defining a generally circular form, and a control handle adapted to actuate a deflection puller wire for deflecting a portion of the elongated body, and a contraction wire for contracting the generally circular form. The generally circular form which carries at least one ring electrode has an off-edge configuration relative to the elongated body such that a longitudinal axis of the elongated body does not intersect the circumference of the circular form and the generally circular form spirals about the longitudinal axis of the elongated body. Moreover, the circular form can have an on-axis configuration such that the longitudinal axis of the elongated body is axially aligned with a central longitudinal axis of the circular form, or an off-axis configuration such that these axes are axially offset from each other. In a more detailed embodiment, the catheter has a distal assembly with a helical form or a crescent form carrying a plurality of irrigated ablation ring electrodes and a plurality of smaller ring electrodes adapted for impedance recording or PV potential recording. A support member with shape memory extends through the distal assembly to provide the helical or crescent form. The support member has 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.
