Catheter with soft distal tip for mapping and ablating tubular region

A catheter includes an elongated body having a longitudinal axis, a distal assembly distal the elongated body, the distal assembly having a tapered helical form comprising a larger, electrode-carrying proximal loop and a smaller, softer distal loop, and a shape-memory support member extending through at least the proximal loop. For example, the helical loop subtends at least about 720 radial degrees, with the proximal loop subtending about 360 radial degrees, and the distal loop subtending about 360 radial degrees. The softer distal loop with a straight distal end atraumatically guides the distal assembly into a tubular region so that the larger proximal loop can sit on the ostium of the tubular region with improved electrode and tissue contact.