A catheter for mapping and/or ablating continuous linear or circumferentiallesions at the intersection of a generally flat structure, such as the left atrium,and the ostium of generally cavernous regions of the heart, including pulmonaryvein and the pulmonary venous antrum, comprises a catheter body with an intermediatesection that is connected to a tip assembly by a highly flexible section. The intermediatesection has at its distal end a preformed section, e.g., a curve, the intermediatesection being deflectable in a direction opposite to the curve. The highly flexiblesection presets the tip assembly at an off-axis and/or off-plane angles fromthe preformed section.