Systems and methods manipulate a support structure to form a composite lesion in a tissue region at or near a sphincter. The support structure carries an array of electrodes attachable to a source of energy capable of heating tissue when transmitted by the electrodes. The systems and methods advance the electrodes to penetrate the tissue region and form, when the energy is transmitted, a first pattern of lesions. The systems and methods retract the electrodes, and shift the position of the electrodes, either rotationally, or axially, or both rotationally and axially. The systems and methods advance the electrodes a second time to form, when the energy is transmitted, a second pattern of lesions either rotationally or axially or both rotationally and axially shifted from the first pattern of lesions. The first and second patterns of lesion together comprise the composite lesion.