A system, for use with a leaflet of a valve of a subject's heart, comprises a catheter, a cutting device, a helical needle, and a suture. The catheter is transluminally advanceable toward the heart. The cutting device is advanceable distally out of the catheter, and is adapted to cut through tissue of the leaflet to form cut tissue and cut edges at the cardiac valve. The helical needle defines a helical lumen, the helical needle configured to be advanced distally out of the catheter and to rotationally extend through, and secure together, two tissue segments of the leaflet. The suture extends through the helical lumen of the helical needle. The helical needle and the suture are configured to extend along the two tissue segments of the leaflet to suture the two tissue segments to each other. Other embodiments are also described.