An anastomosis device formed from a Shape Memory Alloy (SME) wire that is annealed into a tight coil (e.g., flat coil, helical coil, cylindrical coil) that is subsequently substantially straightened (e.g., straight, longitudinally stretched spring-like shape) for being constrained within an elongate member of an anastomosis introducer instrument. After positioning and holding two tissue walls of adjacent lumens into apposition with a distally presented grasper of the instrument, a piercing tip of the anastomosis device is dispensed and inserted through the tissue walls before being allowed to relax to its tight coil shape, thereby forming the anastomosis attachment. The anastomosis device is released from the anastomosis introducer instrument, such as by fully dispensing its proximal end. Thereby, efficient single lumen anastomosis of gastrointestinal, bilatory, or other vessels may be achieved with a minimum of laparoscopic punctures, or perhaps performed fully as an endoscopic procedure.