This is an implantable vaso-occlusive coil which is implanted using minimally invasive surgical techniques. It is a complex, helically wound coil made up of a primary helically wound coil which is then wound into a specific secondary shape. The secondary shape is itself a series of helical turns. At least a portion of the turns in the secondary shape form a cylindrical region and adjacent that region on at least one end is a conical region which tapers from a diameter approximating that of the central cylindrical region to a smaller diameter. The device is desirably self-forming upon exit from the distal end of a delivery catheter. Also, the conical tipped vaso-occlusive device may also utilize thrombus-enhancing filamentary material.