Systems and methods reduce the effective volume of an atrial appendage by deploying first and second devices into the atrium. The first device carries a first element to affect positioning of the tissue surface in a repositioned orientation. The second device carries a second element to affix the tissue surface in the repositioned orientation affected by the first device. In one embodiment, the first device carries a loop structure having a perimeter. The second device is deployed within the perimeter of said loop structure. The systems and methods attach the second device to an interior surface of an atrial appendage, and pull the atrial appendage through said loop structure to cause inversion thereof.