A method is disclosed of enhancing the securing of an intralumenal frame assembly to intralumenal tissue at an in situ target location. The method can comprise delivering an intralumenal frame assembly mounted on a delivery device to a treatment location. The intralumenal frame can be deployed to expand in situ so that anchors on the intralumenal frame atraumatically grasp intralumenal tissue at the target location. A radially inward force can be exerted on the frame assembly to cause the proximal and distal anchors to grasp more forcefully the intralumenal tissue.