Implantable devices for placement at a cavity or opening such as an aneurysm are disclosed. The implantable devices, in a deployed condition, have a generally inverted U-shaped profile with a curved or angled framework support structure sized and configured for placement in proximity to tissue surrounding the opening and anchoring legs extending proximally from the framework structure sized and configured to contact the wall of a neighboring lumen at opposed locations. Occlusive and semi-occlusive membranes may be associated with the framework support structure and deployed over the opening to provide exclusion of the opening and flow diversion. Proximal anchoring segments providing additional lumen wall surface area contact for the implantable device following deployment may be incorporated.
