An implantable device for providing one-way flow of air through a lumen in a human lung to reduce the volume of air trapped in a diseased portion of the lung by occluding the lumen to prevent inhalation while permitting expiration out of the diseased portion. The implantable device is deployable in the lumen with a catheter. The device comprises an umbrella-shaped, one-way valve. The valve is collapsible for containment within a catheter and expandable in situ when deployed to occlude the lumen. The valve defines a longitudinal axis and comprises a plurality of metal struts, a resilient membrane, and a central post. The device further comprises an anchor for securing the implantable device within the lumen. The anchor comprises a tapered distal end for penetrating the wall of the lumen, and a planar member positioned to limit advancement of the anchor into the lumen. The implantable device further comprises a mechanism connecting the one-way valve to the anchor. The mechanism is disposed along the longitudinal axis when the device is collapsed. The mechanism is configured to permit the valve to be oriented at an angle to said anchor when deployed. Accordingly, the anchor can be positioned in a section of the lumen that is at an angle to a section of said lumen in which said one-way valve is positioned.