A medical device for reducing the volume of a left atrial appendage (LAA) may include an elongate shaft having a distal portion, and a volume-reducing means expandable from a collapsed to an expanded state, the volume-reducing means being releasably attached to the distal portion. The volume-reducing means may include an actuatable frame and an impermeable covering disposed over the frame. The volume-reducing means may be sized to fit within the LAA in the expanded state while maintaining an open fluid flow path from a distal region through the ostium of the LAA. A medical device may include a second volume-reducing means to be placed within and substantially occlude a distalmost region of the LAA. A method may include inserting a volume-reducing means into the LAA, expanding the volume-reducing means, and positioning the volume-reducing means such that an open fluid flow path is maintained through an entire cycle of the heart.