Systems and methods for occluding a left atrial appendage are disclosed. A left atrial appendage may be covered with a first occluder device to obstruct the passage of blood out of the left atrial appendage. The first occluder device may include an expandable member, a cover attached to and covering an end of the expandable member, and a one-way valve disposed in the cover. The cover may form a flexible pocket between the cover and the expandable member. The cover may be made of bioprosthetic material. A second occluder device may also be disposed within the left atrial appendage by inserting the second occluder device through the one-way valve in the cover of the first occluder device. The second occluder device may be used to stretch the left atrial appendage to obliterate the left atrial appendage.