An endoluminal device for affixation to a wall of a body lumen having a neck region defined by a relatively narrow width and a shoulder region that diverges from the neck region to a relatively wider width. The device comprises a bulbous portion having a shoulder portion with a diameter profile that conforms to the shoulder region of the lumen, and a converging diameter portion sized not to conform to the body lumen diameter profile. In some embodiments, a plurality of affixation members in an area of the device that typically extends from a distal end of the device through the shoulder portion. In one embodiment, the device comprises an endograft for repair of an aneurysm, such as an abdominal aortic aneurysm (AAA).