A device for implantation into a body lumen having a reduced implantation diameter, comprising: an expandable stent member having upper and lower apices with an eyelet disposed at each of the lower apices, wherein said stent member is capable of securing said device into a body lumen; a plurality of attachment tethers looped through each of the eyelets; a generally tubular graft having a lumen extending therethrough for the flow of bodily fluid, said graft comprising a first open end, a second open end, and a graft wall having an interior surface, an opposed exterior surface and an internal portion, said graft wall comprising a plurality of layers; wherein the eyelets, the lower apices having the eyelets and the plurality of attachment tethers are disposed over a portion of the exterior surface of the graft near the first open end of the graft; and an attachment flap; characterized in that the internal portion of the graft wall consists of layers of laminated graft material; the attachment flap consists of graft material from the internal portion of the graft wall, which consists of layers of laminated graft material, being folded over at said first end and which covers the eyelets, covers the lower apices having the eyelets and covers at least a portion of the plurality of attachment tethers; the attachment flap is secured over the portion of the exterior surface of the graft near the first open end and over the at least portion of the plurality of attachment tethers to define a plurality of attachment sites thereat; and wherein the portion of the exterior surface of the graft near the first open end of the graft, over which the eyelets, the lower apices having the eyelets and the plurality of attachment tethers are disposed, does not form part of the attachment flap. an expandable stent member having upper and lower apices with an eyelet disposed at each of the lower apices, wherein said stent member is capable of securing said device into a body lumen; a plurality of attachment tethers looped through each of the eyelets; a generally tubular graft having a lumen extending therethrough for the flow of bodily fluid, said graft comprising a first open end, a second open end, and a graft wall having an interior surface, an opposed exterior surface and an internal portion, said graft wall comprising a plurality of layers; wherein the eyelets, the lower apices having the eyelets and the plurality of attachment tethers are disposed over a portion of the exterior surface of the graft near the first open end of the graft; and an attachment flap; characterized in that the internal portion of the graft wall consists of layers of laminated graft material; the attachment flap consists of graft material from the internal portion of the graft wall, which consists of layers of laminated graft material, being folded over at said first end and which covers the eyelets, covers the lower apices having the eyelets and covers at least a portion of the plurality of attachment tethers; the attachment flap is secured over the portion of the exterior surface of the graft near the first open end and over the at least portion of the plurality of attachment tethers to define a plurality of attachment sites thereat; and wherein the portion of the exterior surface of the graft near the first open end of the graft, over which the eyelets, the lower apices having the eyelets and the plurality of attachment tethers are disposed, does not form part of the attachment flap.