Woven graft having a taper with a re-engaged warp end

1. A tubular graft for use in a stent graft, the tubular graft comprising:

a first woven layer, wherein the first woven layer forms a first side of the tubular graft, the first woven layer having a set of first warp ends;

a second woven layer, wherein the second woven layer forms a second side of the tubular graft, the second woven layer having a set of second warp ends, wherein the set of second warp ends is distinct from the set of first warp ends; and

a tapered portion having an edge, wherein the edge connects the first woven layer and the second woven layer,

wherein the tapered portion includes a first weft thread, a second weft thread, and a third weft thread, the second weft thread being between the first weft thread and the third weft thread,

wherein each of the first weft thread, the second weft thread, and the third weft thread extends through the first woven layer and the second woven layer,

wherein the first weft thread and the third weft thread engage a first warp end at the edge of the tapered portion such that the first warp end is secured to the edge at the first weft thread and the third weft thread,

wherein a floating portion of the first warp end extends from the first weft thread to the third weft thread such that the floating portion bypasses the second weft thread, and

wherein a first set of warp ends are selectively removed from engagement with a first set of weft threads and then later re-engaged with a second set of weft threads before being permanently released, such that a seam established between the first layer and second layer is provided with enhanced characteristics.

2. The tubular graft of claim 1 , wherein a free end of the first warp end extends from the edge of the tapered portion.

3. The tubular graft of claim 2 , wherein at least two weft threads secure the first warp end to the edge at a location between the floating portion of the first warp end and the free end of the first warp end.

4. The tubular graft of claim 1 , wherein the edge of the tapered portion is located between the floating portion of the first weft thread and a lumen within the tapered portion of the tubular graft.

5. The tubular graft of claim 1 , further comprising a second warp end, wherein the second warp end engages a fourth weft thread and a sixth weft thread, wherein a second floating portion of the second warp end bypasses a fifth weft thread, and wherein the fifth weft thread is located between the fourth weft thread and the sixth weft thread.

6. The tubular graft of claim 1 , wherein the floating portion of the first warp end bypasses at least three weft threads.

7. The tubular graft of claim 1 , wherein the floating portion of the first warp end bypasses at least five weft threads.

8. The tubular graft of claim 1 , wherein the first warp end is heat sealed to the edge of the tapered portion.

9. The tubular graft of claim 1 , wherein at least a portion of the edge of the tapered portion is curved.

10. A tubular graft for use in a stent graft, the tubular graft comprising:

a woven tapered portion, the woven tapered portion having an edge that extends along a decreasing-diameter portion of the tubular graft,

wherein the tapered portion includes a first weft thread, a second weft thread, and a third weft thread, the second weft thread being between the first weft thread and the third weft thread,

wherein the first weft thread and the third weft thread engage a first warp end at the edge of the tapered portion such that the first warp end is secured to the edge at the first weft thread and the third weft thread, and

wherein a floating portion of the first warp end extends from the first weft thread to the third weft thread such that the floating portion bypasses the second weft thread, and

wherein a first set of warp ends are selectively removed from engagement with a first set of weft threads and then later re-engaged with a second set of weft threads before being permanently released, such that a seam established between the first layer and second layer is provided with enhanced characteristics.

11. The tubular graft of claim 10 , wherein a free end of the first warp end extends from the edge of the tapered portion, and wherein at least two weft threads secure the first warp end to the edge at a location between the floating portion of the first warp end and the free end of the first warp end.

12. The tubular graft of claim 10 , wherein the edge of the tapered portion is located between the floating portion of the first weft thread and a lumen within the tapered portion of the tubular graft.