A stent graft leg extension (10) to extend from a bifurcated aortic stent graft into an iliac artery. The stent graft has a tubular body. (12) of a biocompatible graft material and a plurality of self-expanding stents (14) joined to and supporting the tubular body. An uncovered tubular self-expanding stent assembly (26) extends from a first end of the tubular body and is fastened thereto. The uncovered tubular self-expanding stent assembly (26) provides a smooth transition from the leg extension into the iliac artery to reduce the chance of kinks causing problems in the leg extension.