Systems and methods for treating diseased bodily lumens involving branched lumen deployment sites include a main graft or stent-graft deployable in a main artery and a vent device or stent-graft deployable in a branch artery to maintain blood flow through the main artery and from the main artery to the branch artery. Systems and methods for treating diseased bodily lumens involving branched lumen deployment sites may also include a main graft or stent-graft deployable in the main artery, a chimney graft or stent-graft deployable in both branch artery and the main artery to the branch artery and a gutter-sealing device associated with the chimney graft to prevent flow of blood among the chimney graft, the main graft and a wall of the main artery.