Some embodiments relate to endoluminal prostheses having a first stent portion and a second stent portion, a main graft body comprising first, second, and third portions, the second portion having a cross-sectional size that is significantly larger than a cross-sectional size of the first or third portions, and also significantly larger than a cross-sectional size of the target vessel. In some embodiments, the first portion of the main graft body can be attached to the first stent portion and the third portion of the main graft body can be attached to the second stent portion. The prostheses can be configured such that the second portion of the main graft body is not directly attached to the first stent portion, the second stent portion, or any other internal support structure. In some embodiments, one or more openings can be formed in the second portion of the main graft body.