The present disclosure includes a stent-graft (102) comprising a first portion that is configured to engage a vessel wall (100), a second portion that is configured not to engage the vessel wall, and a perfusion window (116) that is configured to permit blood flow. The stent-graft may further comprise a transition portion between the first portion and the second portion, and the perfusion window may be formed in the first portion, the second portion, and/or the transition portion. In a variety of embodiments, one of the first and the second portion may have a smaller diameter than the other. Similarly, in a variety of embodiments, the transition portion may be frustoconically shaped.
