A device includes a first end portion, a second end portion, an intermediate portion between the first end portion and the second end portion, and a graft material coupled to at least the intermediate portion. The first end portion has a first end diameter. The second end portion has a second end diameter larger than the first end diameter. The intermediate portion tapers between the first end portion and the second end portion. A method of diverting fluid flow from a first passage to a second passage comprising deploying the device in a third passage between the first passage and the second passage, expanding the first end portion against sidewalls of the first passage, and expanding the second end portion against sidewalls of the second passage.