A stent-graft comprising a stent and a graft having a supported portion lining or covering at least a portion of the stent, and an unsupported portion extending proximally beyond the proximal end of the stent. The stent-graft may have a length corresponding to at least a mean standard length from a standard incision point to a distal-most portion of a standard lumen into which the distal end of the stent is adapted to be deployed, with the unsupported portion of the graft extending beyond the mean standard length by an amount equal to at least two, if not three or more, standard deviations of the mean standard length. A method for deploying the stent-graft comprises making an incision in a wall of the lumen, introducing and deploying the stent-graft in the lumen so that the proximal end extends beyond the incision, and attaching the graft to a lumen by anastamosis.