An endoluminal prosthesis (10) includes a tubular body of a biocompatible graft material having proximal and distal ends (22,24), anterior and posterior sides, and first and second fenestrations (12,38) spaced from one another circumferentially around the tubular body. The prosthesis includes at least one first diameter reducing tie (60) positioned circumferentially on the posterior side of the prosthesis and engaging at least a circumferential segment of the posterior side to restrain the engaged segment from expansion. The prosthesis also includes at least one second diameter reducing tie positioned circumferentially between the first and second fenestrations on the anterior side of the prosthesis and engaging at least a circumferential segment of the anterior side to restrain the engaged segment from expansion.
