A stent graft for deployment in a curved lumen such as the aortic or thoracic arch comprises a constraining mechanism at its proximal end. A stent provided at the proximal end of the stent graft includes loops of material that co-operate with restraining wires that extend between a central guide wire carrier and a restraining wire cannula. The constraining mechanism acts to maintain the proximal stent constrained at both the proximal and distal ends of the proximal stent. The proximal stent is thus allowed to expand after expansion of the remainder of the stent graft during deployment. In an embodiment, the constraining mechanism acts to constrain two adjacent struts of the proximal stent at three points radially therearound, at the proximal end of the stent and at the distal end of the stent. The proximal stent may then overlap with the interior of an adjacent stent at an inner part of a curved vessel.