A stent graft (18) for deployment in a curved lumen such as the aortic or thoracic arch (130) comprises a constraining mechanism at its proximal end. A stent (4′) provided at the proximal end of the stent graft (18) includes loops of material (11) that co-operate with restraining wires (42) that extend between a central guide wire carrier (24) and a restraining wire cannula (8). The constraining mechanism acts to maintain the proximal stent (4′) constrained at three points around its circumference at both the proximal and distal ends of the proximal stent (4′). The proximal stent (4′) is thus allowed to expand after expansion of the remainder of the stent graft (18) during deployment. In an embodiment, the constraining mechanism acts to constrain two adjacent struts of the proximal stent (4′) at three points radially therearound, at the proximal end of the stent (4′) and at the distal end of the stent (4′). The proximal stent (4′) may then overlap with the interior of an adjacent stent at an inner part (31) of a curved vessel.