A stent graft (40) for treating Type-A dissections in the ascending aorta (22) is provided with a plurality of diameter-reducing suture loops (56-60) operable to constrain the stent graft during deployment thereof in a patient's aorta. The diameter-reducing loops (56-60) allow the stent graft (40) to be partially deployed, in such a manner that its location can be precisely adjusted in the patient's lumen. In this manner, the stent graft can be placed just by the coronary arteries (26, 28) with confidence that these will not be blocked. The stent graft (40) is also provided with proximal and distal bare stents (44,52) for anchoring purposes.