A stent graft for use in a medical procedure to treat a dissection of a patient's ascending thoracic aorta. The stent graft includes bare alignment stents at least at a proximal end, and often with a stent at both ends, each stent having opposing sets of curved apices, where the curved section of one broader set of apices has a radius of curvature that is greater than the curved section of the other narrower set of apices. The proximal stent is flared in a manner such that its broad apices occupy a larger circumference around the stent than do its narrower apices, where this flared feature provides for anchoring engagement near the aortic root in a manner not interfering with the coronary arteries or the aortic valve.