Abstract: Disclosed is a specially tapered balloon such as for sizing an implantable tubular stent that has been positioned within an ostium. In one application of the present invention, a stent is positioned within the right coronary ostium, and the tapered balloon of the present invention is positioned within the stent to provide a radial outward flare on the proximal end of the stent. In this manner, the proximal end of the stent is pressed back against the aortic wall surrounding the right coronary ostium, thereby minimizing any obstruction to blood flow in the aorta, and possibly reducing the risk of restenosis at the right coronary ostium.