Flared stents are disclosed, and apparatus and methods for delivering such stents into a bifurcation between a main vessel and a branch vessel. The stent includes a first tubular portion a second flaring portion that may be flared radially outwardly to contact the ostium. The stent may include variable mechanical properties along its length. The stent may be delivered using a catheter including proximal and distal ends, the stent overlying first and second balloons on the distal end. During use, the catheter is advanced through an ostium into the branch to place the stent within the branch. The first balloon is expanded to flare the stent to contact a wall of the ostium, thereby causing the stent to migrate partially into the ostium. The second balloon is expanded to fully expand the stent within the ostium and branch.
