In one embodiment, balloons are intended for use in valvuloplasty of stenosed aortic valves, with a potential use for valvuloplasty of other heart valves as well. Their common special feature is that the entire or part of their external surface is covered by a drug that is eluted at the valve tissues during the balloon brief contact with them at the time of dilatation. The drug acts against the process of restenosis, which almost uniformly occurs after some time. The shape of the balloon can be the classical cylindrical or an hour-glass shape that facilitates targeted delivery of the drug at the valve tissues. Additional balloon shapes are described for usage after valvuloplasty is carried out in order to achieve targeted drug delivery in the upper or both surfaces of the leaflets, and for prolonged contact with the valve tissues without interruption of blood circulation. An advantage of the balloons is that the local delivery of the drug will significantly reduce the likelihood of restenosis. As a result the procedural benefits for the patient are sustained in the long term, and the procedure from alleviating progresses into end-therapy.