Ventricular fibrillation is the leading cause of sudden cardiac death. In fibrillation, fragmented electrical waves meander erratically through the heart muscle, creating disordered and ineffective contraction. Theoretical and computer studies, as well as recent experimental evidence, have suggested that fibrillation is created and sustained by the property of restitution of the cardiac action potential duration (that is, its dependence on the previous diastolic interval). The restitution hypothesis states that steeply sloped restitution curves create unstable wave propagation that results in wave break, the event that is necessary for fibrillation. Here we present experimental evidence supporting this idea. In particular, we identify the action of the drug bretylium as a prototype for the future development of effective restitution-based antifibrillatory agents. We show that bretylium acts in accord with the restitution hypothesis: by flattening restitution curves, it prevents wave break and thus prevents fibrillation. It even converts existing fibrillation, either to a periodic state (ventricular tachycardia, which is much more easily controlled) or to quiescent healthy tissue.