This paper justifies, in an agency context, the existence of hybrid securities appeared very recently on the organized market: the cocos (contingent convertible bonds). Like the straight debt, they make it possible to profit from tax benefits of debt. And, like stocks, they provide protection against financial distress. Although cocos cannot completely protect banks against bankruptcy, they reduce significantly their probability of failure independent of regulator actions. The structural model shows that the cocos allow an increased valorization of the banks without jeopardizing their stability. However, it should pay special attention to their design under penalty of not being able to provide an efficient mean of financing to investors. Particular attention should be paid to the fixing of the value of the trigger. Its optimal value is highly dependent on the environment (structure and amount of bankruptcy costs, intensity of the dilution of shareholder claims, tax environmental and so on).