Contingent Convertible Bonds (CoCos) have been promoted by regulators as a bail-in mechanism in times of distress. We study the effect of equity holder decisions on conversion efficiency at banks with two layers of CoCos in their capital structure. We assume noisy market signals about fundamentals, and existence of limited cash in the market in bad states of the world. We find that the signaling function of a high trigger CoCo conversion leads to inefficient conversion of the low trigger CoCo if it is market based. We prove uniqueness of equilibrium using the global games run methodology from Goldstein and Pauzner (2005), in which we incorporate the Allen and Gale (1994) cash in the market pricing. Further we construct a measure for book value triggers, and find that accounting measures which incorporate expected credit loss act as efficient bail-in mechanisms as long as the bank measures them accurately. In contrast, under the current accounting definitions of the International Financial Reporting Standards (IFRS), CoCos do not have the capacity to prevent losses before they occur.