This paper analyses two aspects of contingent convertible (Coco) bonds. First, we establish and compare in detail the payoffs to equity and bond holders in different bail-out/in schemes, namely no bail-out/in, government bail-out, equity-conversion Coco bail-in and write-off Coco bail-in. This reveals that the equityholders progressively gain extra incremental option positions at each step of the bail-out/in schemes in the order listed. Second, we investigate two types of agency costs: the wealth-transfer problem and the value destruction problem. We show that these are aggravated under equity-conversion Coco bail-ins, and are even higher under write-off Coco bail-in for larger asset values, suggesting inherent structural incentive issues associated with these bonds