Banks predominantly issue non-dilutive CoCos, contrary to the suggestion that CoCos should be dilutive to reduce risk-taking. In an agency model of two moral hazards, we show that although dilutive CoCos deter ex-ante risk-taking and prevent banks from being undercapitalized, penalizing shareholders of a distressed bank with dilution leads to ex-post risk-shifting. CoCos' design and risk implications depend on bank capitalization: equity-constrained banks prefer non-dilutive CoCos because they maximize the financing capacity by tackling only the ex-post risk-shifting. Non-dilutive CoCos can implement the constrained social optimum for highly leveraged banks, and regulators can induce appropriate CoCo designs with capital regulations.