We consider a model of external financing under ex ante asymmetric information and profit manipulation (non verifiability). Contrary to conventional wisdom, the optimal contract is not standard debt, and it is not monotonic. Instead, it resembles a contingent convertible (CoCo) bond. In particular: (i) if the profit manipulation and/or adverse selection are not severe, there exists a unique separating equilibrium in CoCos; (ii) in the intermediate region, if the distribution of earnings is unbounded above there exists a unique pooling equilibrium in CoCos, otherwise debt might be issued but it is never the unique equilibrium; (iii) finally, if profit manipulation is severe, there is no financing. These findings suggest that the standard monotonicity constraint exogenously imposed in the security design literature must be reconsidered. Crucially, profit manipulation is part of the optimal contract, and non-monotonic, convertible securities mitigate the asymmetric information problem. We discuss milestone payments in venture capital as an application.