We study a security design problem under asymmetric information, in the spirit of Myers and Majluf (1984). We introduce a new condition on the right tail of the firm-value distribution that determines the optimality of debt versus equity-like securities. When asymmetric information has a small impact on the right-tail, risky debt is preferred for low capital needs, but convertible debt is optimal for larger capital needs. In addition, we show that warrants are the optimal financing instruments when the firm has already pre-existing debt in its capital structure. Finally, we provide conditions that generate reversals of the standard pecking order.