Firms' issuance of non-linear securities, such as debt or options, creates risk-shifting incentives that may lead to inefficient outcomes. This widely accepted result rests on the assumption that firms' control rights are coupled with the residual claims, and thus held by equity holders. We relax this assumption and analyze a setting where cash-flow and control rights are allocated independently. Although payoffs are determined solely by rights over realized cash flows, control rights hold value because they influence the probability distribution of those cash flows. Cash-flow and control rights often act as substitutes, but cash-flow rights can reduce investors' payoff when their impact on decision-making is sufficiently strong. When issuers and holders of a non-linear security have sufficiently distinct cash-flow rights, the equilibrium features efficiency with full surplus extraction; as their cash-flow rights converge, a trade-off between efficiency and surplus extraction emerges. In that case, a sufficiently skewed distribution of payoffs can restore efficiency.