We study directed search equilibria in a decentralized market with adverse selection, where uninformed buyers post general trading mechanisms and informed sellers select one of them. We show that this has differing and significant implications with respect to the traditional approach, based on bilateral contracting between the parties. In equilibrium, all buyers post the same mechanism and low-quality sellers receive priority in any meeting with a buyer. Also, buyers make strictly higher profits with low- than with high-type sellers. When adverse selection is severe, the equilibrium features rationing and is constrained inefficient. Compared to the equilibrium with bilateral contracting, the equilibrium with general mechanisms yields a higher surplus for most, but not all, parameter specifications.