We study the welfare implications of different market structures in a model of adverse selection. In particular, we contrast a competitive exchange, where the informed agents can trade simultaneously with multiple principals with an íover-the-counterí setting characterized by search frictions and bilateral trading. We show that the latter can lead to higher ex-ante welfare. The intuition is that non-exclusivity in contracts in the competitive arrangement constrains the principalís ability to provide incentives for truthful revelation. Search frictions mitigate this problem, but create local monopolies. When this tension between competition and incentive provision is resolved in favor of the latter, frictional markets lead to better outcomes.