We model trading and information diffusion in OTC markets, when dealers can engage in many bilateral transactions at the same time. We show that information diffusion is effective, but not efficient. While each bilateral price partially reveals all dealers' private information after a single round of trading, dealers could learn more even within the constraints imposed by our environment. This is not a result of dealers' market power, but arises from the interaction between decentralization and differences in dealers' valuation of the asset. We also derive empirical predictions on the connection of transaction size, its cost and the opaqueness of the asset and confront several explanations for the disruption of OTC markets with stylized facts from the empirical literature with the help of our framework. We find more support for narratives emphasizing increased counterparty risk as opposed to increased informational frictions.