We extend Duffie et al.'s (2005) search-theoretic model of over-the-counter (OTC) asset markets, allowing for a decentralized inter-dealer market with arbitrary heterogeneity in dealers' valuations (or, equivalently, inventory costs). We develop a solution technique that makes the model fully tractable and allows us to derive, in closed form, theoretical formulas for key statistics analysed in empirical studies of the intermediation process in OTC markets. A calibration to the market for municipal bonds allows us to quantify important unobservable characteristics of this market, including the severity of search and bargaining frictions and the nature of heterogeneity across dealers. We use our calibrated model to study the effect of these market characteristics on total welfare and the distribution of gains from trade across customers and dealers.