Utilizing subsets of trades in which dealers act purely as agents, purely as market-makers, and as both, we decompose dealer spreads in U.S. corporate bond OTC markets into components arising from: 1) dealers' market making role, and 2) their role as agents for their non-dealer customers. We find that agent-related spreads are large and comparable in magnitude to market-making spreads. In their role as agents, dealers face liquidity-search and customer interface costs, while in their role as market makers they face inventory and asymmetric information costs. Consistent with this, we find that while market-making spreads are strongly correlated with market risk variables, agent-related spreads are not, depending instead on liquidity driven variables. While market-making spreads are inversely related to trade size, agent-related spreads increase with trade size before leveling off and then declining - possibly indicating that agent-dealers devote less search time to relatively small trades. Market makers trade both with dealers functioning as agents and directly with investors; our evidence indicates that market makers derive an information benefit from direct interaction with traders especially when risk and information asymmetry is high. Except for very small trades, explicit transaction costs of non-dealer customers are lower when they trade directly with market-making dealers than when they route trades through a dealer acting purely as an agent. Our evidence indicates that bond traders tend to employ agent-dealers when the cost of the agent is low relative to the trader's internal search costs. Finally, we show that many existing studies have underestimated average overall trading costs in the corporate bond market by failing to account for both the agent dealer spread and market-making dealer spread on trades which involve both. Given our findings on the size and economic determinants of agent-related dealer costs, our results have significant implications for the extensive empirical literature on dealer spreads in other OTC markets.