We propose a model of trading in the over-the-counter corporate bond market where investors can buy and sell bonds through a dealer and can short bonds by borrowing them in the securities lending market. The model predicts that higher dealer inventory costs are associated with lower short interest for bonds, particularly for high-credit-quality bonds. We construct bond-level proxies for inventory costs and provide empirical evidence in support of the model's prediction. We find that much of the dramatic decline in short interest observed since the Great Financial Crisis (GFC) can be explained by an increase in proxies for inventory costs. We document that the short-sale constraints imposed by higher dealer inventory costs have had a negative impact on price efficiency. Our findings suggest that tighter post-GFC regulation may have had unintended consequences for bond market quality.