We study how firm heterogeneity determines liquidity in over-the-counter markets. Using a rich dataset on trading in the secondary market for sterling corporate bonds, we build and estimate a flexible model of search and trading in which firms have heterogeneous search costs. We show that the 8% most active traders supply as much liquidity as the remaining 92%. Liquidity is thus vulnerable to shocks to these firms: if the 4% most active traders stop trading, liquidity falls by over 60%. Bank capital regulation reduces the willingness of these active traders to hold assets and thus reduces liquidity. However, trader search, holdings and intermediation respond endogenously to reduce the welfare costs of regulation by 30%. These costs are greater in a stress, when these margins of adjustment are constrained. The introduction of trading platforms, which homogenise the ability of traders to trade frequently, improves aggregate welfare but harms the most active traders who currently profit from supplying liquidity.