We develop a simple model of banking regulation with two policy instruments: minimum capital requirements and the supervision of domestic banks. The regulator faces a trade-off: high capital requirements cause a drop in the banks' profitability, whereas strict supervision reduces the scope of intermediation and is costly for taxpayers. We show that a mix of both instruments minimises the costs of preventing the collapse of financial intermediation. Once we allow for cross-border banking, the optimal policy is not feasible. If domestic supervisory effort is not observable, our model predicts a race to the bottom in capital requirement regulation. Therefore, countries are better off by harmonising regulation on an international standard.