We propose a theory of banking in which banks cannot perfectly control deposit flows. Facing uninsurable loan and deposit shocks, banks dynamically manage lending, wholesale funding, deposits, and equity. Deposits create value by lowering funding costs. However, when the bank is undercapitalized and at risk of breaching leverage requirements, the marginal value of deposits can turn negative as deposit inflows, by raising leverage, increase the likelihood of costly equity issuance. Banks’ inability to fully control leverage distinguishes them from non-depository intermediaries. Our model suggests a re-evaluation of leverage regulations and offers new perspectives on banking in a low interest-rate environment.