Previous work on the denomination structure of currency treats as exogenous the distribution of transactions and the denominations held by people. Here, by way of a matching model, both are endogenous. In the model, trades in pairwise meetings alternate in time with the opportunity to freely choose a portfolio of denominations and there is a trade‐off between the benefits of small‐denomination money for transacting and the costliness of carrying a large quantity of small‐denomination money. For a given denomination structure, a monetary steady state is shown to exist. The model implies that too small denominations are abandoned.