We construct a random matching model of a monetary economy with commodity money in the form of potentially different types of silver coins that are distinguishable by the quantity of metal they contain. The quantity of silver in the economy is assumed to be fixed, but agents can mint and melt coins. Coins yield no utility, but can be traded. Uncoined silver yields direct utility to the holder. We find that optimal coin size increases with the probability of trade and with the stock of silver. We use these predictions of our model to analyze the coinage decisions of the monetary authorities in medieval Venice and England. Our model provides theoretical support for the view that decisions about coin sizes and types during the medieval period reflected a desire to improve the economic welfare of the general population, not just the desire for seigniorage revenue.