Models of the exchange process based on search theory can be used to analyze the features of objects that make them more or less likely to emerge as money in equilibrium. These models illustrate the trade-off between endogenous acceptability (an equilibrium property) and intrinsic characteristics of goods, such as storability or recognizability. We look at how the relative supply and demand for various goods affect their likelihood of becoming money. Intuitively, goods in high demand and/or low supply are more likely to appear as commodity money, subject to the qualification that which object ends up circulating as a medium of exchange depends at least partly on convention. Welfare properties and fiat money are discussed.