There are two general ways in which the role of fiat money has been introduced in the standard monetary search-theoretical model. The first is to bring in the model a fiat object with different intrinsic properties. The second is to introduce a centralized institution that favors the use of fiat money through specific transaction policies. We carry out a similar exercise for a modified version of the model in which agents have a different structure of preferences. We characterize the conditions for which there exist equilibria with circulating fiat money and evaluate the main differences with the results derived from the standard model.