I extend and discuss the model of asset liquidity by Lester, Postlewaite, and Wright (2007, 2008). I consider a model with decentralized trades in which claims on a real and divisible asset serve as means of payment. A recognizability problem is introduced by assuming that the claims on the asset can be counterfeited at a positive cost. This formalization nests the models by Lagos and Rocheteau (2008) and Geromichalos, Licari, and Suarez-Lledo (2007) in which there is no recognizability problem, and Lester, Postlewaite, and Wright (2007), in which counterfeits can be produced at no cost. Even though no counterfeiting occurs in equilibrium, the recognizability problem affects the composition of trades: buyers consume less and spend a lower fraction of their asset holdings in matches where sellers are uninformed. Both the asset price and its liquidity (as measured by its transaction velocity) depend on the recognizability of the asset. The asset is more liquid and its return is lower if either the sellers’ ability to recognize counterfeits or the cost of producing counterfeits increases.