A prominent feature of the Kiyotaki and Wright (1989) model of commodity money is the multiplicity of dynamic equilibria. We show that the frequency of search is strongly related to the extent of multiplicity. To isolate the role of frequency of search in generating multiplicity, we (i) vary the frequency of search without changing the frequency of finding a trading partner and (ii) focus on symmetric dynamic equilibria, a class for which we can sharply characterize several features of the set of equilibria. For any finite frequency of search this class retains much of the multiplicity. For each frequency we characterize the full set of equilibrium payoffs, strategies played and dynamic paths of the state variables. Indexed by any of these features, the set of equilibria converges uniformly to a unique equilibrium in the continuous search limit. We conclude that when search is frequent, the seemingly exotic dynamics are irrelevant.