I examine the robustness of monetary equilibriain a random-matching model, where a more efficient mechanismfor trade is available. Agents choose between two tradingsectors: the search and the intermediated sector. In theformer, trade partners arrive randomly and there is atrading externality. In the latter, a costly matchingtechnology provides deterministic double-coincidencematches. Multiple equilibria exist with the extent of costlymatching endogenously determined. Money and “mediated” trademay coexist. This depends on the size of the probability ofa trade, relative to the cost of deterministic matching.This outcome is inferior for an increasing-returnsexternality. Under certain conditions, regimes with onlycostly matching are welfare superior to monetary regimeswith random matching.