The authors study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. The paper focuses on a priori suboptimal mechanisms which under some settings may become optimal once transaction costs associated with more complex mechanisms are taken into account. The main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus, an intermediary's revenue, and the agents' welfare. The presented analysis is similar in spirit to the study by \textit{Z. Neeman} [Games Econ. Behav. 43, No. 2, 214--238 (2003; Zbl 1048.91051)].