Constrained efficiency is characterized in an asset market, subject to search frictions, where sellers are privately informed about the type of their asset. The type determines the opportunity cost of the asset for sellers and the quality of the asset for buyers. The constrained-efficient allocation is implemented using a sales tax schedule. The optimal schedule has a single-crossing property, requiring the trading of low-quality assets to be subsidized and trading of high-quality assets to be taxed. Surprisingly, the optimal schedule could be non-monotonic in the quality or price of assets even when buyers and sellers agree on the ranking of assets. This result implies that using a linear tax schedule, as typically assumed in the literature, could significantly limit the benefits of taxation. The role of traditional search frictions, and the effects of higher measure of distressed sellers, higher quality of assets and more efficient matching technology on the optimal schedule are also studied.