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Wireless relays extend coverage, improve spectral efficiency, and enhance reliability and rates of wireless cellular communication systems. In this work, we introduce the fundamental notion of asymmetric cooperation among cooperating relays in cellular downlinks - different relays are party to different but overlapping knowledge about the messages transmitted from the base station. We argue that asymmetric cooperation arises naturally in most two-phase protocols in which the base station first transmits information to multiple relays that then cooperatively forward the information to the recipient mobile stations in the cell. For a system in which two relays are of the decode-and-forward type and cooperate using linear precoding to communicate with two mobile stations, we formulate the general, but complicated, throughput optimization problem and derive several results that considerably simplify the optimization. We show that under different channel configurations and fairness criteria, asymmetric cooperation is often the throughput-maximizing option. Under typical configurations, a 20-30% throughput enhancement is achieved compared to conventional full-cooperation systems.