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A standard paradigm for the allocation of wireless resources in communication demands symmetry, that is, all users are assumed to be on equal footing and hence get equal shares of the system's communication capabilities. However, there are situations in which “prime users” should be given priority, as for example in the transmission of emergency messages. We examine prioritization policies that could be implemented at the physical layer and propose a new one, termed interference priority (IP), which is shown to have excellent performance. We evaluate the performance of these prioritization techniques both in controlled settings and within the context of a full cellular system and discuss the impact of prioritized use of resources on the unprioritized users.