In this paper, we propose a hybrid network model called Sphinx for cellular wireless packet data networks. Sphinx uses a peer-to-peer network model in tandem with the cellular network model to achieve higher throughput and lower power consumption. At the same time, Sphinx avoids the typical pitfalls of the pure peer-to-peer network model including unfair resource allocation, and throughput degradation due to mobility and traffic locality. We present simulation results showing that Sphinx outperforms the cellular network model in terms of throughput and power consumption, and achieves better fairness and resilience to mobility than the peer-to-peer network model.