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Recently, several mesh-based P2P live streaming systems are adopting a push-pull mechanism instead of the classical pull mechanism. A push-pull mechanism is more efficient in terms of overhead and leads to much better playback delay performance because it eliminates the need of the three steps of pull content retrieval: buffer map broadcast, data request and data sending. Thus, using the pull mechanism is not the best way to evaluate the performance of peering strategies especially the ones targeting playback delay minimization. We propose to revisit the peering strategies with a focus on playback delay minimization. Such strategies will benefit from the push-pull mechanism as the pull part is used mainly at the beginning of the session or to recover lost content. We believe that making the right decisions about node relationships will boost the performance of P2P systems. We propose new peering strategies that are compared, through simulations, with some recent strategies. Results show that one of the proposed strategies outperforms significantly the existing ones with respect to the playback delay experienced by participating nodes.