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Distributed systems benefit substantially from the ability to exchange jobs between temporarily heavily and lightly loaded nodes. Depending on whether the lightly or heavily loaded nodes initiate the job exchange, such strategies are termed pull or push strategies. In this paper we compare the performance of an aggressive push strategy with the more traditional pull strategies in large distributed systems using mean field models. We consider homogeneous systems, systems with fast and slow servers as well as master-worker setups. We show that even at high loads the aggressive push strategy can outperform traditional pull strategies in a homogeneous system (at the expense of increased network traffic), while the pull strategies are superior in a master-worker setup where the proportion of masters is low. We also indicate that the choice of the best strategy is rather insensitive to the variation in the job processing time and that the queue length distribution under the aggressive push strategy decays faster than geometric.