— The inherent trade-off between energy-efficiency and rapidity of event dissemination is characteristic for wireless sensor networks. Scarcity of energy renders it necessary for nodes to spend a large portion of their lifetime in an energyefficient sleep mode during which they do neither receive nor send messages. On the other hand, the longer nodes stay in sleep mode, the slower will be the reaction time for disseminating an external event. The trade-off is prominently exhibited during the deployment phase of sensor networks, if some nodes are deployed earlier than others. In this paper, we study this fundamental trade-off by giving a formal model that enables us to compare the performance of different protocols and algorithms. Based on this model, we propose, analyze, and simulate two novel algorithms which significantly outperform existing solutions.