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In this paper, we present a novel multiperiod spraying algorithm for routing in delay-tolerant networks (DTNs). The goal is to minimize the average copy count used per message until the delivery while maintaining the predefined message delivery rate by the given deadline. In each period, some number of additional copies are sprayed into the network, followed by the wait for message delivery. At any time instance, the total number of message copies distributed to the network depends on the urgency of achieving the delivery rate by the given deadline for that message. Waiting for early delivery in the initial periods with a small number of copies in existence decreases the average number of copies sprayed in the network till delivery. We first discuss two- and three-period variants of our algorithm, and then we also give an idea of how the presented approach can be extended to more periods. We present an in-depth analysis of the algorithm and validate the analytical results with simulations. The results demonstrate that our multiperiod spraying algorithm outperforms the algorithms with a single spraying period.