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The time synchronization problem needs to be considered in a distributed system. In Wireless Sensor Networks (WSNs) this issue must be solved with limited computational, communication and energy resources. Many synchronization protocols exist for WSNs. However, in most cases these protocols are independent entities with specific packets, communication scheme and network hierarchy. This solution is not energy efficient. Because it is very rare for synchronization not to be necessary in WSNs, we advocate integrating the synchronization service into the routing layer. We have implemented this approach in a new synchronization protocol called Routing Integrated Synchronization Service (RISS). Our tests show that RISS is very time and energy efficient and also is characterized by a small overhead. We have compared its performance experimentally to that of the FTSP synchronization protocol and it has proved to offer better time precision than the latter protocol.