With the expansion of the Internet-of-Things, energy-efficient communication is becoming vital. The communication among energy-limited devices (e.g., powered by batteries or harvesting the energy from their environment) must be energy-efficient, prolonging their lifetime or increasing data throughput. This article aims at proposing energy-efficient periodic communication for devices over the ZigBee protocol and powered by a battery. We propose using timing channels for different data priorities, thus, more important data are sent more frequently. The priority is also considered in case of congested traffic, where a central device (coordinator) prioritizes more important communication. We have implemented a simulator, which serves for verification of the proposed solution, and conducted experiments comparing the proposed EEMIP method with the standard nonbeacon ZigBee communication. The experimental results show that the proposed method is more energy efficient.