Different variants of duty-cycle MAC protocols have been designed for wireless sensor networks to reduce energy consumption. However, the synchronization process of these protocols consumes a significant amount of energy. In this paper, we propose a new energy-efficient synchronization algorithm referred to as 1-Sync that can be easily integrated with duty-cycle MAC protocols. We compare 1-Sync with fixed periodic synchronization (F-Sync) algorithm and Intelligent Network Synchronization (INS) algorithm and show that 1-Sync outperforms F-Sync and INS in energy-efficiency over a wide range of node densities. Analytical models that describe the energy consumption behavior and synchronization performance of these synchronization algorithms are also presented.