In this paper, we consider the use of an electric-supplied coordinator exploiting much higher transmission power than battery-supplied nodes in low power and lossy networks (LLNs). Since the coordinator can transmit via one hop instead of multiple hops over downlink, it is possible to reduce the communication overhead significantly. To take this advantage, we propose a single hop downlink protocol (SHDP) which comprises direct downlink transmission, local acknowledgement, neighbor forwarding, and mitigation of forwarding contention. Finally, the performance of the proposed SHDP is mathematically analyzed and evaluated by computer simulation, showing significant performance improvement over conventional multi-hop routing when applied to LLNs.