Motion estimation and motion compensation comprise one of the most important compression methods for video communications. We propose a low-power design of a motion estimation block for a low bit-rate video codec standard H.263. Since the motion estimation is computationally intensive to result in large power consumption, a low-power design is essential for portable or mobile systems. Our block employs the Four-Step Search (4SS) method as its primary algorithm. The design and the algorithm have been optimized to provide adequate results for low-quality video at low-power consumption. The model is developed in VHDL and synthesized using a 0.35 um CMOS library. Power consumption of both gate-level circuits and memory-accesses have been considered. Gate-level simulation shows the proposed design offers a 38% power reduction over a "baseline" implementation of a 4SS model and a 60% power reduction over a baseline Three-Step Search (TSS) model. Power savings through reduction of memory access is 26% over the TSS model and 32% over the 4SS model. The total power consumption of the proposed motion estimation block ranges from 7 - 9 mW and is dependent on the type of video being motion estimated.