Motion estimation is a critical yet computationally intensive task for video encoding. In this paper, we present an enhancement over a normalized partial distortion search (NPDS) algorithm to further reduce block matching motion estimation complexity while retaining video fidelity. The novelty of our algorithm is that, in addition to the halfway-stop technique in NPDS, a dual-halfway-stop (DHS) method, which is based on a dynamic threshold, is proposed, so that block matching is not performed against all matching candidates. An adaptive search range (ASR) mechanism based on inter block distortion further constrains the searching process. Simulation results show that the proposed algorithm has a remarkable computational speedup when compared to that of full search and NPDS algorithms. Particularly, it requires less computation by 92-99% and encounters an average of only 0.08 dB PSNR video degradation when compared to that of full search. The speedup is also very significant when compared to that of fast motion estimation algorithms. This paper describes our work that led to our joint video team (JVT) adopted contribution (included in software JM 10.1 onwards) as well as later enhancements, collectively known as simplified and unified multi-hexagon search (SUMH), a simplified fast motion estimation.