Motion estimation is a vital task in video compression and many algorithms are proposed to reduce its computational complexity. In a conventional Full Search (FS) algorithm, all blocks are searched for a match in the search window, resulting in a very acceptable PSNR compared to the other methods. However it suffers from heavy computational overhead. Three Step Search (TSS) algorithm which limits the search space adaptively, is used in many applications for its simplicity and effectiveness. The PTSS algorithm proposed in this paper decreases the number of search blocks even more, using motion information obtained from its neighboring blocks. Experimental and simulation results show approximately a 20% speed enhancement with the same or slightly improved PSNR in comparison to TSS.