Motion estimation is the key issue in video compressing. Several methods for motion estimation based on the center biased strategy and minimum mean square error trend searching have been proposed, such as TSS, FSS, UCBDS and MIBAS, but these methods yield poor estimates or find local minima. Many other methods predict the starting point for the estimation, these can be fast but are inaccurate. This study addresses the causes of wrong estimates, local minima and incorrect predictions in the prior estimation methods. The Multiple Searching Trend (MST) is proposed to overcome the problems of ineffective searches and local minima, and the Adaptive Dilated Searching Field (ADSF) is described to prevent prediction from wrong location. Applying MST and ADSF to the listed estimating methods, such as UCBDS, a fast and accurate can be reached. For this this reason, the method is called CockTail Searching (CTS). In another proposed method, we try to define the new criteria used to determine a referent macro block within the search window in a referent frame, which matches the estimated current macro block in the current frame, in motion estimation process used in MPEG standard. The Prediction Error(PE) in the Pixel Difference(PD) between the referent macro block and the current macro block is defined to be a new criterion which can get better performance in compressed data length than the Mean Square Error(MSE) used by most of motion estimation methods. The other criterion combined PE and MSE is proposed to get better performance than the PE. Two new criteria is applied to a famous motion estimation method, UCBDS, to show the performance of the new criteria. The evaluation results show that using new criteria in UCBDS can get more 40% reduction in compressed data size than the UCBDS with MSE.