The current paper proposes a new method for reducing the computational overhead of fine-to-coarse multi-resolution motion estimation (MRME) on the finest resolution level based on limiting the search region used to consider the motion vectors from the coarsest resolution subband. Half-pel accuracy motion estimation (HPAME) is used in the baseband to achieve an exact motion vector, which has a significant influence on the reconstructed image. However, since this method involves a high computational overhead, the use of selective interpolation is suggested to reduce the computational overhead. The proposed method uses HPAME to estimate exact motion vectors in the baseband, then based on the characteristics of these motion vectors, the motion vectors in the higher frequency subbands are selectively estimated. That is, motion vectors in the higher frequency subbands are only estimated for those blocks with half-pixel accuracy motion vectors in the baseband. Experimental results show that the proposed algorithm can produce better image quality results than the conventional algorithms.