Recently, we proposed a multiplierless ID Int-DCT improved from our previous proposed Int-DCT by approximating floating multiplications to bit-shift and addition operations. The multiplierless ID Int-DCT can be well operated both lossless coding and lossy coding. However, our multiplierless ID Int-DCT is not focused on how to assign word-length for floating-multiplier approximation as short as possible for reduction of hardware complexity. In this paper, we propose a new Optimum-Word-Length-Assignment (OWLA) multiplierless Int-DCT. Apart from inexpensive hardware complexity, the new OWLA multiplierless ID Int-DCT achieves high coding performance in both lossless and lossy coding. The lossless/lossy coding criterion is applied to evaluate coding performance of the proposed Int-DCT comparing to those of the others Int-DCT.