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Many studies have performed transcoding of compressed video streams in the discrete cosine transform (DCT) domain to reduce computational complexity. On the other hand, most video compression standards recommend motion compensation in the spatial domain. Thus, compressed data that is motion-compensated in the spatial domain should be motion-compensated in the transform domain for the transform-domain transcoding. However, this combination of encoding in the spatial domain and decoding in the transform domain degrades image quality due to mismatches of the inverse DCT and motion compensation. There have been few investigations into this mismatch problem. In this paper, we establish that the rounding in calculation is the major cause of the mismatch. We investigate the mismatch problem in detail and propose a precision lifting method to reduce the effects of the mismatch problem. Experimental results show that our proposed method can effectively reduce the mismatch problem.