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Many studies have performed transcoding of compressed video streams in the discrete cosine transform (DCT) domain to reduce computation complexity. Most video compression standards recommend motion compensation in the spatial domain. On the other hand, compressed data that is motion-compensated in the spatial domain is 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 discrete cosine transform (IDCT) and motion compensation (MC). There have been few investigations into this mismatch problem. We investigate the mismatch problem and propose a precision lifting (PL) method to reduce the effects of the mismatch problem. Experimental results show that our proposed method effectively reduces the mismatch problem.