Video transcoding is an efficient way for. rate adaptation and format conversion in various networked video applications. Many transcoder architectures have been proposed to achieve fast processing. Recently, thanks to its relatively low complexity and acceptable quality, the DCT-domain transcoder (DDT) was proposed to overcome the drift in the open-loop transcoders and the high-complexity in the cascaded transcoders. In this paper, we show that there is still some improvement space for computation reduction in the DDT. We propose a method to fast extract partial low-frequency coefficients in the DCT-domain motion compensation (DCT-MC) operation. We investigate fast algorithms of the DDT based on the proposed fast coefficients extraction scheme. The simulation results show that the proposed methods can achieve significant computation reduction while maintaining close PSNR performance compared to the DDT.