In video coding, motion compensation prediction provides significant increases in overall compression efficiency. The prediction residuals are typically treated as images and compressed by applying two-dimensional transforms such as the two-dimensional discrete cosine transform (2D-DCT). Previous work has found that the use of directionadaptive one-dimensional discrete cosine transforms (1D-DCTs) in coding motion compensation residuals can provide significant additional bitrate savings. However, this requires optimization over all of the available transforms to minimize the overall bitrate, which can be expensive in terms of time and computation.In this thesis, we examine the use of only the horizontal and vertical 1D-DCTs in addition to the 2D-DCT for coding motion compensation residuals. By reducing the number of available transforms, the amount of required computation decreases significantly, with a potential cost in performance. We perform experiments using a modified H.264/AVC codec to compare the performance of using different sets of available transforms. The results indicate that for typical applications of video coding, most of the performance benefit from using directional 1D-DCTs can be retained by keeping only the horizontal and vertical 1D-DCTs.