We present two improved methods for the codebook search in this article. We call them the improved eigenvector method (IEVM) and the improved triangle inequality elimination (ITIE), respectively. IEVM is a full-search (FS) equivalent method, but ITIE is not. In these two methods we propose some techniques, such as the orthogonal checking and the fixed range search, to speed up their performance. According to our experimental results, IEVM is an efficient method. It is faster than FS, TIE, and EVM. Its execution time and number of operations per pixel were 4.86% and 4.76% of those in FS, respectively. As for ITIE, it is always faster than IEVM even if we limit its peak signal-to-noise ratio degradation to be no greater than 3% of the image quality of FS. Under this limitation, the execution time and the number of operations per pixel of ITIE were only 3.08% and 3.05% of those in FS, respectively.