In this paper, we propose compression algorithms for hyperspectral images with pre-emphasizing discriminantly dominant features. When hyperspectral images are compressed using a conventional image compression algorithm, which has been developed to minimize mean squared errors, discriminant features of the original data may be lost during compression process since such discriminant features may not be large in energies. In order to address this problem, we propose to apply preprocessing prior to compression in order to preserve such discriminant information. In particular, we preemphasize discriminantly dominant features before a compression algorithm is applied. Experiments show that the proposed method provides improved classification accuracies than existing compression algorithms.