In this paper, we propose two compression methods for hyperspectral images with discriminant features enhanced. Generally, when hyperspectral images are compressed with conventional image compression algorithms, which mainly minimize mean squared errors, discriminant features of the original data may not be well preserved since they may not be necessarily large in energy. In this paper, we propose two compression methods that do preserve the discriminant information. In the first method, we enhanced the discriminant features and then compressed the enhanced data using conventional image compression algorithms such as 3D JPEG 2000. In the second method, we applied a feature extraction method and extracted the discriminantly dominant feature vectors. By examining the dominant feature vectors, we determined the discriminant usefulness of each spectral band. Based on these findings, we determined the bit allocation of each spectral band assuming 2D compression methods are used. Experiments show that the proposed methods effectively preserved the discriminant information and yielded improved classification accuracies compared to existing compression algorithms.