As the dimensionality of remotely sensed data increases, the need for efficient compression algorithms for hyperspectral images also increases. However, when hyperspectral images are compressed with conventional image compression algorithms, which have been developed to minimize mean squared errors, discriminant information necessary to distinguish among classes may be lost during compression process. In this paper, we propose to enhance such discriminant information prior to compression. In particular, we first find a new basis where class separability is better represented by applying a feature extraction method. However, due to high correlations between adjacent bands of hyperspectral data, we have singularity problems in applying feature extraction methods. In order to address the problem, we first reduce the dimension of data and then find a new basis by applying a feature extraction algorithm. Finally, dominant discriminant features are enhanced and the enhanced data are compressed using a conventional compression algorithm such as 3D SPIHT. Experiments show that the proposed compression method provides improved classification accuracies compared to the existing compression algorithms.