In this paper, an effective lossless compression scheme for hyperspectral images is presented. The proposed scheme is based on a table look-up approach in prediction and employs two novel measures to improve the compression performance. The first measure takes advantage of the spatial data correlation and formulates the derivation of a spectral domain predictor as a process of Wiener filtering. The derived predictor is considered statistically optimal provided that the data within a small context window are stationary. This property holds in most cases due to spatial data correlation. Under the Wiener filtering framework, the proposed predictor can be extended from one-tap to multi-tap prediction to further improve performance. In the second measure, a backward search scheme is used instead of look-up tables, which reduces the memory storage requirement drastically and achieves performance equivalent to that obtained using multiple look-up tables. The search effort is greatly reduced using the quantization index approach. Simulations on parameter settings and refinements on entropy coding are conducted to fine-tune performance. Experiments on 5 sequences of AVIRIS images show that the proposed scheme can yield an average compression ratio of as high as 3.85.