Hyperspectral image compression has become increasingly important in data exploitation because of enormous data volumes and high redundancy provided by hundreds of contiguous spectral channels. Since a hyperspectral image can be viewed as a 3-dimensional (3D) image cube, many efforts have been devoted to extending 2D image compression techniques to perform 3D image compression on hyperspectral image cubes. Unfortunately, some major issues generally encountered in hyperspectral data exploitation at low or very low-bit rate compression, for example, subpixels and mixed pixels which do not occur in traditional pure pixel-based image compression are often overlooked in such a 2D-to-3D compression. Accordingly, a direct application of 2D-to-3D compression techniques to hyperspectral image cubes without taking precaution may result in significant loss of crucial spectral information provided by subtle substances such as small objects, anomalies during low bit-rate lossy compression. This paper takes a rather different view by investigating lossy hyperspectral compression from a perspective of exploring spectral information, referred to as exploitation-based lossy compression and further develops spectral/spatial hyperspectral image compression to effectively preserve crucial and vital spectral information of objects which are generally missed by commonly used mean-squared error (MSE) or signal-to-noise ratio (SNR)-based compression techniques when lossy compression is performed at low bit rates. In order to demonstrate advantages of the proposed spectral/spatial compression approach applications of subpixel target detection and mixed pixel analysis are used for experiments for performance evaluation.