In image processing, classification and compression are very common operations. Compression and classification algorithms are conventionally independent of each other and performed sequentially. However, some class distinctions may be lost after a minimum distortion compression. In this paper, two new schemes are developed that combine the compression and classification operations in order to optimize some classification metrics. In other words, the compression systems are improved under classification constraints. In the first scheme, compression is achieved by using Adaptive Differential Pulse Code Modulation (ADPCM). Optimization of filter coefficients is done by using a simple genetic algorithm (GA). In the second scheme, compression is achieved by image transform and quantization. The parameters in transform and quantization are adapted to improve the compression system and reduce the classification errors. Computer simulations are performed on hyperspectral images. The results are promising and illustrate the performance of the algorithms under various classification constraints and compression schemes.