Hyperspectral images are generated by collecting hundreds of narrow and contiguously spaced spectral bands of data producing a highly correlated long sequence of images. Some application specific data compression techniques may be applied advantageously before we process, store or transmit hyperspectral images. This paper applies asymmetric tree 3DSPIHT (AT-3DSPIHT) for hyperspectral image compression; it also investigates and compares the performance of the AT-3DSPIHT, 3DSPIHT and 3DSPECK on hyperspectral image compression. Results show that the AT-3DSPIHT outperforms the other two by the approximate range of 0.2 to 0.9 dB PSNR. It guarantees over 4 dB PSNR improvement at all rates or rate savings at least a factor of 2.5 over 2D coding of separate spectral bands without axial transformation.