The article aims to provide a solution for multispectral image compression for high color reproducibility with preservation to spectral accuracy. In the method previously proposed to reduce the colorimetric error of the reconstructed multispectral image, a weighting matrix is incorporated to Karhunen-Loeve transform (KLT) as the spectral transform for multispectral image compression, which accounts for the color matching functions of human observers as well as the viewing illuminants. However, the colorimetric improvements are obtained on the cost of degradation of spectral accuracy. In this paper, we show that the reduction of colorimetric error and the preservation of spectral accuracy is a tradeoff that can be controlled by adding a diagonal matrix that is composed of a scalar multiple of an identity matrix to the weighting matrix of KLT. As the result, the small values in the weighting matrix can be lifted up, thus reduce the spectral errors in the corresponding reconstructed multispectral image bands. We implement a multispectral image compression system that integrates the proposed spectral transforms with the addition of diagonal matrix and JPEG2000 for high colorimetric and spectral reproducibility. Experimental results for three 16-band multispectral images show that spectral accuracy can be improved without loss of substantial color reproducibility if the magnitude of the scalar in the diagonal matrix is chosen appropriately