For a long time, the constraints on surface spectral reflectances are the range of 0 to 1, smooth and low frequency. Those constraints are tested to be too loose in practical use, typically for illuminant estimation with spectral recovery. The proposal of linear model and PCA decomposition made it possible to effectively reconstruct spectral reflectances with small numbers of parameters. Based on that, a new constraint on surface spectral reflectance is proposed to have better limitation and description of their characteristics. It is defined as a two-dimensional histogram of the coefficients for the spectral reflectances in the real world. The variables in the two dimensions are the ratios of the parameters from PCA, which describe the “saturation” property of reflectances. There are differences between the application of gamut and histogram in illuminant estimation. Histogram is preferred to gamut when the color space is composed of relative values. Based on that, the original color by correlation method is modified to have better performance especially on real images. The proposed constraint is applied to illuminant detection with spectral recovery. In the method, the recovered surface reflectances are examined by the constraint, and the scene illuminant is detected through possibility comparison. The proposed method is tested to have good efficiency compared with others, both on synthetic and real images.