We recently proposed a color constancy method based on the observations that the human visual system might be "discounting the illuminant" by using space-average color and the highest luminance patches. Based on these observations, our algorithm relies on two assumptions: (i) there are several bright pixels in the scene, and (ii) the world is gray, on average. The main idea of the algorithm is to estimate the illuminant by finding the deviation of the brightest pixels from the gray value. During experiments, we observed that some pixels decrease the performance of the method. In this work, the algorithm is modified to eliminate the impact of these pixels. According to the comprehensive experiments, the proposed method surpasses several existing approaches on two color constancy benchmarks. Also, we show that the performance of some existing color constancy algorithms can be increased by using a block-based approach and salient pixels.