Histogram equalization is the simplest method of image enhancement. Mean brightness and contrast are important parameters of an image. Artifacts are generated if the original mean brightness of an image is not preserved. A high contrast provides good visual quality. Contrast can be increased by increasing entropy of the image. Entropy can be maximized by making the image histogram as flat as possible. In this paper, the trade-off between mean brightness and maximum entropy performed to achieve high contrast image with conserved mean brightness.