Histogram equalisation (HE) is a simple and effective image enhancement technique. However, it suffers from excessive brightness change and provides degradation in the visual aspect of the image. To overcome the shortcomings in the HE, a novel histogram framework is proposed in this study. The image histogram is first segmented into two parts using the Otsu's thresholding method. Then, both of the upper and lower histograms are constrained to control the level of enhancement. These constraint parameters are computed through moth-flame optimisation algorithm. After constraining the histograms, mean shift correction is performed to ensure there is a minimum level of mean shifting from input to output image. Traditional HE is then applied with a modified histogram to obtain mapping function for lower and upper grey level individually. This enhanced image provides a balance between the level of enhancement and preservation of the important features of the image for high-level processing. The effectiveness of the proposed method is highlighted with a detailed comparison with other closely related schemes. Through the proposed routine, the enhanced images achieve a good trade-off between features enhancement, low contrast boosting, and brightness preservation in addition to the natural feel of the original image.