Methods and systems for reducing banding artifacts when displaying high-dynamic-range images are described. Given an input image in a first dynamic range, and an input backward reshaping function mapping codewords from the first dynamic range to a second dynamic range, wherein the second dynamic range is equal or higher than the first dynamic range, statistical data based on the input image and the input backward reshaping function are generated to estimate the risk of banding artifacts in a target image in the second dynamic range generated by applying the input backward reshaping function to the input image. Separate banding alleviation algorithms are applied in the darks and highlights parts of the first dynamic range to generate a modified backward reshaping function, which when applied to the input image to generate the target image eliminates or reduces banding in the target image.