Two-layer schemes provide an effective method of encoding high dynamic range images, while maintaining backward compatibility with the legacy JPEG encoding format. The first layer is the tone-mapped low dynamic range version of the original image, whereas the residual information that cannot be preserved in the first layer is stored in the second layer. Additionally, an inverse tone-mapping function can be used which can reduce the information content in the second layer if designed and used carefully. In this research, we investigate the effect of using the inverse functions on the coding efficiency. We show that just by using a smooth function and hence ensuring that extra energy is not induced in the residual data as the result of inverse tone mapping, significant improvement can be expected in the coding efficiency, i.e., more information can be stored at the same bitrates.