Methods and systems for mapping images from a first dynamic range to a second dynamic on a target display with power limitations are described. Given: an input image in a first dynamic range, input metadata (Smin, Smid, Smax), power-independent luminance characteristics of a target display (Tmin, reference Tmax), and an APL function of the target display, wherein the APL function determines output luminance in the target display as a function of average picture level (APL) input in the target display, a processor generates an adaptive output of the maximum luminance level for the target display (Tmax) so that when mapping the image from the first dynamic range to the second dynamic range, the anchor points of the tone-mapping function are adjusted according to the APL function of the target display.