To enable better encoding of the currently starting to appear high dynamic range images for use in full high dynamic range technical systems (containing an HDR display, and e.g. in an HDR grading application), we invented a method of constructing a code allocation function for allocating pixel colors having pixel luminances to codes encoding such pixel luminances, in which the step of determining the code allocation function to be applied to at least one color coordinate of the pixel to obtain a code value, comprises constructing that function out of at least two partial functions, and similar methods at a receiving side, and apparatuses, and signals for communicating between the two sites. This method allows—in line with applicant's technical approach that HDR images should actually be communicated as a spectrum of differently regraded different dynamic range images of the same scene, e.g. a master HDR image and another image of the same HDR scene encoded with a different dynamic range and peak brightness than the master HDR image, and one of these images should be communicated to receivers together with luminance mapping functions co-communicated in metadata allowing the calculation at the receiving side of the non-transmitted different dynamic range image—a better application of dynamically per scene optimizable luminance mapping functions.