One or more continuous mappings are defined at a digital media encoder to convert input digital media data in a first high dynamic range format to a second format with a smaller dynamic range than the first format. The encoder converts the input digital media data to the second format with the smaller dynamic range using the continuous mapping and one or more conversion parameters relating to the continuous mapping. The encoder encodes the converted digital media data in a bitstream along with the conversion parameter(s). The conversion parameter(s) enable a digital media decoder to convert the converted digital media data back to the first high dynamic range format from the second format with the smaller dynamic range. Techniques for converting different input formats with different dynamic ranges are described.