Innovations in rendering of high dynamic range (“HDR”) content are described. A playback system can adjust a tone mapping function used when rendering the HDR content, thereby improving quality when rendering the HDR content. For example, the playback system includes decision logic, which is configured to receive summary information (e.g., histogram information) for sample values of a picture of HDR content, and set a tone mapping function based at least in part on the summary information. The tone mapping function can be selected from among multiple available tone mapping functions, and parameters of the selected tone mapping function can be determined based at least in part on the summary information. A tone mapper is configured to apply tone mapping to input values for the sample values of the picture of HDR content, according to the tone mapping function, and thereby produce output values.