Methods for the chroma reshaping of high-dynamic range (HDR) signals are presented. For each input pixel, a first scaler is generated based on the pixel luminance and a luma-based chroma reshaping (LCR) function. A second scaler is generated based on a saturation-based chroma reshaping (SCR) function and the saturation value of the pixel. A cascaded scaler is generated by multiplying the first scaler with the second scaler. Reshaped chroma values are generated by multiplying the input chroma values with the cascaded scaler. The characteristics of preferred LCR and SCR functions are discussed. Inverse decoding methods based on chroma-reshaping metadata that define the LCR and SCR functions are also described.