We consider the problem of equalizing the quantization noise between two video encoders operating with video stored using different transfer function. Here, a transfer function is the mapping between linear light and the quantized code words and includes, for example, the well-known “gamma curve” used for most video applications. Our motivation for studying this problem is that the solution enables the direct conversation of a quantization strategy developed for a legacy, standard dynamic range transfer function to be easily mapped to a quantization strategy for a new, high dynamic range transfer function. This is especially timely given the beginning deployment of high dynamic range services throughout the world that use the BT-2020/SMPTE ST 2084 transfer function and not the BT.709/BT.1886 transfer function historically employed for coding high definition digital video. The paper derives a model for the needed relationship. Results show the benefit of the approach.