Efficiency and efficacy are two desirable properties of the utmost importance for any evaluation metric having to do with Standard Dynamic Range (SDR) imaging or High Dynamic Range (HDR) imaging. However, these properties are hard to achieve simultaneously. On the one side, metrics like HDR-VDP2.2 are known to mimic the human visual system (HVS) very accurately, but its high computational cost prevents its widespread use in large evaluation campaigns. On the other side, computationally cheaper alternatives like PSNR or MSE fail to capture many of the crucial aspects of the HVS. In this work, we try to get the best of the two worlds: we present NoR-VDPNet++, an improved variant of a previous deep learning-based metric for distilling HDR-VDP2.2 into a convolutional neural network (CNN). In this work, we try to get the best of the two worlds: we present NoR-VDPNet++, an improved version of a deep learning-based metric for distilling HDR-VDP2.2 into a convolutional neural network (CNN).