Image frames obtained in darkness are special. Just multiplying by a constant doesn't restore the image. Shot noise, quantization effects and camera non-linearities mean that colors and relative light levels are estimated poorly. Current methods learn a mapping using real dark-bright image pairs. These are very hard to capture. A recent paper has shown that simulated data pairs produce real improvements in restoration, likely because huge volumes of simulated data are easy to obtain. In this paper, we show that respecting equivariance -- the color of a restored pixel should be the same, however the image is cropped -- produces real improvements over the state of the art for restoration. We show that a scale selection mechanism can be used to improve reconstructions. Finally, we show that our approach produces improvements on video restoration as well. Our methods are evaluated both quantitatively and qualitatively.