Compressed videos constitute 70% of Internet traffic, and video upload growth rates far outpace compute and storage improvement trends. Past work in leveraging perceptual cues like saliency, i.e., regions where viewers focus their perceptual attention, reduces compressed video size while maintaining perceptual quality, but requires significant changes to video codecs and ignores the data management of this perceptual information. In this paper, we propose Vignette, a compression technique and storage manager for perception-based video compression. Vignette complements off-the-shelf compression software and hardware codec implementations. Vignette's compression technique uses a neural network to predict saliency information used during transcoding, and its storage manager integrates perceptual information into the video storage system to support a perceptual compression feedback loop. Vignette's saliency-based optimizations reduce storage by up to 95% with minimal quality loss, and Vignette videos lead to power savings of 50% on mobile phones during video playback. Our results demonstrate the benefit of embedding information about the human visual system into the architecture of video storage systems.