Due to their tight isolation, low overhead, and efficient packaging of the execution environment, Docker containers have become a prominent solution for deploying modern applications. Containers are created from images which are stored in a Docker registry. An image consists of a list of layers which can be shared among images. Docker registries store a large amount of images and with the increasing popularity of Docker, they continue to grow. For example, Docker Hub-a popular public registry-stores more than half a million public images. In this paper, we analyze over 167TB of uncompressed Docker images and evaluate the potential of file-level deduplication in the registry. Our analysis reveals that only 3% of the files in images are unique and Docker's existing layer sharing mechanism is not sufficient to eliminate this profound redundancy. We then present the design of Slimmer-a Docker registry with file deduplication support-and conduct a simulation-based analysis of its performance implications.