I've had great success with reducing image size by running docker-show-context (https://github.com/pwaller/docker-show-context) and eliminating big and unnecessary files that it reports. This seems to go just a bit further than that with what seems like more complexity. I got timeouts when following their instructions to run it on two different containers, one of which is just a very simple web server.
This is interesting for optimizing build time. But I think it works a bit different from docker-slim, which is focused on the final resulting image size.
If you want a quick double check to verify a handful of common cleanups, check out https://github.com/viraptor/cruftspy, which reports cruft like logs, caches, and git repos.