This web server is running a slightly customized version of a link shortener. I found an open source project that I rather enjoyed and set it up for my personal use.
That should allow me to enjoy short and simple links as well as basic analytics, without relying on any external services that might not respect the users' privacy that much.
That said, currently I do not allow others to use it for shortening their own links. I might do a blog post soon about how to do the setup for anyone who wants to self-host it.