Someone got a Linux image that could run `ls` down to 6.12MB by intercepting file accesses and deleting anything unused... See "How I shrunk a Docker image by 98.8%" (https://news.ycombinator.com/item?id=9438323)
It's an overly simple method but a good start. Will work if the dependencies are static and load at runtime. I don't know enough about the tool to say if it works for more dynamic applications.