[TriLUG] Shrinking docker images

[J. S. Evans via TriLUG]

Is there an application that can delete non-essential parts of a docker 
image?  For example, I wrote a docker image to run a windows app with 
mono using the stock Ubuntu base image. The image works and the 
container that I create with it runs the app, but after the image was 
built, it was > 300MB. I would like to know if there is an easy way to 
determine what parts of the filesystem would be safe to delete.

My guess would be to run ps while it is running and delete anything 
that's not needed such apt/dpkg or anything in /var, /usr/local, etc.  
Does anyone know of an application that I could run that would do this 
for me without the headache?

Jason