Docker image per branch is inefficient

I have a web application that has recently been moved to using Docker. In the past I deployed every branch that is pushed to the BitBucket repository to IIS using web deploy. Each branch would be it's own application, so that testing is easy.

Now that I have moved to using Docker, is there an efficient way to continue deploying the application per branch? I know I can create an image for each branch and deploy those images, but I end up using up a decent amount of space.