We describe preliminary investigations of using Docker for the deployment and testing of astronomy software. Docker is a relatively new containerisation technology that is developing rapidly and being adopted across a range of domains. It is based upon virtualization at operating system level, which presents many advantages in comparison to the more traditional hardware virtualization that underpins most cloud computing infrastructure today. A particular strength of Docker is its simple format for describing and managing software containers, which has benefits for software developers, system administrators and end users. We report on our experiences from two projects -- a simple activity to demonstrate how Docker works, and a more elaborate set of services that demonstrates more of its capabilities and what they can achieve within an astronomical context -- and include an account of how we solved problems through interaction with Docker's very active open source development community, which is currently the key to the most effective use of this rapidly-changing technology.