Privacy, like security, is a non-functional property, yet most software design tools are focused on functional aspects, using for instance Data Flow Diagrams (DFDs). In previous work, a conceptual model was introduced where DFDs were extended into so-called Privacy-Aware Data Flow Diagrams (PA-DFDs) with the aim of adding specific privacy checks to existing DFDs. An implementation to add such automatic checks has also been developed. In this paper, we define the notion of refinement for both DFDs and PA-DFDs as a special type of structure-preserving map (or graph homomorphism). We also provide three algorithms to find, check and transform refinements, and we show that the standard diagram “transform→refine/refine→transform” commutes. We have implemented our algorithms in a proof-of-concept tool called DFD Refinery, and have applied it to realistic scenarios.