Addressing ethical issues arising from AI research, and by extension from most areas of Data Science, is a core challenge in both the academic and industry worlds. The nature of research and the specific set of technical skills involved imply that AI and Data Science researchers are not equipped to identify and anticipate such issues arising, or to establish solutions at the time a specific research project is being designed. In this paper, we discuss the need for a methodology for ethical research design that involves a broader set of skills from the start of the project. We specifically identify, from the relevant literature, a set of requirements that we argue to be needed for such a methodology. We then explore two case studies where such ethical considerations have been explored in conjunction with the development of specific research projects, in order to validate those assumptions and generalise them into a set of principles guiding an "Ethics by Design" method for conducting AI and Data Science research.