Three issues complicate teaching computer ethics in an undergraduate course. The first relates to the often technically intensive knowledge required to fully understand the complexity of real world examples. The second relates to the pedagogic expectations of students who see ethical and professional issues as of little importance to their eventual degrees. The third revolves around the fact that the official accreditation that is required of many professions is not mandatory for computing professionals, and so professional codes of conduct are optional. In this reflective discussion, we discuss these issues and the approach we have taken to resolve them. Our philosophy for teaching computer ethics revolves around the use of social psychology to illuminate the importance of the topic, and case-studies to simultaneously lower the burden of technical expertise while also incorporating hooks for the discussion of real world incidents. We discuss several psychological studies which inform our discussions, and the way in which they are delivered to overcome initial student objections to the material. We then discuss both the Case of the Killer Robot and the Scandal in Academia as case studies appropriate for inclusion in most undergraduate and postgraduate courses on ethics and professional issues.