Conversational agents such as Apple’s Siri or Amazon’s Alexa are becoming more and more prevalent. Almost every smart device comes equipped with such an agent. While on the one hand they can make menial everyday tasks a lot easier for people, there are also more sophisticated use cases in which conversational agents can be helpful. One of these use cases is tutoring in higher education. Several systems to support both formal and informal learning have been developed. There have been many studies about single characteristics of pedagogical conversational agents and how these influence learning outcomes. But what is still missing, is an overview and guideline for atomic design decisions that need to be taken into account when creating such a system. Based on a review of articles on pedagogical conversational agents, this paper provides an extension of existing classifications of characteristics as to include more fine-grained design aspects.