Microservice APIs represent the client perspective on microservice-based software architecture design and related practices. Major issues in API design concern the quality aspects of the API. However, it is not well understood today what the established practices related to those quality aspects are, how these practices are related, and what the major decision drivers are. This leads to great uncertainty in the design process. In this paper, we report on a qualitative, in-depth study of 31 widely used APIs plus 24 API specifications, standards, and technologies. In our study we identified six recurring architectural design decisions in two API design contexts with a total of 40 decision options and a total of 47 decision drivers. We modelled our findings in a formal, reusable architectural decision model. We measured the uncertainty in the resulting design space with and without use of our model, and found that a substantial uncertainty reduction can be potentially achieved by applying our model.