A well-known problem in machine learning is “fairness impossibility”: that is, the mathematically demonstrable result that several intuitively compelling standards of fairness cannot be simultaneously realized, except in a narrow and rare set of cases. Many researchers have proposed responses to fairness impossibility, but there is still no consensus on how to handle the problem. In this paper I briefly review the problem and catalog previous efforts to respond, noting their strengths and weaknesses. I then propose an approach that situates concerns about fairness within a more general theory of ethical decision-making (an “integrative ethical framework”) and recommends responses based on ethically relevant features of the decision context. Several distinctions in this framework are especially important for guiding responses to fairness impossibility in particular situations, including rights vs. goods and substantive vs. procedural ethical considerations. Implications for the fairness impossibility debate include identification of cases where specific responses such as softening fairness requirements, subjecting fairness trade-offs to public opinion, or favoring one fairness metric over others, are preferable over alternatives.