Many states and school districts are rethinking how they do educational assessment. A few are going further: attempting to build "balanced," "comprehensive," or "next-generation" assessment systems. At the same time, practitioners and researchers have long mulled the purposes and parts such systems should have. But just a few have thought deeply about what a system of assessment actually means. In the words of educational psychologist Theodore Coladarci: "A collection of assessments does not entail a system any more than a pile of bricks constitutes a house." This article focuses on building the house. For states that are building, evaluating, or modifying their assessment systems, the authors offer three criteria to look for: coherence, a theory of action, and efficiency. They developed these criteria after reviewing literature on educational assessment systems, and they have been applying them in work with state and district leaders.