The sheer number of attempts to define and classify uncertainty reveals an awareness of its importance in environmental science for policy, though the nature of uncertainty is often misunderstood. The interdisciplinary field of uncertainty analysis is unstable; there are currently several incomplete notions of uncertainty leading to different and incompatible uncertainty classifications. One of the most salient shortcomings of present-day practice is that most of these classifications focus on quantifying uncertainty while ignoring the qualitative aspects that tend to be decisive in the interface between science and policy. Consequently, the current practices of uncertainty analysis contribute to increasing the perceived precision of scientific knowledge, but do not adequately address its lack of sociopolitical relevance. The "positivistic" uncertainty analysis models (like those that dominate the fields of climate change modelling and nuclear or chemical risk assessment) have little social relevance, as they do not influence negotiations between stakeholders. From the perspective of the science-policy interface, the current practices of uncertainty analysis are incomplete and incorrectly focused. We argue that although scientific knowledge produced and used in a context of political decision-making embodies traditional scientific characteristics, it also holds additional properties linked to its influence on social, political, and economic relations. Therefore, the significance of uncertainty cannot be assessed based on quality criteria that refer to the scientific content only; uncertainty must also include quality criteria specific to the properties and roles of this scientific knowledge within political, social, and economic contexts and processes. We propose a conceptual framework designed to account for such substantive, contextual, and procedural criteria of knowledge quality. At the same time, the proposed framework includes and synthesizes the various classes of uncertainty highlighted in the literature.