This paper develops a theoretical framework to assess the feasibility of global environmental sustainability solutions based on one or more value changes. The framework represents four sustainability paradigms (weak sustainability WS, a-growth AG, de-growth DG, strong sustainability SS) and five value changes (i.e., a sense of responsibility for nature Beta, future generations Gamma, or current generations in developing countries Delta; aversion to inequality for current generations Epsilon or future generations Zeta). It defines solutions in terms of consumption, environment use, and welfare for representative individuals in both developed (OECD) and developing (non-OECD) countries. Solutions are characterised by efficiency (i.e., Pareto and Kaldor-Hicks) with respect to welfare and by intra- and inter-generational equality for consumption, environment use, and welfare, by confirming internal consistency and consistency with alternative equity approaches for utilitarianism (i.e., Harsanyi), egalitarianism (i.e., Arneson for welfare; Dworkin for consumption or environment use; Sen for consumption and environment use), and contractarianism (i.e., Rawls). Theoretical and operational insights are described for alternative sustainability paradigms and equity approaches. In terms of feasibility, by considering improved technology Theta, decreased population Eta, and modified consumption Alpha, the ordering is Gamma > Delta > Epsilon > Zeta and AG > SS > DG > WS: Beta is unfeasible. In terms of internal consistency, Gamma > Delta = Epsilon = Zeta and SS > AG > DG: WS is internally inconsistent. In terms of consistency with an equity approach, Gamma > Delta = Zeta > Epsilon and SS > AG > DG > WS.