The focus of this article is distillation design feasibility. It is shown that existing methods for determining feasibility can give incorrect results or produce feasible designs that waste energy due to over-specification and mass balance errors. An iterative refinement procedure based on direct substitution is proposed within the distillation line method of Lucia et al. that automatically adjusts one product composition to determine feasibility. Direct substitution equations are presented in detail and 14 literature examples are used to illustrate the efficacy of iterative refinement. Numerical results show that iterative refinement can find feasible designs that other methods cannot find, often resulting in significant reductions in energy requirements, and that it is all product compositions, not just trace compositions that affect most shortcut methods for distillation design. Iterative refinement can also find minimum energy requirements and identify sets of specifications that give infeasible designs. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 2164-2173, 2011