Residue-curve and distillation-line maps are useful tools in the design of azeotropic distillation sequences. In this work we make use of residue-curve and distillation-line maps to develop a procedure for the design of single-feed columns at finite reflux. The procedure is noniterative with respect to the reflux and boil-up ratios, instead using an ＇operation lear formed by the total and minimum reflux conditions. The operation leafbounds the possible liquid composition profiles in a column section and is calculated from the product composition. The overlap of operation leaves is a necessary and sufficient condition for column feasibility. Special cases of operation leaves where the liquid composition profile strays outside the leaf are also presented. ＇Open leaves＇, where the product distillation lines or residue curves and the pinch-point curves end at different nodes are introduced. These open leaves can be used to facilitate the crossing of total reflux boundaries at finite reflux using side-column flow sheets. The use of side condensers and reboilers is shown to reduce the capital penalty in the crossing of total reflux boundaries. The concept of operation leaves can be applied to the retrofit or reuse of existing distillation columns by defining stage composition lines that bound the composition space within the leaf achievable with a given number of stages.