To recover all the pure components from a homogeneous azeotropic mixture using distillation, one or more recycles are needed. These recycles may have compositions close to those of singular points (i.e., pure components and azeotropes) or may have compositions of mixtures of singular points. The selection of the recycle structure and of the recycle flow rates for a given distillation sequence is a design challenge, as recycles impact on both the feasibility and performance (e.g., the number of stages and the reflux requirement) of separations. This work analyzes recycles with singular point compositions in terms of their effects on the feasibility and performance of splits. On the basis of this analysis, a set of rules and a systematic procedure are developed for selecting recycles with singular point compositions and for identifying promising recycles comprising a mixture of singular points. These rules and procedures allow the recycle structure to be proposed efficiently for a distillation sequence separating a multicomponent homogeneous azeotropic mixture into pure component products.