Optimal separation sequencing or network synthesis (SNS) has been carried out either by a heuristic or mathematical programming method. The former gives rise only to those networks that can be deduced from its heuristic rules, and the latter, only to those networks whose structures are the substructures of the super-structure. If the set of heuristic rules or super-structure is incomplete, a substantial fraction of structures that can be optimal may very likely be excluded from consideration. Our study of various SNS problems involving sharp separators, dividers, and mixers encompasses a wide variety of problems yielding pure or multicomponent product streams from single or multiple feed streams. The counter examples generated indicate that basic structural components, such as recycling or redundancy in separators, may not necessarily render the separation network structures non-optimal. The available methods, however, tend to exclude these basic structural components a priori. The present work parametrically examines hypothetical and real SNS problems to determine under which circumstances recycling or redundancy may be involved in optimal separation structures, and under what situations bypasses should not be maximized in such structures. These results are useful in improving the available synthesis techniques.