This paper examines the essential features of a group of constructions that belong to the family of complementary alternation discourse constructions in English. In this group of constructions, X and Y are two situations such that Y is less likely (or more likely) to happen than X. Each member of this group (X Let Alone Y, X Much Less Y, X Never Mind Y, X Not To Mention Y, Not X Nor Y, X Still Less Y, Not X Not Even Y, and X To Say Nothing of Y) introduces subtle changes in focal structure, resulting in changes on the overall coherence of the text. Based on these theoretical explanations, the paper specifies the conditions for the use of one connector with preference over the others. Finally, the paper argues that in these constructions we find two types of cognitive operations at work: simple cognitive operations (negative addition and/or re-association) and operation amalgams, which combine different cognitive operations.