Qualitative Comparative Analysis (QCA) has often been considered as a great step towards an appropriate methodological design for social inquiry. Consisting in a permanent dialogue between a thick case knowledge and a systematic comparison of these cases, QCA is somehow a mixed-method in itself. However, the main added-value of QCA is certainly residing in its ability to deal with set-theoretic reasoning that is closer form the verbal language of social sciences than traditional correlation-based reasoning. The core idea of set-theoretic methods is to assess causation in terms of sufficiency and necessity. However, most of the published contributions making use of QCA , often fail to properly take advantage of the formal properties of these two concepts. In its first part, this papers clarifies the concepts of sufficiency and necessity with the help of the set-theoretical logic and demonstrates the sub- superset relations that exists between them. Secondly, it proposes to improve the technical procedure of QCA in implementing these theoretical properties and develops a new procedure called "maxi-miminization". This procedure permits to diminish the risk of taking wrong assumptions on counterfactuals, in guiding further the software throughout the data processing. Replicating published analyses, this papers shows concrete examples of the maxi-minimization procedure, and points the difference with the classic QCA minimization.
