Measuring inconsistency is recognized as an important issue for handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named dominance, rarely satisfied by syntactic measures. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.