The research objective is to analyze the interaction of the CNJ with the state courts in order to improve the efficiency levels of the State Justice from 2004 to 2013 from the perspective of ex-councilors. The main questions to be answered were: How have the efforts and actions taken by the State Courts fit the CNJ’s requirements aimed at improving the efficiency of the jurisdictional provision? To what extent has there been a convergence of efforts and results achieved between the CNJ and the State Courts to improve efficiency? Twenty ex-councilors were interviewed, adopting thematic or categorical analysis as the main form of content analysis technique. The categories established for analysis were related to the predominance of divergence (distrust and resistance), the predominance of convergence (acceptance and integration) and the alternation of scenarios (relativism and context of autonomy). In general, respondents pointed to the existence of a convergence of efforts between the CNJ and the State Courts that was being strengthened as the ignorance and distrust about the CNJ gradually dissipated. It was noticed that the relationship of convergence and divergence presents alternations, because the understanding varies according to the perception of loss of autonomy by the courts.