Recent works on the governance of nuclear safety in France have highlighted the existence of a "technical dialogue" between experts, which would be a historic French specificity of the governance of nuclear safety, considered more dialogical and more "limited" than in other countries (in the United States for example). These technical exchanges would be limited to a small number of actors, forming a "small world of safety". Yet, the governance of nuclear safety tends nowadays to increasingly open up to civil society actors. From Chernobyl and its "cloud", to the health crises of the 1990s (infected blood scandal, mad cow disease ...), even in the aftermath of the Fukushima disaster, the organizations in charge of nuclear safety progressively moved away institutionally and evolve today in an environment where these organizations must "report" their activities to civil society, which is deeply supported by an increasing societal focus on accountability for High Risk Organizations. Our work aims to analyze a dialogue between institutional experts and representatives of civil society around the "Safety Option File" of the ANDRA CIGEO deep storage facility. CIGEO is the French project of deep disposal center for radioactive waste managed by ANDRA. It is designed to store the long-lived, high-level radioactive wastes produced by all current nuclear facilities, until their dismantling, and by the treatment of used fuels used in nuclear power plants. In this paper, we will try to analyze what are the modalities of dialogue with civil society on nuclear safety issues and its observed and potential effects on the functioning of the nuclear safety governance system. Through the notion of centering / overflowing, we propose to analyze three concrete cases of discussions around the DOS CIGEO, that overflow the framing of technical exchanges operated by the actors of the nuclear sphere (ASN, IRSN and ANDRA). We analyze the real and potential effects of these overflowing on the dynamics of discussions and on actors. We show how some specific subjects have gone beyond the traditional framework of the organizations in charge of the governance of nuclear safety and in particular how these organizations receive, try to master and / or take into consideration these overflowing. This type of study can lead organizations like IRSN to a form of reflexivity on their practices of openness to society and lead to improvements in their methods of exchanges and dialogues. This analysis is completed by a discussion with the IRSN/LSHS (laboratory Human and Social Sciences Laboratory) director on the experience feedback of this type of device.