Despite the increasing number of countries that have implemented deliberative processes during constitutional changes, the discussion about the criteria for these processes to be deemed fair and democratic remains open. Thus, first, this paper proposes some conditions related to the features of the mechanism of deliberative participation and the method of processing the resulting contents. Second, it is carried out an empirical analysis focused on deliberative processes of constitutional change that were regulated and/or promoted by governments or public institutions (excluding pure private and/or civil society initiatives) and were opened to citizenship (excluding the ones oriented only to experts or political parties); and were addressed to content production (merely informative or educative were excluded). Our analysis identifies five models of deliberative processes: "symbolic", "prejudiced", "participatory overflow", "constituent opening" and "constituent participation". The conclusions go beyond the sui generis commitment to implement participatory mechanisms and suggest minimal criteria that deliberative processes should fulfill to be considered democratic.