Despite the increasing number of countries that have implemented deliberative processes during constitutional changes, the discussion remains open about the criteria for these processes to be deemed fair and democratic. Thus, this article first proposes some conditions related to the features of the mechanism of deliberative participation and the method of processing the resulting contents. Next an empirical analysis is carried out, focused on deliberative processes of constitutional change that were regulated and/or promoted by governments or public institutions; were opened to citizenship, excluding the ones oriented only to experts or political parties; and promoted the generation of contents compared to the merely informative or educative ones. Between 1970 and 2018, 29 processes were identified in 27 countries. The analysis identified five models of deliberative processes: symbolic, controlled, participatory overflow, constituent opening and constituent participation. The conclusions invite to go beyond the sui generis commitment to implement participatory mechanisms and replace it with the definition of minimal criteria the deliberative processes should fulfil to be considered democratic.