Some authors who oppose the currently dominant constitutional practice have defended some “minimum” constitutional entrenchment as a weak form of constitutionalism that allows democratic majorities to override judicial determination of fundamental rights. This paper offers some critical reflections on this proposal, adopting an approach based on (what I try to identify as) the intrinsic rationality of contemporary constitutional practice in liberal democracies. The critical argument evolves as follows. First, the formal (or institutional-based) distinction between “strong” and “weak” systems of constitutional review is discussed. Secondly, the alleged relevance of constitutional amendments in the historical realization of fundamental rights is objected to. Finally, the minimum constitutional rigidity is rejected as part of a genuinely alternative constitutional model (here referred to as “strong popular sovereignty”) designed to replace the dominant constitutional practice.