Abstract Mediano et al. (The strength of weak integrated information theory. Trends Cogn Sci 2022;26: 646–55.) separate out strong and weak flavours of the integrated information theory (IIT) of consciousness. They describe ‘strong IIT’ as attempting to derive a universal formula for consciousness and ‘weak IIT’ as searching for empirically measurable correlates of aspects of consciousness. We put forward that their overall notion of ‘weak IIT’ may be too weak. Rather, it should be separated out to distinguish ‘aspirational-IIT’, which aims to empirically test IIT by making trade-offs to its proposed measures, and ‘IIT-inspired’ approaches, which adopt high-level ideas of IIT while dropping the mathematical framework it reaches through its introspective, first-principles approach to consciousness.