This paper argues that mind-reading hypotheses (MRHs), of any kind, are not needed to best describe or best explain basic acts of social cognition. It considers the two most popular MRHs: one-ToM and two-ToM theories. These MRHs face competition in the form of complementary behaviour reading hypotheses (CBRHs). Following Buckner (Mind Lang 29:566–589, 2014), it is argued that the best strategy for putting CBRHs out of play is to appeal to theoretical considerations about the psychosemantics of basic acts of social cognition. In particular, need-based accounts that satisfy a teleological criterion have the ability to put CBRHs out of play. Yet, against this backdrop, a new competitor for MRHs is revealed: mind minding hypothesis (MMHs). MMHs are capable of explaining all the known facts about basic forms of social cognition and they also satisfy the teleological criterion. In conclusion, some objections concerning the theoretical tenability of MMHs are addressed and prospects for further research are canvassed.