Recent evidence that young children seem to both understand false belief in one sense, but not in another, has led to two-systems theorizing about mindreading. By analyzing the most detailed two-systems approach in studying social cognition—the theory of mindreading defended by Ian Apperly and Stephen Butterfill—I argue that that even when dutifully constructed, two-systems approaches in social cognition struggle to adequately define the mindreading systems in terms of signature processing limits, an issue that becomes most apparent when investigating mindreading in (...) infancy. I end the article by developing several challenges that face any two-systems account of mindreading. (shrink)