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.