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Neo-Russellians and neo-Fregeans both claim that some of our thoughts are irreducibly singular, because they are acquaintance-based. This relation of acquaintance imposes a condition of recognitional transparency on the objects of thought: it precludes cases in which two objects of acquaintance, A and B, are the same and yet we fail to know that A is B. To avoid this unwelcome consequence, we can either reject the presentational conception of acquaintance and replace it with a causal conception, as some neo-Russellians do, or we can keep the original notion and make it consistent with the cognitive constraints imposed by Frege’s and Campbell’s puzzles. I argue that this last option is not easily carried out, as the acquaintance constraint affects the modes of presentation themselves and forces them to fulfill two incompatible functions: the function of presenting an object, and the function of singling it out from among other objects.