The principle of Counter-Closure embodies the widespread view that when a proposition is believed solely as the conclusion of single-premise deduction, it can be known only if the premise is also known. I raise a problem for the compatibility of Jason Stanley's Interest-Relative Invariantism (IRI) with Counter-Closure. I explore the landscape of options that might help Stanley resolve this tension and argue that a trilemma confronts Stanley: he must either (i) renounce a key intuition that lies at the foundation of (...) his view; or (ii) admit into his epistemology an IRI-specific novel brand of Gettier case; or (iii) abandon Counter-Closure. (shrink)