In this paper, I develop a serious new dilemma involving necessary truths for safety-based theories of knowledge, a dilemma that I argue safety theorists cannot resolve or avoid by relativizing safety to either the subject’s basis or method of belief formation in close worlds or to a set of related or sufficiently similar propositions. I develop this dilemma primarily in conversation with Duncan Pritchard’s well-known, oft-modeled safety-based theories of knowledge. I show that Pritchard’s well-regarded anti-luck virtue theory of knowledge and (...) his recently proposed (allegedly superior) anti-risk virtue theory of knowledge clearly succumb to the dilemma, and so they are inadequate as they stand. If Pritchard’s safety-based theories of knowledge are shown to be inadequate by the dilemma that is developed in this paper, then a number of other safety-based theories of knowledge (e.g., Beddor and Pavese’s, Luper’s, Dutant’s, early Pritchard’s, and others) look to be in jeopardy in this connection as well. (shrink)