Philosophical understanding of the problem of skepticism and its sources has grown in recent years, but important questions remain about the contribution of underdetermination and closure principles to skeptical arguments. My aim here is to improve upon this situation. Sections 1, 2 compare a closure principle I call Weakening to a principle I call Underdetermination. It appears that the former doesn’t follow from, and is less plausible than, the latter. Section 3 examines Dretske’s Zebra Case as a putative counterexample to Weakening. The New Zebra Case, a variant of the original, indicates that Weakening is preserved after all. Sections 4, 5 establish that Weakening and Underdetermination converge in a canonical skeptical argument, the Misleading Evidence Argument. Such convergence is significant, because it is widely thought that abandoning Weakening allows us to escape skepticism. Section 6 takes up Martin Smith’s claim that underdetermination principles don’t underwrite a skeptical argument of any interest. I argue that this assessment is mistaken.