A new strategy in philosophy of law appeals to explanatory gap arguments to attack legal positivism. We argue that the strategy faces a dilemma, which derives from there being two available readings of the constraint it places on legal grounding. To this end, we elaborate the most promising ways of spelling out the epistemic constraints governing law-determination, and show that each of the arguments based on them has problems. Throughout the paper, we evaluate a number of explanatory requirements, ultimately with (...) a view to shedding light on the explanatory nature of both grounding in general, and legal grounding in particular. (shrink)