Do grounding claims entail corresponding supervenience claims? The question matters, as a positive answer would help grounding theorists address worries that their hyperintensional primitive is obscure, and also increase the argumentative strategies that are available within ground-theoretic frameworks for metaphysical inquiry. Leuenberger (Erkenntnis 79:227–240, 2014a) argues for a negative response, by specifying some candidate principles of entailment and then claiming that each of them is subject to counterexamples. In this paper, I critically assess those principles and the objections he raises (...) against them, and advocate a novel entailment principle that overcomes all the problems suffered by those other principles. The principle I defend places a supervenience-based constraint on grounding claims, and secures a substantive connection between grounding and modality, weaker than necessitation. (shrink)