In this talk, I shall examine the natural laws' special (and yet notoriously obscure) relation to counterfactuals. I shall propose a non-circular means of distinguishing the natural laws (and their logical consequences) from the accidental truths. A product of this analysis is an account of the sense in which the laws and their logical consequences (but no accidents) possess a kind of "necessity". An analogous account applies to the logical necessities as well. I shall also examine in some detail how this account might apply to laws of a "special science." Were there such laws, they would possess a distinctive kind of necessity, and therefore figure in explanations that are irreducible to explanations in terms of the fundamental laws of physics.