Advocates and opponents of Humean Supervenience (HS) have neglected a crucial feature of nomic explanation: laws can explain by generating descriptions of possibilities. Dretske and Armstrong have opposed HS by arguing that laws construed as Humean regularities cannot explain, but their arguments fail precisely because they neglect to consider this generating role of laws. Humeans have dismissed the intuitive violations of HS manifested by John Carroll's Mirror Worlds as erroneous, but distinguishing the laws' generating role from the non-Humean notion that laws govern undermines such responses, and renews the force of Carroll's critique of HS. However, it also undermines the assumption that HS is constitutive of Humeanism. The generating role of laws readily motivates a non-reductive Humeanism that violates HS. An account is sketched, and is seen to provide a novel explanation of the governing intuition.