According to Humeanism à la Lewis (1973, 1986b), the laws of nature are (roughly) the simplest and strongest codifications of the 'Humean mosaic', which consists entirely of local matters of particular fact. Although Humeanism is extremely popular and mainstream in modern analytic metaphysics, it faces many questions, inter alia: (1) How to adapt the programme so as to render it compatible with modern physics?; (2) How to make more precise the notions of simplicity and strength tied up in the programme?; (3) Under what conditions will the mosaic be sufficiently heterogeneous for there to be a unique simplest and strongest codification thereof? In this article, we take up and answer these questions by availing ourselves of some technical resources recently introduced to philosophers by Weatherall and March (forthcoming). In so doing, we hope to significantly advance and raise the level of precision of philosophical discussions of the metaphysics of laws of nature. ( direct link )