This chapter examines the important special case of fair distribution through a hierarchical network. A central authority allocates resources to regions, and each region distributes its allocation, combined with its own resources, to subregions (or subunits of some other kind). Somewhat paradoxically, a distribution problem need not be regionally decomposable. That is, the solution of a given region’s distribution problem may assign different allotments to its subregions than the centralized solution, even if it is based on the same social welfare function. The chapter shows, however, that a problem is regionally decomposable when the social welfare function satisfies a technical property (monotonic separability). About half of the social welfare functions studied in the book are monotonically separable.