In this paper we examine optimal and near-optimal continuous review policies for a deterministic arborescent inventory system: Known and constant outside demand must be met without backlogging or lost sales at minimum average system cost per unit time. Costs are of two types: A fixed order cost at each stage and proportional holding costs on each stage's echelon inventory. We describe some characteristics of optimal policies and, under fairly mild conditions (e.g., zero initial inventory), prove that the optimal stationary policy is a "single-cycle" policy. We present an efficient branch-and-bound algorithm for determining optimal single-cycle policies for arborescent systems. We also examine the near-optimality of "system myopic" single-cycle policies.