Despite increased investments in procurement of essential medicines, their availability at health facilities remains extremely low in many low- and middle-income countries. The lack of a well-functioning supply chain for essential medicines is often the cause of this poor availability. Using a randomized trial conducted in 439 health facilities and 24 districts in Zambia, this study helps understand the optimal supply chain structure for essential medicines distribution in the public sector in low-income countries. It shows that a more direct distribution system where clinics order and receive medicines supply directly from the central agency through a cross-docking arrangement significantly reduces the duration and frequency of stockouts compared to a traditional three-level drug distribution system. As an example, the frequency of stockouts for first line pediatric malaria medicines reduced from 47.9% to 13.3% and the number of days of stockout in a quarter reduced from 27 days to 5 days. The direct flow of demand and order information from health facilities to the central supply agency reduces the problem of diffuse accountability that exists in multi-tiered distribution systems. It also shifts the locus of decision making for complex supply chain functions such as scarce stock allocation and adjustment of health facility order quantities to levels in the system where staff competency is aligned with what the function needs. Even when supply chain system redesign such as the one evaluated in this paper are demonstrated to be technically robust using rigorous evidence, they often require navigating a complex political economy within the overall health system and its actors.