Material flow control mechanisms determine: (i) whether an order should be released onto the shop floor; and (ii) whether a station should be authorized to produce. Well‐known approaches include Kanban, Drum‐Buffer‐Rope (DBR), Constant Work‐in‐Process (ConWIP), Paired‐cell Overlapping Loops of Cards with Authorization (POLCA), Workload Control (WLC), and Control of Balance by Card Based Navigation (COBACABANA). The literature typically treats these approaches as competing, meaning studies argue for the superiority of one over another. However, a closer look reveals that existing mechanisms either focus on order release (ConWIP, DBR, WLC, and COBACABANA) or on production authorization (Kanban and POLCA). This study therefore calls for a paradigm shift and argues that the different mechanisms may play complementary rather than competing roles. Using simulation, we assess the performance of COBACABANA and POLCA in a high‐variety make‐to‐order shop, a type of shop arguably in most need of material flow control given the importance of throughput times and delivery time adherence. Results demonstrate that COBACABANA outperforms POLCA, but the simultaneous adoption of both control mechanisms outperforms the use of either one in isolation. More specifically, adding POLCA production authorization to COBACABANA order release enables the superfluous direct load to be further reduced, resulting in shop floor throughput time reductions of between 15% and 26% while further reducing the percentage tardy and mean tardiness by up to 14%. Compared to no material flow control, the new combined mechanism realizes a reduction of almost 50% in the percentage tardy and more than 30% in mean tardiness.