We investigate optimal production controls for a tandem two-machine system with an internal buffer and unreliable machines. First, numerical methods are used to generate optimal policies for specific examples. Then, based on diese numerical results, an approximate suboptimal control policy is developed that divides the state space into distinct regions and uses only simple hedging-point policies in each region. Algorithms to obtain hedging points are provided. Comparing the approximation to the optimal control for several examples suggests that its decision regions are close to the optimal decision regions for the important case where demand is close to system capacity. In addition, simulation results show that the costs of the two policies are also very close. The results suggest that appropriately constructed hedging-point policies are close to optimal. Extensions to more complicated systems are also discussed.