In this paper, we consider a production-clearing system with compound Poisson demand under continuous review. The production facility produces one type of item without stopping and at a constant rate, and stores the product into a buffer to meet future demand. To prevent high inventory levels, a clearing operation occasionally removes all or part of the inventory from the buffer. We prove that an (m, q)-policy, i.e., a policy that clears the buffer to level m as soon as the inventory hits a level q, minimizes the long run average holding and clearing cost. We also derive a numerically very efficient approach to compute the optimal parameters of the (m, q)-policy for models with backlogging and models with lost sales. With these numerical methods we show that tuning the clearing levels m and q in concert can lead to substantial cost savings.