This paper deals with production-inventory control models with a variable production rate. The demand process is a compound Poisson process. The production rate is controlled by the well-known (m, M)-policy. Simple and accurate approximations are given for operating characteristics of the system. It turns out that a sequential determination of M - m and m yields a rule that minimizes average costs subject to a service level constraint. Numerical results are given to show the accuracy of the approximations.