This paper considers (S -1, S) inventory models which have wide applications in reparable spare parts inventory systems and multi-echelon systems. We assume a discrete compounds Poisson demand and order size dependent delivery times ; when the replenishment order size is n, we assume the delivery time distribution is arbitrary with finite mean $b_{n}$ . On the basis of the fact the outstanding orders follow a certain queueing process, we introduce the results of Fakinos (1982). We develop the efficient recursive formulae to find the optimal $S^{*}$ under several performance measures as a function of the decision variable S. The results of this paper can be applied to the multi-echelon systems such as MEETRIC.C.