This paper analyzes an (s, S) Inventory system where arrivals of customers form a Poisson process. When inventory level reaches zero due to demands, further demands are sent to a pool which has capacity M(<∞). Service to the pooled customers will be provided after replenishment against the order placed on reaching that level s. Further they are served only if the inventory level is at least s + 1. The lead-time is exponentially distributed. The joint probability distribution of the number of customers in the pool and the Inventory level is obtained in both the transient and steady state cases. Some measures of the system performance in the steady state are derived and some numerical illustrations are provided.