Order expediting is an inventory control practice that allows companies to reduce inventory while maintaining service levels. However, expediting outstanding orders is costly and a trade-off must be made between expediting orders and holding inventory. We model the problem as a periodic-review inventory system with the option to move outstanding units forward in the replenishment pipeline. The objective is to minimize the sum of expected inventory holding and expediting costs per period subject to a minimum expected service level constraint. We consider a generalized base-stock policy where outstanding units are expedited when the inventory level drops below a certain threshold. We develop structural properties and present an efficient procedure to determine the optimal policy parameters. In a numerical study with real-world data, we show that our expediting policy offers substantial savings compared to other policies. We also provide managerial insights by numerically analyzing how the model parameters impact the savings.