We study a model of a firm managing its inventory of a single product by sourcing supplies from two supply sources, a regular supplier who offers a lower unit cost and a longer lead time than a second, emergency, supplier. A practically implementable policy for such a firm is a tailored base-surge (TBS) policy [Allon G, Van Mieghem JA (2010) Global dual sourcing: Tailored base-surge allocation to near- and offshore production. Management Sci. 56(1):110-124] to manage its inventory. Under this policy, the firm procures a constant quantity from the regular supplier in every period and dynamically makes procurement decisions for the emergency supplier. Allon and Van Mieghem describe this practice as using the regular supplier to meet a base level of demand and the emergency supplier to manage demand surges, and they conjecture that this practice is most effective when the lead time difference between the two suppliers is large. We confirm these statements in two ways. First, we show the following analytical result: When demand is composed of a base demand random component plus a surge demand random component, which occurs with a certain small probability, the best TBS policy is close to optimal (over all policies) in a well-defined sense. Second, we also numerically investigate the cost effectiveness of the best TBS policy on a test bed of problem instances. The emphasis of this investigation is the study of the effect of the lead time difference between the two suppliers. Our study reveals that the cost difference between the best TBS policy and the optimal policy decreases dramatically as the lead time of the regular supplier increases. On our test bed, this cost difference decreases from an average (over the test bed) of 21% when the lead time from the regular supplier is two periods (the emergency supplier offers instant delivery) to 3.5% when that lead time is seven periods.