We study an inventory system under periodic review in the presence of two suppliers (or delivery modes). The emergency supplier has a shorter lead-time than the regular supplier, but the unit price he offers is higher. Excess demand is backlogged. We show that the classical “Lost Sales inventory problem” is a special case of this problem. Then, we generalize the recently studied class of Dual Index policies (Veeraraghavan and Scheller-Wolf (2007)) by proposing two classes of policies. The first class consists of policies that have an orderup-to structure for the emergency supplier. We provide analytical results that are useful for determining optimal or near-optimal policies within this class. This analysis and the policies that we propose leverage the connections we make between our problem and the lost sales problem. The second class consists of policies that have an order-up-to structure for the combined orders of the two suppliers. Here, we derive bounds on the optimal order...