To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier’s production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre-established price, we examine whether the supplier should offer advance-order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance-order discount contract is Pareto-improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre-specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance-order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first-best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto-improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one-supplier-one-manufacturer case continue to hold when we have two manufacturers.