We investigate procurement in a setting in which the buyer is bound by sourcing rules. Sourcing rules may limit the minimum and maximum amounts of business that can be awarded to a single supplier or dictate the minimum number of suppliers who are awarded business, thus necessitating split awards. The buyer announces the splits before the auction, and suppliers bid accordingly. We consider two auction formats: the sealed-bid first-price auction, and a version of the open-bid descending-price auction.We characterize the suppliers' symmetric equilibrium bidding strategy for both formats and find that the two formats yield the same expected buyer's cost.We characterize the cost of multisourcing, showing among other things that it is always costly for the buyer to split its award among more suppliers if the suppliers' costs are regularly distributed, but that doing so can actually reduce the buyer's expected auction payment if the suppliers' costs are not regularly distributed. The results from controlled laboratory experiments, involving human subjects, indicate that expected cost equivalence fails when costs are regularly distributed because suppliers bid more aggressively in the sealed-bid auction. However, for split-award auctions with nonregularly distributed costs, the sealed-bid prices are actually higher than predicted by theory. We explain these mismatches between observations and theory through a behavioral model based on bidders' aversion to anticipated regret. The experimental results indicate that the theory does a good job of predicting the relationship between the buyer's average cost and the award splits, as well as the cost of multisourcing. Importantly, the experiments confirm that when suppliers' costs come from a nonregular distribution, it may be to the buyer's advantage to diversify the supply base more than is strictly necessitated by sourcing rules.