Electronic reverse auctions are the most used competitive method for procurement of goods and non-consulting services by the Federal Government of Brazil. These auctions are closed randomly, which perfectly satisfies fairness considerations but may be suboptimal from an efficiency perspective. There are concerns that tenders are closed too early and randomness favors bidders with algorithmic bidding software, leading to high prices. Hence, this paper investigates what would happen if the random closing rule was replaced by another rule. The paper uses the complete data set of completed electronic actions in 2015-17 comprising 112 million bids for 0.9 million items purchased. Exploiting the random closing rule, simple OLS models are run with a wide set of fixed effects as well as covariates capturing competition. The findings point at alternative strategies to optimize auction design: simple actions such as increasing the average and minimum length of the random phase can result in 2.8 and 0.6 percent price savings, respectively, or R40 million and R16 million per year
or more complex designs such as setting the length to the maximum for the random phase if there are 15 bidders or more can yield 2.6 percent or R500 million a year in price savings, or doing the same if a large discount is placed within three minutes to closing can yield 1.1 percent lower prices or R210 million a year in savings.