We analyze a regime change from beauty contests to first‐price sealed‐bid and scoring auctions, using Swedish data on public procurement of cleaning services. In beauty contests, the lowest bid often lost, leaving substantial money on the table. The procurement costs were similar before and after the regime change: (i) Entry strongly decreases the procurement cost but did not change. Entry would have decreased had the municipalities not adjusted the objects of auctions. (ii) Municipalities favored in‐house suppliers in the old regime, leading to more aggressive bidding by others. With favoritism reduced, these changes balanced each other out.