The uniform-price auction is used in many regional electricity procurement auctions and its “collusive-seeming equilibria ” have been linked to potential exercise of market power. Such equilibria do not exist, however, if a small amount of cash is split among rationed bidders. To shed light on what drives this result, I also examine variations in which the auctioneer is able to increase and/or decrease quantity after receiving the bids. “Increasable demand ” also eliminates all collusive-seeming equilibria. These results suggest ways to modify the uniform-price auction in order to reduce the potential exercise of market power.