Most research suggests that negotiators gain value by making first offers in negotiations. The current research examines the proposition that extreme first offers offend their recipients and cause them to walk away, resulting in an impasse. Results across two experiments support this proposition. As a result, extreme offers can be risky: even though they can anchor counteroffers and final outcomes, bringing benefit to the offerer, they only do so when impasses are avoided. In addition, we find support for the proposition that power moderates the relationship between extreme offers and impasses: although low- and high-power negotiators are equally offended by extreme offers, it is the low-power negotiators who walk away from the negotiation.