We examined whether and why range offers (e.g., "I want $7,200 to $7,600 for my car") matter in negotiations. A selective-attention account predicts that motivated and skeptical offer-recipients focus overwhelmingly on the attractive endpoint (i.e., a buyer would hear, in effect, "I want $7,200"). In contrast, we propose a tandem anchoring account, arguing that offer-recipients are often influenced by both endpoints as they judge the offer-maker's reservation price (i.e., bottom line) as well as how polite they believe an extreme (nonaccommodating) counteroffer would be. In 5 studies, featuring scripted negotiation scenarios and live dyadic negotiations, we find that certain range offers yield improved settlement terms for offer-makers without relational costs, whereas others may yield relationship benefits without deal costs. We clarify the types of range offers that evoke these benefits and identify boundaries to their impact, including range width and extremity. In addition, our studies reveal evidence consistent with 2 proposed mechanisms, one involving an informational effect (both endpoints of range offers can be taken as signals of an offer-maker's reservation price) and another involving a politeness effect (range offers can make extreme counteroffers seem less polite). Our results have implications for models of negotiation behavior and outcomes and, more broadly, for the nature of social exchange.