Although most scholars recommend making the first offer in negotiations, recent research and practitioners’ experience have uncovered a second-mover advantage in certain situations. In the current article, we explore this first- versus second-mover dynamic by investigating the circumstances under which negotiators would make less favorable first offers than they would receive were they to move second, focusing on the effects of negotiation power in the form of alternatives. Additionally, we examine the effects of low power on reservation prices and whether these effects could be mitigated using an anchor-debiasing technique. In Study 1, we manipulated negotiators’ power in the form of the best alternative to the negotiated agreement and examined its effect on first offers and reservation prices. Our results showed that low-power negotiators would receive more favorable first offers than they would have made themselves when facing either low- or medium-power counterparts. Also, our results suggest that low-power negotiators had less favorable reservation prices than their medium- and high- power counterparts. In Study 2, we investigated whether this effect would persist in the face of anchor-debiasing techniques. Our results showed that while anchor-debiasing techniques did improve their first offers, low-power negotiators would still benefit from making the counteroffer rather than moving first. Our findings uncover the disadvantageous effects of low power on first-offer magnitude while offering practical advice to negotiators.