In negotiations, higher first offers from sellers drive up sale prices—reversely, buyers benefit from lower first offers. Whereas abundant research has replicated this robust anchoring effect of opening offers, little is known about the impact of anchors’ precision or the interplay of extremity and precision. We propose that precision moderates the effect of anchor extremity, in that precise anchors gain in plausibility and thereby magnify the first-mover advantage. Two experiments tested this assumption. Study 1 shows that increasing precision strengthens the anchoring potency of first offers—sellers assimilate more to strong and precise anchors, which ultimately results in a particularly pronounced first-mover advantage. Study 2 replicates this moderating effect for buyers and indicates that an increased plausibility of precise anchors accounts for the findings. Implications for anchor theorizing, negotiation research, and the first minutes at a bargaining table are discussed.