A negotiation commonly starts with one party sending and the counterpart receiving a first offer. This first offer anchors recipients and yields higher profits to the sender. Recent research has shown that precise anchors (e.g., $28.75) - those featuring fewer trailing zeros - are more potent than round anchors ($30.00). The present studies extend this literature in two ways: First, prior research has exclusively focused on anchor recipients while ignoring the sender. Here, we examine precision effects for (1) recipients, (2) senders, and (3) both recipients and senders in a dyadic negotiation. Three experiments establish distinct and opposing effects: Whereas increasing precision elevates a first offer's anchoring potency for recipients, it lowers the first-offer extremity that senders opt for. Second, prior research has disagreed upon the theoretical mechanisms behind the precision effect: The . scale-granularity account posits that decision-makers adjust in smaller steps on a finer-grained mental scale. The . attribution-of-competence account posits that people ascribe more competence to a precise-opening individual. We examine these competing theoretical accounts simultaneously. Multiple mediation analyses across all three experiments suggested consistently that the beneficial impact of precise anchors on recipients is due to a social attribution-of-competence, whereas the detrimental impact on anchor-senders is due to a cognitive scale-granularity process. In all, the present findings show (a) that senders and recipients are distinctly affected by anchor precision, and (b) that these opposing effects are due to distinct psychological processes.