Prior research shows that precise first offers strongly anchor negotiation outcomes. This precision advantage, however, has been documented only when the parties were already in a negotiation. We introduce the concept of negotiation entry, i.e., the decision to enter a negotiation with a particular party. We predict that precise prices create barriers-to-entry, reducing a counterpart's likelihood of entering a negotiation. Six studies (N = 1580) and one archival analysis of real estate data (N = 11,203) support our barrier-to-entry prediction: Potential negotiators were less likely to enter a negotiation with precise- versus round-offer makers. Using both statistical mediation and experimental-causal-chain analyses, we establish that perceptions of offer-maker inflexibility underlie the precision barrier. Furthermore, we demonstrate that the precision mechanism (inflexibility) is distinct from the extremity mechanism (being offended) that produces barriers-to-entry from extreme first offers. The discussion theoretically integrates research on first-offer precision and extremity by offering the Precision-Extremity Model of First Offers.