We propose a mixed analytical–ab initio method for the accurate calculation of the conductance in monovalent atomic wires. The method relies on the most general formula for ballistic transport through a monovalent wire, whose parameters can be determined from first-principles calculations. Our central result is the demonstration of the highly nonuniversal behavior of the conductance, which depends on the fine details of the contacts to the leads. We are therefore able to reconcile a large number of the apparently contradictory results that have recently appeared in the literature.