Zeuthen's multi-round solution to the bilateral monopoly problem is demonstrably restricted to bargainers who, at each round, almost perversely ignore the preceding succession of modified offers, and persist in a consideration of outcomes limited to total capitulation. Alternatively, the Zeuthen solution is a single-round solution. A Zeuthen-type model is developed and utilized to show that, whether single- or multi-round, the wage outcome is confined to a range delimited by those rates which maximize the expected gain from no-concession for each bargainer.