Considers the treatment of openness and imperfect competition in the influential analysis of Layard, Nickell and Jackman's (LNJ's) Unemployment: Macroeconomic Performance and the Labour Market. Clarifies and completes LNJ's treatment of openness through the provision of explicit analytical solutions to their model under fixed and flexible exchange rate regimes. Also provides a (largely informal) analysis of the sensitivity of the LNJ model's results to the particular forms of imperfect competition assumed. It is argued that openness is crucial to the model's properties, whereas imperfect competition is not. However, imperfect competitive behaviour may, more generally, have a major impact if it is not confined to the “well-behaved form” allowed by LNJ.