This article explores a model in which a union confronts many competitive workers, firms, and consumers. Under "monopoly" unionism, union coverage may be incomplete; then, union wages and employment are insensitive to product demand variation. Under "efficient" unionism, coverage can never be incomplete; some union variables necessarily vary with product demand. Preliminary evidence on the demand independence under incomplete coverage hypothesis is presented. Also, more structure is imposed and further hypotheses are derived, and the manner in which the model can be enriched to allow for a variety of union-related issues within a consistent framework is set out.