In an analysis of the formation of unions within a single firm, this paper addresses conditions under which encompassing unions form. It is shown that a production function satisfying decreasing marginal productivity leads to the formation of encompassing unions. This result holds for different ways of dividing the surplus within the union. The effects of changes in heterogeneity, e.g. increased demand for skilled labor, are also analyzed. In the most reasonable setup, a change in heterogeneity does not affect the decision whether to form a union or not. This contrasts with the result in Jun (1989).