Wage premia related to union membership and coverage are examined over 1991-2003, a period involving first decline, then stabilization, of unionization. Differences in union premia across workers and over time are studied using individual-level British Household Panel Survey data and quantile regression techniques allowing for endogeneity of the membership decision. Raw differentials suggest the presence of large positive membership and coverage premia that are stronger at the bottom of the wage distribution in both private and public sectors. After controlling for other factors influencing wages, union asymmetries are no longer apparent in the private sector. When endogeneity of union membership is taken into account, the private sector union wage premium disappears, indicating that individuals positively select into unions. In contrast, the public sector total union wage premium remains significant – entirely due to a coverage effect; it is stronger at the bottom among males, while for females the premium is constant across workers and substantial over the whole period, reflecting the continuing strength of public sector unions. Once we control for endogeneity, the membership premium is nowhere significant; there is no free rider puzzle in the private sector, as there is no coverage premium, but the puzzle persists for the public sector.