This paper studies the wage differentials between the public and private sectors in Spain, as well as its distribution across different educational levels and by gender. To do so, the well-known Oaxaca-Blinder decomposition of mincerian wage regressions is applied for both sectors, breaking down the (public-private) wage gap into a component explained by differences in characteristics and another one capturing differences in returns to those characteristics. Data is drawn from the Wage Structure Survey by INE for 2010, 2014 and 2018. The main findings are: (i) strong wage compression by skills for all workers, and (ii) a female wage premium in the private sector. Both empirical results are rationalised by means of a monopoly-union wage model with monopsonistic features and female statistical discrimination.