This paper analyses the gender wage gaps by education throughout the wage distribution in Spain. Quantile regressions are used to estimate the wage returns to the different characteristics at the more relevant percentiles. A correction for the selection bias is included for the group of less educated women. The Oaxaca-Blinder decomposition is then implemented at each quantile in order to estimate the component of the gender gap not explained by differences in characteristics. Our main findings are twofold. On the one hand, when dealing with the group with tertiary education, we find higher discrimination at the top than at the bottom of the distribution, in accordance with the conventional "glass ceiling" hypothesis. On the other, for the group with primary and secondary education, the converse result holds, pointing out to the existence of lower wages for women at the bottom of the distribution due to their prospects of lower job stability, a phenomenon that we refer to as "glass floors".