In an ASSA session "Consequences of Gendered Labor Markets" chaired by one and only Silvia Berger we discussed our novel estimator for labor market segmentation and gender wage inequality. Gender wage gap (adjusted for individual characteristics) as a phenomenon means that women are paid unjustifiably less than men, i.e. below their productivity. Meanwhile, efficiency wages as a phenomenon mean that a group of workers is paid in excess of productivity. However, productivity is typically unobservable, hence it is proxied by some observable characteristics. If efficiency wages are effective only in selected occupations and/or industries, and these happen to be dominated by men, measures of adjusted gender wage gaps will confound (possibly) below productivity compensating of women with above productivity efficiency wage prevalence. We propose to utilize endogenous switching models to estimate adjusted gender wage gaps. We find that indeed access to privileged market is gendered in a sense that there is unexplained gender inequality. Quantitatively more relevant, however, is the extent of unexplained gender wage inequality in the privileged market -- substantially above the estimates from the pooled sample, i.e. without allowing for the prevalence of the efficiency wages. We find that this result is relatively robust to how the markets are effectively split. There appears also to be a substantial amount of country heterogeneity in how privileged and standard markets reward women's work.