We use a first-hand linked employer-employee dataset representing the formal sector of Bangladesh to explain gender wage gaps by the inclusion of measures of cognitive skills and personality traits. Our results show that while cognitive skills are important in determining mean wages, personality traits have little explanatory power. However, quantile regressions indicate that personality traits do matter in certain parts of the conditional wage distribution, especially for wages of females. Cognitive skills as measured by reading and numeracy also confer different benefits across the wage distribution to females and males respectively. Quantile decompositions indicate that these skills and traits reduce the unexplained gender gap, mainly in the upper parts of the wage distribution. Finally, results suggest that employers place greater consideration on observables such as academic background and prior work experience, and may also make assumptions about the existence of sex-specific skills of their workers, which could then widen the within-firm gender wage gap.