In this paper I present a methodology that uses matching comparisons to explain gender differences in wages. The approach emphasizes gender differences in the supports of the distributions of observable characteristics and provides useful insights about the distribution of the unexplained gender differences in pay. The proposed methodology, a non-parametric alternative to the Blinder-Oaxaca (BO) wage gap decomposition, does not require the estimation of earnings equations. It breaks down the gap into four additive elements, two of which are analogous to the elements of the BO decomposition (but computed only over the common support of the distributions of characteristics), while the other two account for differences in the supports. Using data for Peru in the period 1986-2000, I found that this problem of non-comparability accounts for 23% and 30% of the male and female working populations respectively. The matching methodology allows us to quantify the effect of explicitly recognizing these differences in the supports. In this way, the 45% gender wage gap in Peru is decomposed as: 11% explained by differences in the supports, 6% explained by differences in the distributions of individual characteristics and the remaining 28% cannot be explained by differences in observable individuals? characteristics. Approximately half of the latter is due to unexplained differences in the highest quintile of the wage distribution.