Reports of the difficulties of elite women in finding suitable mates have been increasing despite the growing availability and value of men in China. We rationalize this "leftover women" phenomenon within the directed/competitive search framework, which uniquely allows for equilibrium crowding out. Within this framework, we show that the leftover women phenomenon can be the result of women's aversion to men who have a lower income than themselves (hereafter, ALM) and the long-predicted complementarity between women's non-market traits (in particular, beauty) and male earnings. For high-income (h-)women, even when high-income (H-)men are more plentiful and richer, the direct effect of the greater number of desirable men can be overwhelmed by the indirect effect of competitive 'entry' by low-income (l-)women, particularly, the beautiful. We test for these competitive search effects using online dating field experimental, Census, and household survey data. Consistent with the competitive entry of lwomen, when sex ratio and H-men's income increase, the search intensity of beautiful l-women for H-men increases. In response to this competitive entry, plain h-women, who are constrained by their ALM to search predominantly for H-men, also increase the search intensity. However, only their marriage probability decreases. Our evidence is consistent with intra-female competitive search for spouses who can cover the labor market opportunity cost of marriage and childbirth, which increases with a woman's income.