Determining the mechanisms governing sex-ratio variation in dioecious organisms represents a central problem in evolutionary biology. It has been proposed that in plants with sex chromosomes competition between pollen tubes of female- versus male-determining microgametophytes (certation) causes female-biased primary sex ratios. Experimental support for this hypothesis is limited and recent workers have cast doubt on whether pollen-tube competition can modify sex ratios in dioecious plants. Here we investigate the influence of variation in pollination intensity on sex ratios in Rumex nivalis, a wind-pollinated alpine herb with strongly female-biased sex ratios. In a garden experiment, we experimentally manipulated pollination intensity using three concentric rings of female recipient plants at different distances from a central group of male pollen donors. This design enabled us to test the hypothesis that increasing pollen load size, by intensifying gametophyte competition, promotes female-biased sex ratios in R. nivalis. We detected a significant decline in pollen load at successive distance classes with concomitant reductions in seed set. Sex ratios of progeny were always female biased, but plants at the closest distance to male donors exhibited significantly greater female bias than more distant plants. The amount of female bias was positively correlated with the seed set of inflorescences. Hand pollination of stigmas resulted in approximately 100-fold higher stigmatic pollen loads than wind-pollinated stigmas and produced exceptionally female-biased progenies (female frequency = 0.96). Our results are the first to demonstrate a functional relation between stigmatic pollen capture, seed set, and sex ratio and suggest that certation can contribute towards female-biased sex ratios in dioecious plants.