Hamilton's local mate competition theory provided an explanation for extraordinary female-biased sex ratios in a range of organisms. When mating takes place locally, in structured populations, a female-biased sex ratio is favoured to reduce competition between related males, and to provide more mates for males. However, there are a number of wasp species where the sex ratios appear to more female-biased than predicted by Hamilton's theory. It has been hypothesized that the additional female bias in these wasps species results from cooperative interactions between females. We investigated theoretically the extent to which cooperation between related females can interact with local mate competition to favour even more female-biased sex ratios. We found that: (i) cooperation between females can lead to sex ratios that are more female-biased than predicted by local competition theory alone; (ii) sex ratios can be more female-biased when the cooperation occurs from offspring to mothers before dispersal, rather than cooperation between siblings after dispersal. Our models formally confirm the verbal predictions made in previous experimental studies, which could be applied to a range of organisms. Specifically, cooperation can help explain sex ratio biases in Sclerodermus and Melittobia wasps, although quantitative comparisons between predictions and data suggest that some additional factors may be operating.