We consider a single-period dual-sourcing problem in which a buyer purchases its products from two different suppliers and sells them to a market with uncertain demand. One supplier is cheaper but less responsive, whereas the other supplier is more responsive but more expensive. The buyer determines the order quantity from the low-cost supplier and the capacity level from the responsive supplier in such a way that maximises its profit. We apply extreme value theory to analyse the impact of tail heaviness of demand distribution on optimal dual-sourcing strategy. We numerically find that tail heaviness moderates the effect of increasing demand uncertainty on optimal order levels. We also show that dual sourcing allows companies to increase their fill rates cost effectively under heavy-tailed demand if the capacity reservation cost of the responsive supplier is relatively low.