We investigate dual-source supply chains, where fast sourcing is not only more expensive than slow sourcing, it is also less flexible. The slow supplier has a longer lead time, but has full flexibility with sourcing costs linear to the ordered volumes. The fast supplier is more expensive, and also charges an overtime premium per unit sourced beyond a pre-specified threshold. We prove that when the lead time difference between both suppliers is one period, the optimal policy is a generalized dual base-stock policy. The order from the fast supplier follows a base-stock policy with hysteresis, i.e. it has two base-stock levels and a region of inaction. In the region of inaction, the fast order is capped to avoid the overtime premium. It is better to wait and replenish at regular cost from the slow supply rather than replenishing fast at overtime cost. This postponement effect smoothes the fast orders. The order from the slow supplier is characterized by a conventional base-stock policy. In contrast to the single sourcing variant of our model, we can characterize the optimal policy parameters. This allows us to to capture analytically how inflexibility results in substitution effects in the sourcing split between (overtime) fast and slow supply.