We ask what conditions transmission contracts increase or mitigate market power. We show that the allocation process of transmission rights is crucial. In an efficient arbitraged uniform price auction, generators will only obtain contracts that mitigate their market power. However, if generators inherit transmission contracts or buy them in a ‘pay-as-bid’ auction, then these contracts can enhance market power. In the two-node network case, banning generators from holding transmission contracts that do not correspond to delivery of their own energy mitigates market power. Meshed networks differ in important ways as constrained links no longer isolate prices in competitive markets from market manipulation. The paper suggests ways of minimising market power considerations when designing transmission contracts. (This abstract was borrowed from another version of this item.)