Numerous studies have found facilitation for lexical processing in highly constraining contexts. However, less is known about cases in which immediately preceding (local) and broader (global) contextual constraint conflict. In two eye-tracking while reading experiments, local and global context were manipulated independently, creating a critical condition where local context biases towards a word that is incongruent with global context. Global context consisted of a clause introduced by a concessive marker generating broad expectations about upcoming material. Experiment 1 compared high- and low-predictability critical words, whereas Experiment 2 held the critical word constant and manipulated the preceding verb to impose different levels of local constraint. Facilitation from local context was reduced when it was incongruent with global context, supporting models in which information from global and local context is rapidly integrated during early lexical processing over models that would initially prioritise only local or only global context.