During sentence comprehension, real-time identification of a referent is driven both by local, context-independent lexical information and by more global sentential information related to the meaning of the utterance as a whole. This paper investigates the cognitive factors that limit the consideration of referents that are supported by local lexical information but not supported by more global sentential information. In an eye-tracking paradigm, participants heard sentences like "She will eat the red pear" while viewing four black-and-white (colorless) line-drawings. In the experimental condition, the display contained a "local attractor" (e.g., a heart), which was locally compatible with the adjective but incompatible with the context ("eat"). In the control condition, the local attractor was replaced by a picture which was incompatible with the adjective (e.g., "igloo"). A second factor manipulated contextual constraint, by using either a constraining verb (e.g., "eat"), or a non-constraining one (e.g., "see"). Results showed consideration of the local attractor, the magnitude of which was modulated by verb constraint, but also by each subject's cognitive control abilities, as measured in a separate Flanker task run on the same subjects. The findings are compatible with a processing model in which the interplay between local attraction, context, and domain-general control mechanisms determines the consideration of possible referents.