The current study examines the interplay between global and local processes in bilingual language control. We investigated language-switching performance of unbalanced Arabic-Hebrew bilinguals in cued picture naming, using 5 different cuing parameters. The language cue could precede the picture, follow it, or appear simultaneously with it. Naming latencies were reduced with precuing, demonstrating bilinguals' ability to globally modulate language activation, and more strongly reduced with postcuing, demonstrating bilinguals' ability to locally activate lemmas in both languages. Precuing reduced switching costs in reaction time (RT), and postcuing significantly reduced switching costs in accuracy, but not in RT. Switching costs were mostly symmetric for both languages, although participants were unbalanced bilinguals. These results support the notion that both global language selection and resolution of competition between activated lemmas are involved in bilingual language control. They further demonstrate that persisting language schema activation and local lemma selection and inhibition are equal across both languages of unbalanced bilinguals. Finally, results demonstrate that experimental manipulations of cuing parameters can have dissociable influences on overall RTs, and switch costs in latency and accuracy, suggesting that language-switching performance reflects complex interactions of bilingual profiles and task demands.