Is language production dynamically regulated by cognitive control? If so, how domain-general is this process? In two experiments, we studied conflict adaptation, or conflict-driven adjustments of control, in two paradigms: Picture-Word Interference (PWI), which induces linguistic conflict, and Prime-Probe (PP), which induces visuospatial conflict. Exp. 1 tested within-task conflict adaptation separately in PWI and PP. Exp. 2 tested cross-task adaptation by alternating the two tasks in a task-switching paradigm. We found reliable within-task conflict adaptation in both PWI and PP, but neither an analysis of individual differences (Exp. 1), nor a direct manipulation of between-task conflict (Exp. 2) revealed cross-task adaptation. We further report a robust 2-back within-task adaptation in Exp. 2 to refute alternative accounts of null cross-task adaptation. These findings support models of dynamic, top-down control in language production that posit at least some degree of domain-specificity.