Debates about the function of the prefrontal cortex are as old as the field of neuropsychology—often dated to Paul Broca’s seminal work. Theories of the functional organization of the prefrontal cortex can be roughly divided into those that describe organization by process and those that describe organization by material. Recent studies of the function of the posterior, left inferior frontal gyrus (pLIFG) have yielded two quite different interpretations: One hypothesis holds that the pLIFG plays a domain-specific role in phonological processing, whereas another hypothesis describes a more general function of the pLIFG in cognitive control. In the current study, we distinguish effects of increasing cognitive control demands from effects of phonological processing. The results support the hypothesized role for the pLIFG in cognitive control, and more task-specific roles for posterior areas in phonology and semantics. Thus, these results suggest an alternative explanation of previously reported phonology-specific effects in the pLIFG.