The executive function of fluency describes the ability to generate items according to specific rules. Production of words beginning with a certain letter (phonemic fluency) is impaired in dyslexia, while generation of words belonging to a certain semantic category (semantic fluency) is typically unimpaired. However, in dyslexia, verbal fluency has generally been studied only in terms of overall words produced. Furthermore, performance of adults with dyslexia on non‐verbal design fluency tasks has not been explored but would indicate whether deficits could be explained by executive control, rather than phonological processing, difficulties. Phonemic, semantic and design fluency tasks were presented to adults with dyslexia and without dyslexia, using fine‐grained performance measures and controlling for IQ. Hierarchical regressions indicated that dyslexia predicted lower phonemic fluency, but not semantic or design fluency. At the fine‐grained level, dyslexia predicted a smaller number of switches between subcategories on phonemic fluency, while dyslexia did not predict the size of phonemically related clusters of items. Overall, the results suggested that phonological processing problems were at the root of dyslexia‐related fluency deficits; however, executive control difficulties could not be completely ruled out as an alternative explanation. Developments in research methodology, equating executive demands across fluency tasks, may resolve this issue. Copyright © 2017 John Wiley & Sons, Ltd.