The definition of cognitive flexibility remains debated in the literature. Some refer to flexibility as a general shifting ability. Others argue that it is a context-dependent skill. For others, flexibility is a dimensional construct including reactive flexibility and spontaneous flexibility. To help decide between these views, we analyzed the performances of first-graders across four flexibility tasks. Two tasks focused on reactive flexibility (rule-shifting and verbally-cued-shifting), and two targeted spontaneous flexibility (role-shifting and divergent thinking). Three additional executive tasks investigated the contribution of inhibition, working memory, and processing speed. Significant-though moderate-positive correlations emerged between all but one of the pairs of flexibility tasks. Besides, executive functions were not found to systematically correlate with any measure of flexibility. Furthermore, confirmatory factorial analyses failed to identify a unique or bi-dimensional structure of flexibility. Taken together, these results did not provide evidence for a domain-general ability. Implications and future directions are discussed.